Selection vs. accountability: an experimental investigation of
campaign promises in a moral–hazard environment
Nick Feltovich∗
Department of Economics
Monash University
Clayton VIC 3800, Australia
nicholas.feltovich@monash.edu
Francesco Giovannoni
Department of Economics
University of Bristol
8 Woodland Road
Bristol, BS8 1TN, UK
francesco.giovannoni@bristol.ac.uk
Abstract
We examine retrospective– and prospective–voting considerations in an experiment implementing a simple voting model. In each period, the official chooses how much rent to appropriate from a social endowment. Announcement of this choice is followed by an election between the official and a randomly selected
challenger, with the winner becoming the official in the next period. We vary two features of the setting:
(a) the discount factor, and (b) whether candidates can make costless, non–binding “campaign promises”
about their behaviour if elected. Consistent with the model’s predictions, both raising the discount factor
and introducing campaign promises lead to lower rent appropriation by officials and worse electoral outcomes (other things equal) for incumbents. Campaign promises, despite being cheap talk, have real effects:
promising less appropriation is rewarded by voters, but breaking such promises is punished. Finally, we find
a weak positive association between campaign promises and officials’ subsequent behaviour.
Journal of Economic Literature classifications: D72, D73, C91, C73.
Keywords: retrospective voting; prospective voting; political economy; cheap talk; corruption.
∗
Some of this research took place while Feltovich was at University of Aberdeen. Financial support from the University of Aberdeen and Monash University is gratefully acknowledged. We thank an editor, two referees, Nejat Anbarci, Miguel Costa–Gomes,
Marco Faravelli, Miguel Fonseca, Santiago Sánchez-Pagés, Joe Swierzbinski, and seminar participants at Queensland University of
Technology, University of Innsbruck and University of New South Wales for helpful suggestions and comments.
1
1
Background
In a representative democracy, elections play a crucial role as (often) the only instrument allowing citizens to
(1) select officials from the pool of candidates and (2) hold officials accountable for their actions in office.
These tasks are distinct: accountability requires a judgement on a politician’s past behaviour while selection
requires predicting the politician’s likely future behaviour. The goal of understanding how elections work must
therefore begin with the need to understand whether voters focus on accountability (retrospective voting) or
selection (prospective voting), so it is not surprising that this has become one of the most studied questions in the
voting literature. This literature has typically focussed on settings where incumbents’ policy decisions provide
voters with information about their (heterogeneous) characteristics; voters then decide whether to confirm an
incumbent or replace her with a challenger knowing that the winning candidate will make more policy decisions
in the future.1 The potential conflict between retrospective and prospective voting is clear in these models. For
example, a relatively low–ability incumbent who had produced decent policy results in the past through high
effort (or even luck) would be replaced by prospective voters but would survive re–election with retrospective
voters, while a relatively high–ability incumbent who had produced disappointing policy results in the past
because of low effort or bad luck would be re–elected by prospective voters but replaced by retrospective
voters. A crucial feature of these models is that retrospective voting is not rational: bygones are bygones, and if
we expect candidate A to have better potential for the future than candidate B we should vote for A regardless of
either’s past behaviour.2 Retrospective voting would only be rational if there were no such intrinsic differences,
and even then, there is no strict incentive for it.
A common criticism of this argument is that selection between candidates with intrinsic differences may
require solving complicated signal extraction problems that require voters to have unrealistic levels of cognitive
ability. For example, in uncertain environments where outcomes depend on politicians’ innate abilities but are
not fully determined by them, voters see only outcomes but prospective voting requires that they use these outcomes to form expectations about politicians’ underlying abilities. In contrast, retrospective voting would only
require evaluating the outcomes.3 Such arguments suggest a rule of thumb: one would expect prospective voting to obtain if voters are sufficiently sophisticated, but otherwise the inability to select candidates beforehand
should lead voters to take on the easier task of sanctioning them afterwards, leading to retrospective voting.
Following on from these arguments, the question of whether voters behave retrospectively or prospectively is
not solved, but just reduced to the question of how rational voters are.
Since the question of retrospective versus prospective voting cannot be resolved theoretically, the issue has
been taken up by the empirical literature. One branch of this literature has taken the issue of voters’ level of
sophistication directly to the data (MacKuen, Erikson and Stimson, 1992; Erikson, MacKuen and Stimson,
2000; Clarke and Stewart, 1994), but with largely inconclusive results. Another branch relies on exploiting
natural differences in electoral institutions, such as term limits (Besley and Case 1995, 2003; Alt, Bueno de
Mesquita and Rose 2011; Ferraz and Finnan 2011) or differences in electoral rules (Persson, Tabellini and
Trebbi 2003; Chang and Golden 2006). This has also had limited success, since while this type of analysis may
tell us which institutions can provide better outcomes, it cannot really capture the difference between the two
types of voting behaviour. For example, if term limits or large district sizes turn out to increase corruption, is
this because they increase the difficulty of making politicians accountable, or because they make it harder to
select better politicians?
Laboratory experiments provide a useful way to test whether theoretical arguments about voting apply to
1
See Persson and Tabellini (2000), Chap. 9.1 for an example.
See Fearon (1999) for a thorough discussion of this point.
3
See Woon (2012) for a discussion.
2
2
real elections, as they allow the researcher to (1) induce preferences over outcomes using monetary rewards,
instead of having to infer them or make assumptions about them as in field–data studies, and (2) vary features
of the environment (including the choices available to decision makers and the information they receive) in a
controlled way, which combined with random assignment of subjects to treatments eliminates many issues of
endogeneity and selection.4 The small experimental literature examining retrospective and prospective voting
has tended to find strong support for retrospective voting. Azfar and Nelson (2007) find that voters vote retrospectively, tending not to re–elect officials found to be corrupt. (Their experiment also allowed “campaign
speeches”, but they did not report any analysis of these messages or how they impacted voting.) Landa (2010)
finds that voters retrospectively reward effort, even though it provides no information about officials’ intrinsic
characteristics, in an environment where outcomes depend on both officials’ quality and their effort choices. He
also finds that candidates anticipate this retrospective voting, exerting more effort than predicted.5 Woon (2012)
considers a setting where voters have incomplete information about the state of the world and the official’s type,
and finds that officials approximately best–respond to voters’ behaviour, but voters tend to vote retrospectively
even when conditions call for prospective voting. He attributes this excessive sanctioning not only to voters’
recognising their bounded ability to make inferences, but also to a preference for sanctioning errant politicians.
Our experiment also examines behaviour in a setting that combines accountability and selection considerations, but in a novel way that departs from the usual identification of retrospective (prospective) voting with
unsophisticated (sophisticated) voters. We begin with a simple voting model in a standard moral–hazard environment: in each round, officials choose a level of rent appropriation and then face the voters in an election.
Intrinsic differences between candidates are absent, so the demands on voters’ sophistication are significantly
reduced. As a test of retrospective voting, we compare two versions of this basic game that differ only in the
discount factor; officials with higher discount factors should accept lower current rents as the price for staying
in office for another period.
We investigate prospective voting in one treatment by modifying the basic model so that incumbent and
challenger can costlessly make non–binding pre–election “campaign promises”: announcements of the candidate’s salary choice should he/she win the election. These are cheap talk and hence have no effect on the set of
possible equilibrium rents. However, they may affect which equilibrium is selected, and hence what rents are
actually chosen.6 If voters take campaign promises seriously by voting out incumbents who have broken their
promises, then they should vote for the candidate promising to take fewer rents in the next period, and their
4
See Morton and Williams (2010) for discussions of the history and methodology of experimental political science, and see Wilson
(2011) for a discussion of the relevance of results from economics experiments for political science.
5
Interestingly, Landa (2010) considers both a setting where outcomes are deterministic functions of ability and effort and a setting
where there is an additional stochastic component, and finds that voters reward effort more in the latter setting where signal extraction
is more difficult. This suggests that voters treat effort choices as costly signals of future effort. In the current paper, we investigate the
possibility that costless signals (campaign promises) influence voter behaviour.
6
We use “cheap talk” in the standard game–theoretic way to mean communication that is costless, in the sense of the game’s payoffs
or the induced payoffs of the experiment, and non–binding in the sense of having no effect on the sender’s subsequent action choice set
or corresponding payoffs. We note that cheap talk is not necessarily cheap under certain non–standard preferences such as an aversion
to lying. Some theorists have modelled electoral lying as an activity that is psychologically costly (Banks 1990; Callander and Wilkie
2007), parallelling a corresponding theoretical literature in general strategic environments (e.g., Ellingsen and Johannesson 2004;
Hurkens and Kartik 2009; Kartik 2009; López-Pérez 2012; Miettinen 2013), and in contrast to the traditional approach to campaign
promises in the economics literature exemplified by Barro (1973), where they are considered to be ineffective. There is also a growing
experimental literature looking at individuals’ aversion to lying (Gneezy 2005; Sánchez-Pagés and Vorsatz 2007, 2009; Lundquist et
al. 2009; López-Pérez and Spiegelman 2013), though it should be noted that some experiments find lying to be rampant (Wilson and
Sell 1997; Duffy and Feltovich 2002). To the extent that people in experiments face psychic costs to lying, campaign promises could
be viewed as carrying some information content. However, if lying has a positive effect on electoral success, selection pressures might
make politicians less honest on average than the ordinary people who participate in experiments (Callander and Wilkie 2007).
3
most–preferred equilibrium will be attained.7 Thus, in our context, prospective voting does not need to rely on
the ability of voters to make potentially complex calculations but, on the contrary, is facilitated by campaign
promises.
Our experimental results offer broadly positive support for the theory. Consistent with retrospective voting,
we find that officials choosing to take higher rents perform worse in subsequent elections; moreover, raising
the discount factor results in lower rents and (ceteris paribus) worse electoral outcomes for incumbents, though
these differences are not always significant. Allowing campaign promises gives rise to several effects. Most
importantly, voters use them to vote prospectively: either a promise of low rent appropriation or a high promise
by the opponent increases a candidate’s vote share and the associated chance of winning. Voters also use past
campaign promises for retrospective voting: appropriating a higher rent than promised leads to worse electoral
outcomes for the incumbent, even after controlling for the rent itself. Finally, we find suggestive evidence that
campaign promises really are informative in some cases, and more generally they lead to officials appropriating
fewer rents than when such promises can’t be made.
There have been few previous experimental tests of endogenous campaign promises in settings with opposed official and voter interests. A notable exception is the recent work by Corazzini et al. (2013), who find
a significant positive association in a one–shot setting between the portion of a social endowment politicians
choose to distribute to the members of their group, and the portion they had promised to distribute during the
election campaign; that is, campaign promises are informative. However, the results of our experiment suggest
that Corazzini et al.’s results may be due to the specifics of their design: an analysis of our first–round data
alone would have implied similar conclusions to theirs, but the analysis of our entire data–set shows campaign
promises to be much less informative overall.
2
Theory and experiment
The experiment is built upon an adaptation of Persson, Roland and Tabellini’s (1997) voting model.8 A
discrete–time economy comprises one official and N citizens (so the total population is N + 1), and lasts
for infinitely many periods; in the experiment, these were called “years”, but we will often refer to them as
“rounds”. In the first round, the official is chosen randomly with each member of the population equally likely;
thereafter, the official is chosen by an election. There is no production; the economy is endowed with a per–
round income of M , which is allocated by the official. The stage game is essentially a dictator game: the
official chooses an amount s ∈ [0, M ] to take from the endowment, with the remainder divided evenly amongst
the citizens. The official’s stage–game payoff is thus π o = s, and each citizen receives a stage–game payoff of
π c = MN−s . The variable s admits multiple interpretations. In the experiment, it was framed as the official’s
“salary”, and we will often use that term here, though s can also be interpreted as behaviour that is illegal,
unethical, or even simply unseemly.
In the basic game, after the official’s allocation decision is made and announced to the citizens, there is an
election. The official runs as the incumbent; the challenger is chosen randomly out of the population, with each
of the N citizens equally likely. No information about the challenger is disseminated to the voters, including
his identity (in particular, they do not know whether the challenger had been an official in previous rounds, or
7
The idea that retrospective and prospective voting may be compatible if voters select the best equilibrium for them amongst different
equilibria with accountability is discussed in Ashworth, Bueno de Mesquita and Friedenberg (2013), although they don’t discuss the
role of campaign promises in helping to achieve this selection.
8
By virtue of its simplicity and flexibility, the model has become a work–horse for theoretical study of many political–economy
phenomena. See Persson, Roland and Tabellini (2000) for an early application of the model to comparing various governmental
structures, and see Abbink and Pezzini (2005) for an application to the determinants of political revolutions.
4
any choices he made as either official or voter). Standing for election is costless for both candidates. Each
member of the economy (the N citizens and the official) casts a single vote (also at zero cost); abstaining is not
possible. The candidate with more votes wins the election and will be the official in the next round; in case of
a tie, the incumbent remains in office. The election loser remains in the economy as an ordinary citizen.
The game with campaign promises is similar, but with one important difference. After the official’s salary
decision is announced and before voting takes place, the incumbent and challenger are each able to send a single
message to the electorate, indicating the salary they will choose in the next round, conditional on winning; it
is also possible to send no message. These messages are cheap talk: they are costless and non–binding. Here,
we will often refer to these messages as “campaign promises”, though in the experiment they were described
to the subjects as “announcements”.
This stage game (either with or without promises) is infinitely repeated. All players have the same additively–
separable lifetime utility function:
U (π1 , π2 , ...) =
∞
X
δ t−1 u (πt ) ,
t=1
where δ ∈ [0, 1) is the common discount factor and u(·) is a common differentiable and strictly increasing
utility function.
2.1
Equilibria of the basic game
In the analysis presented here, we assume for simplicity that individuals only care about their own monetary
payoffs (they are self–regarding) and are risk neutral, so without loss of generality we can assume u(π) = π.
In the online appendix we show that our results continue to hold when these assumptions are relaxed to allow
for risk aversion or inequity aversion.
As is common in games with majority voting, the basic game has a large number of equilibria. Since
all citizens – other than the official and the citizen selected to be the challenger – are identical, we restrict
consideration to equilibria where these voters select identical voting strategies. (The official and challenger
weakly prefer always to vote for themselves, so their votes cancel each other out and the remaining voters
determine the outcome.) Under this symmetry assumption, no individual citizen is pivotal, and thus all are
indifferent between any two voting strategies, as is standard in moral–hazard voting models.9 An immediate
consequence is that verifying an equilibrium requires only confirming that the official plays a best response
given the non–candidate citizens’ voting strategy. Following standard practice, we further restrict the class of
equilibria by focusing on stationary equilibria in which citizens’ voting strategy depends only on the official’s
current–round salary choice, and in the same way in all rounds. In particular, if the official chooses a salary
s ≤ s (for some s ∈ [0, M ], then she is re–elected, but choosing any higher salary would result in being voted
out. Clearly, an official wishing to stay in office will select st = s in every round t, for a lifetime utility of
P∞ t−1
s
s = 1−δ
. Citizens will then receive a stage–game payoff of MN−s in every round, for a lifetime utility
t=1 δ
M −s
of (1−δ)N
. For a given s, compliance by the official obtains if it does not pay for her to deviate by taking the
entire endowment in round t and being voted out, and by stationarity, it suffices simply to check the first round.
The consequence of being voted out after taking the whole endowment in round 1 is equilibrium play with a
different official so that the ex–official will never regain office, and she will receive a stage–game payoff of
(M −s)
M −s
N in every future round after getting M in the first round, for a lifetime utility of M + δ (1−δ)N . In this case,
9
Indeed, in retrospective–voting models like ours, non–candidate voters would be indifferent even if they were pivotal (i.e., if the
total group size were only 3). This is because there are no differences across individuals in characteristics like preferences or quality,
so that voting an incumbent out merely results in a new official who is identical to the old official in every way.
5
the official will prefer a salary of s in every round (i.e., will comply) if
Nδ
s
δ(M − s)
≥M+
⇐⇒ s ≥ 1 −
M ≡ smin .
1−δ
(1 − δ)N
N +δ
We can therefore characterise the set of stationary equilibria with compliance. For any s ≥ smin , there exists
an equilibrium with the official choosing a salary of s in every round and all voters voting for the incumbent if
and only if s ≤ s (so that the official does indeed remain in office).10 The value of smin characterises the lower
bound of the set of stationary equilibria with compliance, and therefore the most equitable such equilibrium.
We call this the benevolent equilibrium. While this is only a subset of an infinite set of stationary equilibria
with compliance, it is the one that maximises voter welfare, and as noted by Landa (2010), it “is the standard
prediction in sanctioning models” (p. 4).11
An important consequence of our analysis is that smin is strictly decreasing in δ:
∂smin
N2
=−
M < 0.
∂δ
(N + δ)2
So, raising the discount factor leads to lower salaries consistent with stationary equilibrium with compliance.
A wide variety of deterministic and stochastic equilibrium–selection rules would imply that as the left endpoint
of the set of equilibrium salaries decreases (with the right endpoint remaining fixed), the expected salary should
decrease as δ increases.
Our experiment will have a treatment using the basic game with δ = 0.8 (BASE–0.8 cell) and one with
δ = 0.9 (BASE–0.9 cell). The predicted values of smin for these discount factors and for N ∈ {4, 5, ..., 8}
(i.e., economy sizes from 5 up to 9) are shown in Table 1. Consistent with the discussion above, for each group
Table 1: Benevolent–equilibrium salaries, as shares of the endowment M
Size of economy (N + 1) BASE–0.8/COMM–0.8 BASE–0.9
5
6
7
8
9
0.333
0.310
0.294
0.282
0.273
0.265
0.237
0.217
0.203
0.191
size smin is lower at the larger value of δ, implying the following prediction:
Hypothesis 1 Officials’ salaries are higher in the BASE–0.8 cell than in the BASE–0.9 cell.
10
Of course, non–stationary re–election strategies that depend on the s chosen in earlier periods can also support these equilibria.
For example, citizens may use strategies where they never confirm an official once a previous official has deviated. It is easy to check
that for the risk–neutral case, the same condition s ≥ smin obtains again. More importantly, for more general preferences, one can
show that our main results are unaffected. Details are available upon request.
11
There is, nevertheless, an issue of how exactly officials and voters are able to coordinate on the benevolent equilibrium. In many
theoretical papers in this literature (e.g., Persson, Roland and Tabellini 1997), voters are assumed to announce their voting rule prior
to the official’s salary choice. For example, voters could implement the benevolent equilibrium by announcing that they will vote to
re–elect if and only if the official chooses a salary of smin or less. Such an assumption has the advantage of making clear how voters
and politicians coordinate, but begs several questions, such as how the voters themselves manage to coordinate, and how in practice
they communicate their intentions to politicians. One possible answer to the latter question is the use of opinion polls, though these
arguably represent only a very noisy signal of the true re–election rule, since they typically take place shortly before an election and
are meant to express how voters intend to vote, rather than counter–factuals like how they would vote conditional on a certain pattern
of official behaviour between the poll and election dates.
6
This also means that there is a range of salary levels – specifically, those below smin,δ=0.8 but above
smin,δ=0.9 – which are consistent with equilibrium when δ = 0.9 but not when δ = 0.8. Since in any stationary equilibrium with salary s, the official would be re–elected with certainty after any salary lower than s
and be voted out for sure after any higher salary, this means that in the interval s ∈ [smin,δ=0.9 , smin,δ=0.8 ),
re–election probabilities below one are possible when δ = 0.9 but not when δ = 0.8. Since there is no interval where the reverse is true, this means it is weakly more difficult for the incumbent to be re–elected in the
BASE–0.9 cell than in the BASE–0.8 cell:
Hypothesis 2 Conditional on the official’s salary, she will receive a higher vote share, and be re–elected with
higher likelihood, in the BASE–0.8 cell than in the BASE–0.9 cell.
Of course, in a stationary equilibrium, voters may choose to require an even larger share of resources
(s < smin ). In that case, it is optimal for the official not to comply, but instead to grab the entire endowment.
Such behaviour characterises a kleptocratic equilibrium. In each round of a kleptocratic equilibrium, the official
takes the entire endowment (s = M ) and is immediately voted out of office, to be replaced by another official
who will do the same.12 These equilibria are important because they provide citizens with strictly the same
expected payoffs as the benevolent equilibrium and so, for citizens who are risk neutral and care only about
their own payoff, they strictly dominate any non–benevolent stationary equilibrium with compliance. On the
other hand, for risk averse or inequity–averse citizens, there is a strict subset of stationary equilibria with
compliance that dominate kleptocratic ones, justifying our focus on the former.13
2.2
Equilibria with campaign promises
We now turn to the effects of campaign promises. As pointed out earlier, campaign promises are cheap talk and
do not affect the set of possible equilibrium outcomes, but the multiplicity of equilibria means that theory does
not rule out promises having an effect on subsequent voting behaviour. Indeed, we will argue that campaign
promises may make it easier for players to coordinate on specific equilibria.
To pursue this possibility, we continue with our assumption that all citizens adopt the same stationary voting
strategy, but we relax the definition of “stationary” to include campaign promises as well as salary choices.
Specifically, a stationary voting strategy for citizens is a strategy that depends at most on (st , pt, pt−1 , ρt) in
the same way for all t, where st the official’s round–t salary choice, pt is her round–t promise (the salary she
promises to choose in round t + 1), pt−1 is her previous–round promise, and ρt is the current challenger’s
promise. This will allow us to consider equilibria in which voting is both retrospective and prospective. A
voting strategy is retrospective if it depends on either or both of st and pt−1 (the actions relating to salary
choices that have already taken place), it is prospective if it depends on either or both of pt and ρt (relating
to salary choices that have yet to take place), and it is retrospective–prospective if it is both retrospective and
prospective. Then, it is easy to see that a stationary equilibrium with compliance on a salary s ≥ smin can be
implemented by a retrospective–prospective voting strategy. For example, one such strategy would require that
the incumbent official be confirmed iff st ≤ s and pt ≤ s. Similarly, if s < smin then kleptocratic equilibria
are also still possible.14
Given this multiplicity of equilibria, the question of on what exact value s ∈ [smin , M ] citizens and officials
should coordinate is no easier to solve than in the setting without campaign promises, because there is no clear
12
This response from officials can also be generated by a voting strategy where the incumbent is always replaced, or indeed any
strategy independent of the salary choice. This is obviously outcome–equivalent to the equilibria described in the main text.
13
Proofs of these claims are in the online appendix.
14
Since promises are cheap talk, the condition that s ≥ smin is enough to guarantee compliance to the official just as in the game
without campaign promises. Conversely, if s < smin then compliance will not obtain in equilibrium, just as in the game without
campaign promises.
7
theory of how exactly officials and citizens should come up with s. We address this issue by focussing on a
special class of retrospective–prospective equilibria. Specifically, consider the citizens’ strategy to re–elect the
official if and only if
i. She kept her promise from last round (st ≤ pt−1 ), and
ii. Either
(a) her promised salary for next round is credible and no higher than the challenger’s (smin ≤ pt ≤ ρt),
or
(b) her promised salary is credible while the challenger’s is not (ρt < smin ≤ pt ).15
This voting strategy is clearly retrospective in its first component (voters punish breaking past promises) and
prospective in the second component (voters select the candidate who makes the best credible promises).
Given this voting strategy and assuming (i) is satisfied, it must be that pt = ρt = smin in equilibrium
because if either the official or the challenger were to promise a higher salary, the opponent could guarantee
election and a positive rent by proposing a salary strictly lower but still larger than smin , whereas promises of
a lower salary than smin would imply losing the election. Conversely, given the citizens’ voting strategy and
given that pt = ρt = smin , in each round, then the election winner will find it rational to comply in the next
round. The consequence is that st = smin in each round, and the incumbent will always be confirmed, as in
a benevolent equilibrium. We call this equilibrium the retrospective–prospective equilibrium with emergent
coordination because the citizens’ voting strategy doesn’t specify a particular value of s; instead s arises from
candidates “bidding” with their promises, and election winners preferring to keep them, thus coordinating with
voters on the lowest credible promise.
It is important to note that voting strategies where s emerges through campaign promises, but are only
retrospective or only prospective, would not be sensible from the citizens’ point of view. In both cases, the
incumbent could guarantee herself a salary st = M in each round and still be re–elected. With only retrospective voting, she could always promise M because the promise would never be broken. With only prospective
voting it would suffice that pt = smin because breaking the promise would not be punished. Conversely, it is
only with the possibility of making campaign promises that retrospective–prospective equilibria with emergent
coordination can be generated.
Another important aspect of our retrospective–prospective equilibria with emergent coordination is that they
support prospective voting without the need to assume any underlying selection problem based on intrinsic
heterogeneity. Of course, this does not mean that such selection problems will not exist in practice. In the
experiment, while our public reading of the instructions ought to imply common knowledge of the rules and
of identical monetary incentives, it is not possible to guarantee that there is common knowledge of identical
preferences. For example, individuals may differ in their attitudes toward risk or inequity; since these attitudes
affect the value of smin (as shown in the online appendix), they are payoff–relevant to voters, so that selection
based on these differences is sensible. Moreover, even if officials’ preferences do not vary, it may still be the
case that voters believe they vary. It is important to stress, however, that retrospective–prospective equilibria
with emergent coordination are fully compatible with heterogeneity in preferences (e.g., variation in attitudes
towards risk or inequity).16
15
We assume that citizens treat the absence of a promise negatively and equivalent to a promise to take the entire endowment (see
Section 3.3 for evidence that they do so in the experiment). Also, note that if t = 1 then only (ii) applies which means that this voting
strategy does not impose any restriction on s1 .
16
To see this, suppose we identify an individual i’s “type” as the value of smin corresponding to her preferences (i.e., she is indifferent
between taking smin (i) in every period and taking the entire endowment once before being voted out). Call i “more generous” than j
8
In our experiment we have a treatment with discount factor δ = 0.8 but with campaign promises (COMM–
0.8 cell) and we can compare it with the treatment with the same discount factor but without campaign promises
(BASE–0.8 cell). Our first hypothesis about the COMM–0.8 cell is that campaign promises, by allowing the
two candidates to bid for votes, make retrospective–prospective equilibria with emergent coordination possible,
thus making it easier for candidates and voters to reach the salary smin .
Hypothesis 3 Officials’ salaries are higher in the BASE–0.8 cell than in the COMM–0.8 cell.
Then, similar to the argument for Hypothesis 2, if lower–salary equilibria are played in the COMM–0.8 cell
than in the BASE–0.8 cell, then there will be a range of salaries that would result in re–election in BASE–0.8 and
voting the incumbent out in COMM–0.8. Without making potentially strong assumptions about preferences,
the exact range of salaries cannot be identified, but as with Hypothesis 2, we can formulate a weaker hypothesis:
Hypothesis 4 Conditional on the official’s salary, she will receive a higher vote share, and be re–elected with
higher likelihood, in the BASE–0.8 cell than in the COMM–0.8 cell.
Beyond the effect on the official’s salary, our conjecture about the COMM–0.8 cell implies that voters’
behaviour depends on whether campaign promises are kept. We should expect the vote share and probability
of re–election to be higher when promises are kept than when they are broken:
Hypothesis 5 In the COMM–0.8 cell, officials should receive a higher vote share, and be re–elected with
higher likelihood, when their promises are kept than when they are not.
Also, the COMM–0.8 equilibrium requires that promises are kept:
Hypothesis 6 In the COMM–0.8 cell, officials’ salaries depend on their past promises.
Finally, voters in this cell vote for the candidates who makes the best salary promises:
Hypothesis 7 In the COMM–0.8 cell, officials should receive a higher vote share and be re–elected with higher
likelihood when they promise to take lower salaries than the challenger.
2.3
Experimental procedures
Twenty–seven sessions were conducted, 4 of each cell at University of Aberdeen (a public university in the
United Kingdom) and 5 of each cell at Monash University (a public university in Australia). Each session
involved between 12 and 19 subjects (421 in total) and comprised six supergames (see Table 2).17 Subjects were
primarily undergraduate students, and were recruited using the ORSEE recruiting software (Greiner 2004). No
one took part more than once. The experiment was computerised, and programmed in z–Tree (Fischbacher
if smin (i) < smin (j) (though these values can reflect both generosity and unrelated factors such as risk aversion), and let there be a
“most generous” type i∗ . Then there is an equilibrium in which (1) citizens utilise the same retrospective–prospective voting rule as
in the identical–preferences case (except now smin (i∗ ) is the minimum credible promise); (2) in any period in which the official kept
her promise, both she and the challenger promise smin (i∗ ); (3) in any period in which the official broke her promise, the challenger
promises to take the entire endowment; and (4) all promises are kept except for promises of smin (i∗ ) by types other than i∗ , in which
case the entire endowment is subsequently taken. Then any official with a type different from i∗ will be voted out after at most two
periods (having broken a campaign promise), and an official with the i∗ type will always be re–elected and, except possibly for the
first term in office, always take smin (i∗ ) (thus never breaking a campaign promise). Thus the difference between identical officials
(discussed in the main text) and heterogeneous officials is that the latter allows the possibility of broken promises in equilibrium,
though these will decrease in frequency over time as i∗ types replace other types in office.
17
Due to a programming error, one BASE–0.8 session only had five supergames.
9
Table 2: Experimental session information
Cell
BASE–0.8U
COMM–0.8U
BASE–0.9U
Location Discount Campaign Sessions Subjects
factor (δ) promises?
UK
BASE–0.8A
COMM–0.8A Australia
BASE–0.9A
0.8
0.8
0.9
No
Yes
No
4
4
4
62
62
61
0.8
0.8
0.9
No
Yes
No
5
5
5
76
80
80
2007). At the beginning of a session, subjects were seated in a single room and given written instructions,
which were then read aloud in an attempt to make them common knowledge.18 Then, the first supergame
began.
As usual when implementing models with infinite repetition and discounting, we transformed the game
into one of indefinite repetition, using a continuation probability identical to the discount factor of the original
infinitely–repeated game. (This alters the interpretation of players’ utility functions from present values to
expected utilities, but leaves the analysis unchanged as long as they are expected–utility maximisers.) Thus,
at the end of a given round of a supergame, there was a fixed probability of either 0.8 or 0.9 of the supergame
continuing for at least another round, with no further discounting of payoffs.
Subjects were randomly assigned to groups of size 5, 6, 7, 8 or 9 at the beginning of each supergame, and
their composition was fixed for the duration of a supergame. Subjects were visually isolated and asked not to
communicate during the session, and no identifying information was given about the other group members.
For example, when a challenger was nominated in some round, other voters would not be able to determine
whether he/she had been a challenger or official before – let alone any decisions that he/she might have made.
This restriction on the information given to subjects was necessary to give pure retrospective voting its best
possible chance in our baseline cells.
Each round began with subjects’ screens displaying their group’s population N + 1 and endowment M ,
which was a deterministic function of the population: M = 3(N + 1) − 1 in the UK and M = 6(N + 1) − 2
in Australia. (At the time, one British pound (GBP) averaged about 1.5 Australian dollars (AUD) at market
rates, but about 2 AUD in purchasing power.) The linear dependence on N + 1 makes different–sized groups
reasonably comparable on a per capita basis, while the non–zero intercept was chosen in the hope of nudging
subjects away from reflexively choosing equal splits by making the calculation of M/(N + 1) less trivial.
Officials chose their salaries – which could be any multiple of 0.01 – and these salaries were displayed on
group members’ screens, along with the income per citizen and the subject’s own payoff.
In the BASE–0.8 and BASE–0.9 cells, this feedback was followed by the election. The official in each group
was reminded that he/she would be the incumbent. Citizens randomly chosen to be challengers were informed
of their nomination; the others were told only that a different citizen had been nominated. Each group member
(including the incumbent and the challenger) was prompted to vote; voting was simultaneous, and abstaining
was not possible. Winners were determined by majority vote; in case of a tie, the incumbent remained in office.
All subjects’ screens displayed the winner and both candidates’ vote counts. After subjects had clicked a button
18
Sample instructions and screen–shots are in the online appendix. Additional experimental materials, as well as the raw data from
the experiment, are available from the corresponding author upon request.
10
to continue, their screens displayed whether the supergame would continue or end. If another round was to be
played, subjects were told that the election winner would be the official in the next round; if not, they were
told that the supergame had ended and (when applicable) a new one would begin. Since the announcement of
whether the supergame continues or ends was made at the very end of a round, all decisions in a round were
made without knowing how long the supergame would continue.
In the COMM–0.8 cell, both candidates were able to send messages after the challengers were selected. The
message space was nearly identical to the official’s salary choice set, with the exception that a null message
(framed as “making no announcement”) was also possible. Message choices were made simultaneously and
then announced to all group members, including both candidates, after which voting took place.
At the end of the sixth supergame, one round from each supergame was randomly chosen for each subject
to determine his/her earnings. The exchange rate was one–to–one between experimental and real money, and
there was no show–up fee. Sessions typically lasted 60–90 minutes, and total earnings averaged about £16 in
the UK sessions and $33 in the Australia sessions.
3
Experimental results
While the size of an individual group ranged from 5 to 9 in the experiment, the mean group sizes were fairly
similar across cells. The mean of 6.57 in the BASE–0.8 cell was not significantly less than the mean of 6.71 in
the BASE–0.9 cell (one–tailed robust rank–order test, individual–group data, p ≈ 0.39), nor was it significantly
greater than the mean of 6.39 in the COMM–0.8 cell (p ≈ 0.37).19 Because of this similarity across cells,
we will sometimes pool the data from different group sizes when assessing treatment effects, though in our
regressions we will err on the side of conservatism by including controls for group size.
3.1
Salary choices
Figure 1 reports average salary choices by treatment. Here, and throughout the results section unless stated
otherwise, quantities such as salaries, campaign promises and payoffs are expressed as proportions or percents
of the endowment M , in order to facilitate comparisons across different group sizes. Comparison of the BASE–
0.8 and BASE–0.9 cells suggests lower officials’ salaries as δ increases, while comparison of the BASE–0.8
and COMM–0.8 cells suggests that allowing campaign promises is also associated with lower salaries. These
differences – consistent with Hypotheses 1 and 3 respectively – are marginally significant according to non–
parametric robust rank–order tests on the session–level data (Ù = 1.68, p ≈ 0.058 for BASE–0.8 vs. BASE–
0.9; Ù = 2.03, p ≈ 0.036 for BASE–0.8 vs. COMM–0.8).20
Figure 2 shows some additional detail: the distributions of official salary choices for each cell, with the
action space divided into intervals equal to 9% of the endowment. For example, a point plotted between
the horizontal coordinates 45 and 54 represents the fraction of salary choices between 45% and 54% of the
19
We use one–tailed tests here to give the best chance to the alternative hypothesis of differing group sizes across cells, in contrast
to later where we do so because the alternative hypotheses are directional. The robust rank–order test statistic Ù has a symmetric
distribution under the null hypothesis, so the interested reader can always calculate a two–tailed p–value by doubling the corresponding
one–tailed value. See Siegel and Castellan (1988) for descriptions of the non–parametric statistical tests used in this paper, and Feltovich
(2005) for critical values for the robust rank–order test.
20
The difference between the BASE–0.9 and BASE–0.8 cells either remains unchanged or becomes more significant if we drop the
second half of each supergame in that cell (to equate the expected number of rounds per supergame across cells). Also, the significance
of differences between BASE–0.8 and either BASE–0.9 or COMM–0.8 is not affected by normalising salary choices by subtracting
the corresponding benevolent–equilibrium salary for δ = 0.8 given the group size, to control for differences in group sizes across cells
(though as noted at the beginning of the results section, the similar average group sizes across cells suggest that any effect driven by
group size alone should be fairly minor).
11
Figure 1: Mean salary choices by treatment
0.6
BASE–0.8
BASE–0.9
COMM–0.8
0.5
0.4
s/M
0.3
0.2
0.1
0.0
UK sessions
Australia sessions
All sessions
endowment in a given cell of the experiment.21 (Similar labelling is used in Figures 3, 4 and 5.) As the figure
Figure 2: Salary choice frequencies in BASE–0.8, BASE–0.9 and COMM–0.8 cells
0.5
d BASE–0.8
qqqqtqqq BASE–0.9
p p p p p COMM–0.8
qqtqq
0.4 p ppp ppp pppp pppqqqpppqqqqqpppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp
q
qq qqqq
Frequency
qqq qqqqq
p
q
qq p p p p qqppppqqqp p ppppppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp
ppppppp qqq pp
0.3 p ppp ppp pppp pppqqqq pppppppdpppppppp
pppqqppdpp
q pp
qqqppp pp
tqqpp ppp
qqq ppp
qqqppp pp
qqqppp pp
qqq ppp
qqpqpp ppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppppdppp
0.2 p ppp ppp ppppqq ppppp ppp pppp ppp ppp pppp
qqpqpp ppp
t
ppqq
qq pp
qqpqpp pp
pqqqpp ppp
pp qpqq
qq pp
qpqpqp ppp
p q pp
qp
qpqpqp pp
pqpqqppppp
qqppp
p
p
q
p
q
qp p
p
0.1 p ppp pppqqpppp
pp ppp ppp pppp ppp ppp pppp pppqpqpqpqpppppppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp pppppqpqpqpppppp pppp ppp
pqpqpq p p p
p
p
qqqppp
q
p
pqtdpqpqpqpppppp p
pqppqpqppp
qp
qqqqpqppppppppdpp
p
p
d
p
p
p
qqqqq p p ppppppppppppppp
p
p
p
p
p
p
p
p
qqppqp
q
pppdppppppppp pppp
qqqtqqqqqqqqqqqqqqqqpqpd
tqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqtdpqpqpqpqpqpqppqpqppqpqppqpqppqpqpqqtpqqpqqpqqpqqpqqpqppqpqppqpqppqpqtdppqqpqqpqqpqqpqqpqqpqqpqqtpp
qp
0 td
0
9
18
27
36
45
54
63
72
81
90 100
Salary (% of endowment)
shows, the averages reported in Figure 1 hide a substantial amount of heterogeneity. Three features are worth
particular emphasis. First, there is non–trivial mass on or near the kleptocratic equilibrium, as officials grab the
entire endowment about 15–20% of the time in each cell. Second, the distributions are bimodal with additional
peaks at salary choices just below 20% of the endowment. This is sufficiently low that it is not compatible
with benevolent equilibrium under an assumption of own–expected–payoff maximisation, but as discussed in
the online appendix, it is compatible under weaker assumptions such as risk or inequity aversion.22 Third, the
21
A width of 9% was chosen because it was the smallest that allowed roughly equal–sized intervals to partition the choice set,
along with having the benevolent equilibria in the same interval for group populations of 5 up to 9; see Table 1 for these theoretical
predictions.
22
Still another possibility is subjects being concerned about their “image” with regard to other subjects or the experimenter (Andreoni
and Bernheim 2009).
12
treatment effects from Figure 1 are visible here also; salaries are lower in either BASE–0.9 or COMM–0.8 than
in BASE–0.8.
Table 3: Classification of salary choices – number and percent of observations by
consistency with various equilibrium or non–equilibrium behavioural rules
Non–equilibria
Below
equal
” h Equal split” hBelow–benevolent
”
h
0.95
1.05
1.05
0.95
0, N
+1
N +1 , N +1
N +1 , 0.95smin
BASE–0.8
BASE–0.9
COMM–0.8
49 (6.6%)
92 (7.5%)
57 (7.1%)
218 (29.2%)
490 (40.1%)
226 (28.0%)
Stationary equilibria
Benevolent
Other stationary
[0.95smin , 1.05smin ) [1.05smin , 0.9)
184 (24.7%)
174 (14.2%)
274 (34.0%)
5 (0.7%)
31 (2.5%)
14 (1.7%)
139 (18.6%)
201 (16.4%)
112 (13.9%)
Kleptocratic
equilibria
[0.9, 0.95)
[0.95, 1]
10 (1.3%) 141 (18.9%)
7 (0.6%) 227 (18.6%)
8 (1.0%) 115 (14.3%)
Table 3 re–characterises the information from Figure 2, with salaries classified according to whether they
were consistent with the kleptocratic equilibrium, a stationary equilibrium (given δ and N ), or no equilibrium
at all, and into relevant sub–categories within these.23 This table shows the preponderance of low salaries even
more starkly than the figure did: over half of all salary choices are below the benevolent equilibrium, and these
are split between salaries giving the official a rent that is positive (i.e., more than any individual citizen gets)
but less than that in the benevolent equilibrium, and those amounting to roughly equal splits.
3.2
Retrospective voting
Figure 3 illustrates the association between officials’ salary choices and the resulting voting outcomes for each
cell, using the same intervals of salary choices as in Figure 2. Several features are apparent. First, there is
Figure 3: Observed election results in BASE–0.8, BASE–0.9 and COMM–0.8 cells
Incumbent vote share (excl. candidates)
1.0
d BASE–0.8
qqqtqqqq BASE–0.9
p p p p p COMM–0.8
0.8 p ppppqtqpppqqq ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp ppp
p p p qqqq
p p pqq
pqpqqp
qqpqp p p
q p p ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp ppp
0.6 p pppp ppp ppp pppppp pqptdqppppqpqpqpqpqppppqppqpqpqppppp
pp
ppp p ppqpqpqpqpqpqqptppp
pppdqpqq p p
ppp p
pqpqpq ppp
p
qpqpqp p pp
pdpp
qp p
0.4 p pppp ppp ppp pppp ppp ppp pppp ppp pppqqqpqpqpppppppppp ppppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp ppp
qqqppp pp p
qqqppp p p p
qqq ppdp p p p p
qqq ppp p p p p p p p p p p p p p p p p
pp pp
q pp
p ppppp p ppp pppp ppp ppp ppp pppp pppppppp p pppp ppp ppp ppp
0.2 p pppp ppp ppp pppp ppp ppp pppp ppp ppp ppppqtqpppqqqqqpppqppppppppp pppp ppp ppp pppp ppp ppp pppp
p p
qqqqqppp
pppdpppppppp p p p p p p p p p p p p p p p p p p p p p p p
p
qqqqpqd
p
p
ppppp
pp
ptqpqpqpqpqpq
p
pqpqpqpqpqpqqqqqtqqqqppqqpqqqqqqqqqqqtqqqqqqqqqqqqpqpqpqpqt
dpqpqpqpqpqpqpqpqppppp
pppppdpp
qqqqqpqppdpppppppppppppppppdppppppqpqqpqppqqppqqppqpqqpd
qqtqqqqqqqqqqqqqqqqqtqqqq t
0.0
0
9
18
27
36
45
54
63
72
81
90 100
Re–election frequency
tqqq
qqq
qqq
qqq
qqq d
qpp
pp qtqqpqpqppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp pp
qqqppp
0.8 pp ppp pppp pppp pppppp pppp
qqqpp
p
qqpqpp
pp p
qqpqpp
ppd
qdtqpqp
pppp
qpqqpp
pppp
qqpqpp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp pp
p p p pppp ppp pppp
0.6 pp ppp pppp ppp pppppppp
p p p p qqpqqpppp
p p p qqqpp
p pqqpqppp
qqqppp p
qqqppp p p p p
p p p ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp pp
0.4 pp ppp pppp ppp ppp pppp ppp ppp pppp pppqqqqqpppppppp pppp
p
qqqppp p p p p p
p
qqqppp
p pp p p p p p p p p p p p p p p
pp pp pp
qqqpdpp
ppppp
pppppp
qqq ppp
pppp ppppppp
p
p
p
p
p
p
p
p
qtq pp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp pppp pppp pppp ppp ppp ppp pppp ppp pp
qqq ppp
0.2 pp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp qpppp
qqqppp
qqqppp
ppdpp
qqqppp
p pp pppppp
p
p
pppp
p
qqpqpp
p pp
p
qpqpqp
p
p
p
dtqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpdtqqqqqqqqqqqqqqqqqtqqqqqqqqqqqqqqpqpqpqtdpqpqppqpqpqpqpqqpqpqpqpqpqppqpqpqtdpqpqqpqpqpqpqpqppqpqpqpqqpqpqpqpqptdqppqqpqpqpqpqpqpqpqpqpqpqpqpqpqptd
0.0
1.0
0
9
18
27
36
45
54
63
72
81
90 100
Official salary (% of endowment)
strong evidence of retrospective voting in all three cells. Officials choosing very low salaries receive between
one–half and two–thirds of the vote, and are returned to office with high, but not certain, likelihood. (Recall
however from Figure 2 that the lowest interval and those between 36 and 90% of the endowment contain small
23
See also Figure 7 in the online appendix, which shows the distributions of salary choices as in Figure 2, but separately for each
group size as well as cell.
13
numbers of observations.) As salaries increase, vote shares and re–election frequencies steadily decline, so that
an incumbent taking a salary of roughly half the endowment can expect to receive about one–tenth of the vote
(not including her own vote and the challenger’s, which typically cancel each other out in the vote count) and
have a 15% likelihood of re–election in the baseline cells – with both a bit higher in the COMM–0.8 cell. An
official taking the entire endowment is very unlikely to be re–elected, even in the COMM–0.8 cell, and indeed
stands to receive no votes other than her own.
Second, the relationships between salary choices and both vote shares and re–election probability are not
as sharp as required by stationary equilibria. These relationships have the expected negative sign, but officials
choosing low salaries receive “too few” votes in relation to any stationary equilibrium, and thus have too low
of a likelihood of re–election; conversely, officials choosing high salaries receive “too many” votes and are
re–elected too often. One implication of this relatively weak relationship between salary and election result is
that the official’s monetary best response is to grab the entire endowment as long as she remains in office. That
is, under expected–payoff maximisation, the only equilibrium supported by this voter behaviour has s = M :
essentially the kleptocratic equilibrium, but even better for the official since she is re–elected with positive
probability. As noted already, however, officials who are risk averse or inequity averse could rationally choose
lower salaries like those seen in the data.
Third, there is some evidence of treatment effects. For a given salary choice, officials are more likely
to be re–elected in the COMM–0.8 treatment than in the BASE–0.8 treatment, particularly at higher salaries.
Differences between the BASE–0.8 and BASE–0.9 treatments appear small, though when they do differ, it is
typically in the direction of increased strictness in BASE–0.9 compared to BASE–0.8.
In order to assess the significance of these apparent effects, we estimate two probit models: one with an
indicator for a vote for the incumbent as the dependent variable (using individual–level data, but with the
current incumbent and challenger removed from the data–set) and the other with an indicator for re–election
(using group–level data). On the right–hand side, both models include a constant term and indicators for the
COMM–0.8 and BASE–0.9 treatments (so the baseline is BASE–0.8), and the official’s salary (as a fraction
of the endowment) on its own and interacted with the two treatment dummies. As controls for the group size,
we included the value of smin given the group size and δ = 0.8 (under own–expected–payoff maximisation),
along with the product of this variable with the BASE–0.9 indicator.24 To control for time dependence, we
include the round number and the supergame number, on their own and interacted with the treatment dummies
and official’s salary. Additional nuisance variables are an indicator for an even–numbered population (as the
tie–breaking rule made it slightly more difficult to unseat an incumbent when the economy size was 6 or 8), the
group size itself, an indicator for a session taking place in Australia, and in the model for incumbent vote, the
subject’s decision time (the time from the beginning of the relevant stage to when the decision was entered, in
minutes).
Both models used individual–subject random effects, and were estimated using Stata (version 12). Table 4
displays average marginal effects and standard errors for all variables. Additionally, it shows the marginal
effects of our treatment dummies (BASE–0.9 and COMM-0.8) at three particular salaries: a low salary of
25% of the endowment (the highest multiple of 5% below the benevolent–equilibrium salary when δ = 0.8),
a moderate salary of 40% of the endowment (roughly the top of the distribution of non–kleptocratic salary
choices, and a high salary of 100% of the endowment (the kleptocratic–equilibrium salary).25 The relatively
small effect of the BASE–0.9 indicator on incumbent vote share seen in Figure 3 is also seen here; it is nearly
24
The reason we used smin (δ = 0.8) for all observations, rather than using smin (δ = 0.9) for those observations with δ = 0.9, is
that we did not want to introduce a second control for the BASE–0.9 treatment.
25
Figure 8 in the online appendix illustrates the predicted incumbent vote share and re–election probability for many more combinations of treatment and official salary choice, based on these regression results.
14
Table 4: Probit results – average marginal effects unless stated otherwise (std. errors in parentheses)
[1]
Vote for incumbent (excl. candidates)
[2]
Re–election
0.005
(0.027)
0.006
(0.035)
–0.028
(0.028)
–0.013
(0.009)
–0.030
(0.022)
−0.249∗∗∗
(0.046)
−0.111∗∗∗
(0.031)
–0.010
(0.007)
0.042
(0.028)
0.054
(0.035)
0.103∗∗∗
(0.029)
0.042∗∗∗
(0.013)
–0.024
(0.025)
0.000
(0.038)
0.127∗∗∗
(0.036)
0.022∗∗
(0.011)
BASE–0.9
...when s/M = 0.25
...when s/M = 0.40
...when s/M = 1.00
COMM–0.8
...when s/M = 0.25
...when s/M = 0.40
...when s/M = 1.00
−0.853∗∗∗
−2.014∗∗∗
(0.017)
(0.107)
smin (δ = 0.8)/M
2.506
5.623∗∗
(1.617)
(2.625)
Australia session
0.001
–0.007
(0.022)
(0.019)
supergame
0.026∗∗∗
0.019∗∗∗
(0.003)
(0.005)
round
0.003∗∗∗
0.005∗∗
(0.001)
(0.002)
economy population
0.021
0.039
(0.026)
(0.042)
even population size
–0.003
0.065∗∗∗
(0.012)
(0.019)
decision time
0.314∗∗∗
(in min.)
(0.045)
N
12867
2774
|ln(L)|
6157.12
1077.90
* (**,***): Marginal effect significantly different from zero at the 10% (5%, 1%) level.
official’s salary (s/M )
zero at a salary of one–fourth the endowment, and at higher salaries it is negative but not significant. This effect
is amplified somewhat for re–election probability, with incumbents significantly less likely to be re–elected in
the BASE–0.9 cell than in the BASE–0.8 cell after choosing low or moderate salaries. For its part, the effect
of the COMM–0.8 indicator on incumbent voting outcomes is positive but insignificant at the low salary, but
positive and significant at moderate and high salaries.
3.3
Campaign promises and voting
In the COMM–0.8 cell, the opportunity for candidates to make campaign promises was generally taken; in 806
elections, incumbents chose not to make a campaign promise only 47 times (5.8%), and challengers chose not
to do so only 23 times (2.9%). Figure 4 highlights voters’ use of campaign promises for prospective voting.
15
Specifically, this figure shows the relationship between official salaries and election outcomes in the COMM–
Figure 4: Observed election results in COMM–0.8 cell by incumbent and challenger campaign promises
Incumbent vote share (excl. candidates)
1.0
d incumbent promise < challenger promise
qqqtqqqq incumbent promise > challenger promise
tqqq
qq
0.8 p pppp pppqqqqqppp pppp
ppdppppppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp ppp
ppp p pppppppppp
qq ppp
ppdpp
ppp
ppqpqqp
ppp
dp ppp qqqq
ppp
qqq
pp
qqq
p
pppp
ppp
ppp
pppp
ppp
ppp
pppp
ppp
ppp
ppppppppdpppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp ppp
qqq
0.6
ppp
qtqqqq
qqqqqq
ppp
qqqqq
ppp
qtqq
ppp
qqq
pdppppp
qqqppp pppp ppp pppppppppp pppp ppppppppppp ppppp
ppppppppppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp ppp
p
pppp
ppp
ppp
pppp
ppp
ppp
pppp
ppp
ppp pp
ppppp
qqq
0.4
pdpp
ppp ppppp
qqq
ppp
dp
qqq
ppp
qqq
ppp
pp ppppdppp
qqtq
pppppp ppppppp
ppp
p
qqqqqq
p
p
p
ppp ppp pppp ppp ppp pppp ppp pppppp pppp ppppppppp ppppppdpppp ppp ppp pppp ppppppppppp ppp
0.2 p pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp pppqqqqpppqqqqqpppp
pd
p pppppp
qtqqqqqqqqqqqqqqqqqtqqqqqqqq
qqqqqqq qqqqqqqqqqqpqppqpt
dqpqpqpq
qtqqq
qqqq
qqq
qqqt
qqqq qqqqqqqqqqtqqqqqqqqqqqqq
qqtqqqqq
0.0
0
9
18
27
36
45
54
63
72
81
90 100
Re–election frequency
pdtqqpqppp
qqq ppppp
p
qqq ppppp
qqq pdpppp
qqq ppppp
ppp
qq
pp
ppp
pppp
pppqqqqppp pppp ppp ppppppppdppppp
pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp pp
0.8
qqq
pppp
qqq
pppp
qqq
pppdp
tqqqq
ppp
pdpp
qqq
ppp
pp ppppppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp pp
qpppqqq ppp pppp ppp ppp pppp
p
pp
ppp
pppp
ppp
ppp
pppp
ppp
ppp
ppp
pppp
ppp
p
ppp
p
0.6
qqqq
ppp
pp ppppp
qqtq
ppp
ppp
qqq
pp p
ppp
ppp
qqq
p
p
ppp
p
qqq
ppp p
q
p
qqpppq ppp pppp ppppppppp pppp pppp ppp ppp pppp pppdppppppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp pp
pp
ppp
pppp
ppp
ppp
pppp
ppp
ppp
pppp
0.4
ppp p
ppp
qqq
ppdppp
ppp pp
ppp
qqq
p
p
pp pppp
ppp
qqq
pd
p
p
ppp
qqq
pp ppppp
ppp qqqtqqq
qqtq
p
ppp
q
q
p
qqq ppp ppp ppp pppp ppp ppp pppp ppp ppp pppppppqq ppp pppqqq pppp ppp ppp ppppp ppp ppp ppp pppp
ppp ppp pp
qqqq
qppp qq
0.2 pp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp
q
p
q
q
ppd
q
p
qqqq
p
q
q
p
q
q
p
qqqq
qqqtq pppp qqqq pp
q
q
q
q
q
q
q
q
q
tqqqqqqqqqqqqqqqqtqqqqq
ppp
q
ppp qqqqq ppp
ppdpppppppppppppppqpqpdtqpqqqqqqqqqqqqqqqqtqqqqqqqqqqqqqqqqt
0.0
1.0
0
9
18
27
36
45
54
63
72
81
90 100
Official salary (% of endowment)
0.8 cell, with separate curves according to which candidate promised a higher salary. (Not shown are the cases
where either candidate chose not to make a campaign promise, or where both made the same promise.) For
a wide range of salary choices, and in particular for choices in the ranges that constitute the vast majority of
observations (from 9 to 36 percent of the endowment and above 90 percent of the endowment), the official’s
expected vote share and likelihood of re–election are substantially higher (on the order of 20 percentage points)
when her campaign promise was lower than the challenger’s, compared to having a campaign promise higher
than the challenger’s.
In addition to using current–round campaign promises for prospective voting, there is some evidence that
voters use previous campaign promises for retrospective voting. Define a campaign promise to be broken,
conditional on winning the corresponding election, if the subsequent salary choice is higher than the promised
amount, and kept otherwise. Then, Figure 5 shows incumbents’ vote shares and re–election frequencies by
salary choice, broken down according to whether the incumbent’s previous–round campaign promise was broken or kept. There are few clear differences at high salaries (where the small number of observations means that
apparent differences are likely due to random noise), but at low salaries (up to about a third of the endowment),
officials are more likely to be re–elected following a kept previous–round campaign promise than following a
broken promise, and there is a corresponding though smaller difference in vote shares.
We further investigate the effects of campaign promises with four new probit regressions: two with voting
for the incumbent as the dependent variable (using the individual–level data but excluding current candidates)
and two with re–election on the left–hand side (using group–level data). Right–hand–side variables include
a constant term, the official’s salary choice, the supergame and round numbers, the economy’s population, a
dummy for an even–numbered population, a dummy for a session taking place in Australia, and for the two
incumbent–vote probits, the voter’s decision time.
The two models for each dependent variable differed in which explanatory variables were used to capture
campaign promises. The odd–numbered models included the promises themselves as continuous variables,
and used the subset of the COMM–0.8 data for which both candidates made campaign promises. The even–
numbered models instead included three dummy variables: one for the incumbent promising a lower salary
16
Figure 5: Observed election results by kept/broken campaign promise (COMM–0.8, rounds 2+)
Incumbent vote share (excl. candidates)
1.0
d kept promise
qqqqtqqq broken promise
0.8 p pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp ppp
pdpppp
ppppp
ppppp
ppd
0.6 p pppp ppp ppp pppp ppppppppppppppppppppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp ppp
qtqqqqqqqqq ppppppd
qqqqqqqtqppp
qqppqp
qpqppq
pqpq ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp ppp
0.4 p pppp ppp ppp pppp ppp ppp pppp ppp ppppqppqppppp
qpqq
pppqqqt
ppp qqq
qqtq
pdpppqqq
qqq qqqqq
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q
q
pqpq pppqqqppp pppp pppqqqqppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppptpppp ppp ppp ppp
qqq
qq
qqqqq
0.2 p pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppppqppppqpqpqpqppppp
qpqpqpdpppppp
qqq qqqqqqqqqq
ptqppqpqppp
qpqd
q
p
p
q
qqqt
ppppppp ppp ppppp tqqqqqqqpqppppppppp
qqq
qqqqqqq pdppppppp
pppdpp
qqtqqqqqqqqpqpqpqpqpppp qqqqq
qqqqpqtdpppppppppppppppppdppppppppppppppppd
0.0
0
9
18
27
36
45
54
63
72
81
90 100
Re–election frequency
1.0
dpppp
pppp
pppp
pppp
ppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp pp
pp
ppp
pppp
ppp
ppppdppppp
0.8
ppp
ppp
ppp
ppp
pdpp
ppp
qtqqq
pp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp pp
pp
ppp
pppp
ppp
ppp
pppp
ppp
ppp
qqqq pppp
0.6
qqqq ppppp
qqqq pp
qtqq ppp
qqq pp
qqq ppp
qqqppppppppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp pp
pp
ppp
pppp
ppp
ppp
pppp
ppp
ppp
pppp
0.4
qqq ppp
qqq ppp
qqq pdppp
tqq
qqq ppp
qq qqqqq
qtqq ppp
q
q qq
q
0.2 pp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppppqqqqqpppppppp ppp ppp ppppqqppp ppp ppppqqqqqppp ppp pppp ppp ppp pppp ppp ppp pppp ppptqpppq ppp pppp ppp pp
q
q ppdp
qqq pppp q
qq qqq
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qqq ppp qq
p
p
q
p
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q
qqq pdppppqppppppppp pp ppp qqqqqq ppppp
qt
qqq
qqqqq ppp
qqq qq pppdp
qqqqqpdpppppppppppppppppqpqpqpqppppppppp ppppdppppppppppppppppd
qqtq
t
t
d
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
q
0.0
0
9
18
27
36
45
54
63
72
81
90 100
Official salary (% of endowment)
than the challenger, one for both promising the same salary (this happened about 9% of the time), and one for
the incumbent making no promise (this happened about 6% of the time). These used the data in which the
challenger made a campaign promise.26 Finally, we include an indicator, “broken promise”, which takes on a
value of one if the previous–round campaign promise was broken. Since this variable is not defined in the first
round of a supergame, we further restrict our data set to rounds two and higher.
The results are shown in Table 5. The main results from Table 4 continue to hold, but the novel results
concern the impact of campaign promises. Models 3 and 5 show that despite being cheap talk, promises are
taken seriously by voters: incumbents receive more votes and are more likely to be re–elected, the lower
the future salary they announce, and the higher the challenger’s announcement. The effects are significant
(p < 0.01) and quite strong: decreasing the promised salary by one–tenth of the endowment translates to a
20–percentage–point increase in the likelihood of winning the election. Models 4 and 6 present similar results:
lower promised salaries are rewarded by voters (p < 0.01), while making no campaign promise at all is a
disastrous choice for an incumbent, leading to a substantial (and significant: p < 0.01) decrease in votes and
re–election probability. Apparently, voters expect the worst when they don’t receive a campaign promise from
a candidate. Finally, the “broken promise” indicator has a negative and significant marginal effect. This effect
is substantial: breaking one’s promise translates to a decrease in the likelihood of being re–elected of roughly
20–25 percentage points.
3.4
Campaign promises and salary choices
Since campaign promises affect election results, it is important to understand how they relate to officials’ actual
salary choices. Figure 6 shows scatter–plots of the official’s previous–round campaign promise and subsequent (current–round) salary choice. For both re–elected and newly–elected officials, the figure shows two
distinct patterns. Low campaign promises (below about 30% of the endowment) make up the vast majority
of promises and are fairly uninformative, with subsequent salary choices ranging from at or even below the
26
Only 23 observations (about 3%) had the challenger making no promise. Since this is too infrequent for any meaningful statistical
analysis, we dropped these observations from the sample for these probits, though we note here that the challenger subsequently lost
20 of these 23 elections (87%), while incumbents making no campaign promise lost 34 of 47 elections (72%).
17
Table 5: Voter behaviour in the COMM–0.8 cell – marginal effects and std. errors in parentheses
[3]
[4]
Vote for incumbent (excl. candidates)
official’s salary
incumbent promise
challenger promise
−0.452∗∗∗
(0.047)
−1.773∗∗∗
(0.214)
0.765∗∗∗
(0.132)
−0.539∗∗∗
(0.045)
−1.033∗∗∗ −1.573∗∗∗
(0.210)
(0.328)
∗∗∗
−2.292
(0.411)
1.820∗∗∗
(0.400)
−0.218∗∗∗
(0.051)
0.260∗∗∗
(0.032)
0.140∗∗
(0.066)
−0.250∗∗
(0.107)
−0.241∗∗∗
(0.048)
–0.026
(0.017)
–0.022
(0.043)
0.025∗
(0.013)
0.000
(0.006)
0.111∗∗∗
(0.040)
–0.045
(0.024)
–0.002
(0.042)
0.017
(0.012)
0.006
(0.006)
0.074∗
(0.039)
broken promise
−0.176∗∗∗
(0.027)
0.219∗∗∗
(0.018)
0.198∗∗∗
(0.037)
−0.118∗∗∗
(0.041)
−0.187∗∗∗
(0.025)
economy population
−0.028∗∗∗
(0.009)
–0.037
(0.033)
0.020∗∗∗
(0.007)
0.004
(0.003)
0.006
(0.023)
0.268∗∗
(0.110)
−0.016∗∗
(0.008)
–0.034
(0.032)
0.025∗∗∗
(0.006)
0.008∗∗∗
(0.002)
0.003
(0.021)
0.274∗∗∗
(0.103)
incumbent makes lower promise
incumbent makes same promise
incumbent makes no promise
Australia session
supergame
round
even population size
decision time (in min.)
[5]
[6]
Re–election
N
2721
2998
611
|ln(L)|
1466.25
1596.35
254.40
* (**,***): Marginal effect significantly different from zero at the 10% (5%, 1%) level.
674
282.69
promised amount, all the way up to the entire endowment. The corresponding segment of the lowess smoother
lies well above the 45◦ line, meaning that such campaign promises are on average understatements of the official’s salary. By contrast, higher campaign promises, though rare, are nearly unbiased estimates of subsequent
salary choices.
We estimate Tobit models using the COMM–0.8 data, with salary choice as the dependent variable. Model
7 has as right–hand–side variables the official’s previous–round campaign promise and its square, the official’s
previous–round vote share, a dummy for being a re–elected incumbent (as opposed to newly–elected), all
products of these variables (including the triple products), a dummy for an Australia session, and a constant.
This Tobit is estimated on the sample of COMM–0.8 officials who made a campaign promise in the previous
round. Model 8 is estimated using only the data from completely inexperienced subjects: the second round of
the first supergame (i.e., the first instance where there is a previous–round promise). Given the much smaller
sample size (21 observations), by necessity we use a minimal set of explanatory variables: the previous–round
promise, the previous–round vote share, and their product. Both models include a constant term; Model 7 also
includes individual–subject random effects.
The results are shown in Table 6. For Model 7, the sample size allows us to compute the marginal effect
18
Figure 6: Scatter–plots of campaign promises and actual subsequent salary choices, as fractions of endowment
(Area of a circle is proportional to the number of observations it represents)
Re–elected
a official
a a (was incumbent)
1 a a ababacaababaaaaab acbaaa
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0.8
Actual
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round t
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defaults)
0.2
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0
0
1a
0.2
0.4
0.6
0.8
Promise in round (t − 1) for round t
0.6
0.4
a
0.2 a
6 0
1
0
[Blank]
official (was challenger)
a a Newly
aa aaaba aacaa a a elected
a
Lowess
a
smoother
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(using
Stata
a
defaults) `
A
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Promise in round (t − 1) for round t
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6
1
[Blank]
of the previous–round promise separately for newly–elected and re–elected officials, and for promises of 20%,
30%, 40% and 50% of the endowment. For newly–elected officials, these marginals reinforce the U–shaped
relationship between campaign promises and subsequent salary choices seen in Figure 6; beyond a threshold,
higher promises tend to be associated with higher salaries, but this relationship breaks down at lower promised
salaries. For re–elected officials, on the other hand, there is no significant evidence of a U–shaped effect. The
bottom of Table 6 shows that the effect of vote share on subsequent salary choices is confined to returning
incumbents, as there is no significant effect for winning challengers.
Although the small sample size for Model 8 only allows computation of unconditional marginal effects,
the results are fairly striking. They show that if we look only at completely inexperienced subjects, we see
strong relationships between the official’s salary choice and both her previous promise and her share of the
subsequent vote, with either an decrease in the promised salary or an increase in the vote share associated with
a roughly one–for–one decrease in the actual salary choice. This last result adds perspective to Corazzini et
al.’s (2013) recent finding, noted in our introduction, of very informative campaign promises in an experiment
involving a one–shot game played a single time. In our most analogous sub–sample (the second round of the
first supergame) using a regression with a similar set of variables to Corazzini et al.’s, we find a similar result
to theirs. However, contrasting our results from this sub–sample with those from our entire data–set, we see
that while inexperienced officials are indeed fairly truthful in their campaign promises, it doesn’t take much
experience before only newly–elected officials keep their promises, and even for them, only certain promises
are kept. Thus, while Corazzini et al.’s results taken literally would seem to imply broadly positive conclusions
about campaign promises, we suggest that generalisations from these results to real political decision making
should be made very cautiously.
3.5
Summary of results
Here, we list our main results, each with a brief description of the support for it, and if applicable, the hypothesis
to which is corresponds. Our first two results relate to the effect of the discount factor.
19
Table 6: Salary choices in the COMM–0.8 cell – marginal effects and std. errors in parentheses
Variable
Condition
[7]
[8]
(Supergames/rounds with
(1st supergame, 2nd round,
promise made in prev. round) promise in prev. round)
[unconditional]
+1.049∗∗∗
(0.371)
∗∗∗
new official, promised s/M = 0.2
−0.952
(0.250)
...promised s/M = 0.3
–0.172
(0.152)
...promised s/M = 0.4
+0.577∗∗
(0.230)
previous–
...promised s/M = 0.5
+1.396∗∗∗
round
(0.398)
promise re–elected, promised s/M = 0.2
–0.065
(0.274)
...promised s/M = 0.3
+0.090
(0.270)
...promised s/M = 0.4
+0.247
(0.448)
...promised s/M = 0.5
+0.410
(0.690)
[unconditional]
−0.918∗∗∗
previous–
(0.314)
round
new official
+0.090
vote
(0.123)
share
re–elected
−0.229∗∗
(0.110)
N
659
21
|ln(L)|
265.44
2.517
* (**,***): Marginal effect significantly different from zero at the 10% (5%, 1%) level.
Result 1 Officials’ salaries are higher in the BASE–0.8 cell than in the BASE–0.9 cell.
Result 2 Re–election is less likely in the BASE–0.9 cell than in the BASE–0.8 cell for a wide range of salary
choices. Incumbent vote shares are also lower following many salary choices, but the difference is never
significant.
Evidence for Result 1, which supports Hypothesis 1, comes from the non–parametric tests on aggregate data
reported in the discussion of Figure 1 in Section 3. Evidence for Result 2, which supports Hypothesis 2, comes
visually from Figure 3 in Section 3.2, and from the regression results presented in Table 4 and surrounding
discussion, as well as Figure 8 in the online appendix.
The next two results relate to the effect of allowing campaign promises, in comparison to when campaign
promises are not possible.
Result 3 Officials’ salaries are higher in the BASE–0.8 cell than in the COMM–0.8 cell.
20
Result 4 Voters are less responsive to officials’ salaries in the COMM–0.8 cell than in the BASE–0.8 cell:
following low salary choices, vote shares and re–election probabilities are lower (though the difference in vote
shares is not significant), and following high salary choices, both are significantly higher.
The evidence for these results (which support Hypothesis 3 and Hypothesis 4 respectively) parallels that for
Results 1 and 2 above. Result 3 is based on the non–parametric tests connected with Figure 1, while Result 4
is based on Figure 3, Table 4 and surrounding discussion, and Figure 8 in the online appendix.
The next three results relate to what information campaign promises provide to voters, and how voters
respond to them.
Result 5 Previous campaign promises are used for retrospective voting. For a given salary choice, vote shares
and re–election probabilities are lower if the previous campaign promise was “broken” than if it was “kept”.
This result is consistent with Hypothesis 5, a key component of the retrospective–prospective voting strategy
we consider. Support is found in Figure 5 and in the regression results reported in Table 5.
Result 6 In the COMM–0.8 cell, the implication of the campaign promise for the official’s subsequent salary
choice depends on its level. Low promised salaries are uninformative, and largely under–state the actual
salary. High promised salaries are rare, but tend to be roughly truthful. These relationships between promised
and actual salaries are stronger for successful challengers than re–elected incumbents, and are strongest at the
beginning of the experiment.
Result 6 weakly supports Hypothesis 6, and is based on the regression results reported in Table 6, as well as
visual information presented in Figure 6.
Result 7 Voters in the COMM–0.8 cell vote prospectively. As promised salaries increase, the candidate’s vote
share and election probability decrease. For incumbents, choosing not to make a promise decreases vote share
and re–election probability.
Despite the limited information value of campaign promises (Result 6), Result 7 shows that voters take them seriously as indications of how officials will subsequently behave. This is the other component of the retrospective–
prospective voting strategy, and is consistent with Hypothesis 7. Support for this result is found in Figure 4 and
in the regression results reported in Table 5.
Our final two results do not correspond directly to any of our hypotheses, but represent strong regularities
we observed in the data.
Result 8 A substantial fraction of officials’ salary choices in all three cells are too low to be consistent with
any equilibrium (under the standard assumption of own–expected–payoff maximisation).
Support for this result is seen in Figure 2 and Table 3, both of which show a large number of salary choices
between the equal–split amount and the benevolent–equilibrium amount. As noted earlier (and elaborated in
the online appendix), either risk aversion or inequity aversion is a potential explanation for this result, since
both imply lower values of smin compared to the baseline (risk–neutral self–regarding) case.
Result 9 There is a negative relationship in all three cells between incumbents’ salary choices and their electoral outcomes.
Support for this result comes from nearly every part of the voting data, including the regressions in Tables 4
and 5, as well as in Figures 3, 4 and 5.
21
4
Discussion
We study retrospective and prospective voting with an experiment. We consider a moral–hazard framework
where theory suggests only retrospective voting should apply, but we depart from the previous literature by introducing campaign promises. We argue that such promises can be used by candidates and voters to coordinate
on the voter–optimal equilibrium, and allow for prospective voting (candidates who make better promises get
votes) as well as additional forms of retrospective voting (incumbents who break their promises lose votes).
In the experiment, we observe that higher official salaries tend to receive fewer votes and that higher discount factors are associated with lower salaries, both indicating the presence of retrospective voting. Campaign
promises are observed to matter in multiple ways. At an aggregate level, officials’ salaries are lower when
campaign promises are possible. At a more disaggregated level, voters reward candidates who promise low
salaries and punish them if they break their campaign promises. We even find evidence that officials react to
this pattern of voter behaviour, with some campaign promises being informative about the election winner’s
subsequent salary choice, though this informativeness is fragile.27
Our results fit nicely with others recently seen in the literature. Both Landa (2010) and Woon (2012) emphasise how important it is for voters to hold misbehaving officials accountable even in environments where the
setting is stacked in favour of prospective voting. We reach a complementary conclusion: while retrospective
voting is indeed an important feature of actual voting behaviour, we identify a role for prospective voting even
when the environment dictates that retrospective voting should predominate. Corazzini et al. (2013) show that
campaign promises, despite being cheap–talk, are taken seriously by voters. Our results are even stronger in
this regard: voters continue to take account of campaign promises, even when retrospective voting is possible
and the official’s record in office is known, and despite the tenuous connection between these records and officials’ previous campaign promises.28 Indeed our results suggest not only that retrospective and prospective
voting are compatible phenomena, but also that retrospective voting gives credibility to campaign promises and,
consequently, to prospective voting. We conjecture that even in settings where candidates differ intrinsically,
pre–electoral communication from candidates to voters might provide the necessary amount of coordination
to select candidates in the manner described by Ashworth, Bueno de Mesquita and Friedenberg (2013), thus
finally providing a rationale for the co–existence of prospective and retrospective voting in the most general
framework. Future experimental work should focus on this issue.
More generally, aside from contributing to the retrospective versus prospective voting debate, our results
suggest that voters take promises more seriously than the literature, particularly the rational choice literature,
suggests. This is another area that should be explored further in the future.
References
27
As mentioned in Section 2.2, these last two results have an alternative explanation: that prospective voting is being used not
only to aid coordination, but also to select officials based on perceptions of intrinsic characteristics such as preferences for equitable
income distributions or for honesty. Some of the results presented in this paper (e.g., systematic responsiveness of salary choices to
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28
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Section 3.4 suggests that this difference is largely attributable to different procedures between the two experiments – and in particular
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25
A
Online appendix
A.1
Robustness of theoretical predictions
Here, we show that compared to self–regarding expected–payoff maximisation, either risk aversion or inequity
aversion will imply a reduced smin , meaning that the point predictions of the model depend on what assumptions
are made about preferences. More importantly, we confirm that even in these cases, and indeed more generally,
smin is decreasing in δ, so that the comparative statics – and in particular our Hypotheses 1 and 2 – are robust
to many specific assumptions about preferences.
A.1.1 The general model
We begin by generalising our analysis for a utility function u that need only be continuous and strictly increasing, rather than affine as assumed in Section 2. In a stationary equilibrium with compliance, the official receives
P
t−1 u(s) = 1 u(s). Citizens receive a
a stage–game payoff of s in every round, for a lifetime utility of ∞
t=1 δ
1−δ
1
u MN−s , so that compliance obtains
stage–game payoff of u MN−s in every round, for a lifetime utility of 1−δ
whenever
1
M −s
δ
u (s) ≥ u (M ) +
u
;
1−δ
1−δ
N
or equivalently
M −s
u (s) − (1 − δ) u(M ) + δu
≥ 0.
N
(1)
Since u is strictly increasing, the left hand side of (1) is increasing in s. It is also strictly positive for s = M and
strictly negative for s = 0. By continuity, there is a value smin such that (1) holds with equality for s = smin
and at least weak inequality for s > smin .
Finally, implicit differentiation yields
u
M −smin
N
∂smin
=
∂δ
smin ·
∂u
∂s
+
− u(M )
δ M −smin ∂u
N
N
∂s
< 0.
Thus, smin is decreasing in the discount factor δ so that Hypotheses 1 and 2 continue to hold regardless of
attitudes towards risk or inequality.
A.1.2 Risk aversion
We first relax the assumption of risk neutrality (while keeping the assumption of self–regard), and show that
with risk aversion smin is lower than with risk neutrality. Define sRN
min to be the value of smin under risk
neutrality:
Nδ
RN
smin = 1 −
M.
N +δ
Suppose u is strictly concave. Then Jensen’s inequality implies
u
sRN
min
M − sRN
M − sRN
min
min
= u (1 − δ)M + δ
> (1 − δ)u(M ) + δu
,
N
N
RA
which implies sRN
min > smin , where the latter is defined by
u
sRA
min
= (1 − δ)u(M ) + δu
M − sRA
min
N
.
As a numerical example, if δ = 0.9, N = 6, M = 34 and u(x) =
√
x, then
sRN
min ≈ 0.217
sRA
min ≈ 0.186.
Lastly, we prove that citizens strictly prefer a benevolent equilibrium to a kleptocratic one under risk averK
sion. Let uB
c be the expected utility for a risk averse citizen in a benevolent equilibrium whereas uc is the
corresponding expected utility in a kleptocratic equilibrium. Note first that
M − sRN
N
N
min
=
·0+ 1−
· M.
N
N +δ
N +δ
Then, strict concavity of u and Jensen’s inequality imply
M − sRN
N
N
min
>
u(0) + 1 −
u(M ).
u
N
N +δ
N +δ
But
uB
c =
uK
c =
1
u
1−δ
M − sRA
min
N
and
N
δ
u(0) +
u(M ),
(1 − δ) (N + δ)
(1 − δ) (N + δ)
RN
and since we know already that sRA
min < smin then
uB
c
1
>
u
1−δ
M − sRN
min
N
> uK
c
follows immediately.29
A.1.3 Inequity aversion
Suppose individuals are risk–neutral, but dislike inequity (both advantageous and disadvantageous) as in Fehr
and Schmidt’s (1999) model. In general, an allocation x = (x1 , x2 , ..., xN +1) in a given period will yield
per–period utility
ui (x) = xi − α
1 X
1 X
M ax{xj − xi , 0} − β
M ax{xi − xj , 0}
N
N
j6=i
j6=i
for Player i, with 0 ≤ β ≤ α and β ≤ 1. Then, for a given salary choice s with s ≥ M/(N + 1) (the official
takes more than a proportional share of the endowment), the official’s utility and a representative citizen’s utility
are given by
β
M −s
N − β − Nβ
Mβ
u(s) = s −
·N s−
=
s+
;
N
N
N
N
M −s
M −s
α
M −s
N + α + Nα
M (N + α)
u
=
−
· s−
=−
s+
.
2
N
N
N
N
N
N2
Assume β < NN+1 (otherwise, utility will not be increasing beyond an equal split of the endowment). Then, in
a stationary equilibrium with compliance with salary choice s ≥ M/(N + 1), we have
N − β − Nβ
Mβ
u(s) =
s+
N
N
29
This also shows that under risk neutrality a benevolent and a kleptocratic equilibrium are payoff–equivalent for citizens.
for the official, while the utility of the citizen is
M −s
N + α + Nα
M (N + α)
=−
.
u
s+
N
N2
N2
In particular, u(M ) = M (1 − β) for the official and u(0) = − αM
N for the citizen. Thus,
α + N − βN
sIA
=
1
−
δN
M.
min
δ(α + N − αN ) + N (β + N − βN )
RN
When α = β = 0 (standard risk neutral self–regarding preferences), sIA
min collapses to smin .
It is easy to see that when 0 ≤ β ≤ α and β ≤ NN+1 ,
IA
sRN
min − smin =
N 2 δ(1 + δ) (α − β)
≥ 0.
(N + δ) [δ(α + N − αN ) + N (β + N − βN )]
Also, sIA
min will be decreasing in δ:
∂sIA
N 2 (N + α − N β)(N + β − N β)
min
=−
< 0.
∂δ
[(δ(α + N − αN ) + N (β + N − βN )]2
Finally, to see how sIA
min changes as inequity aversion changes, suppose α = kβ with k > 1, so that as
we change β, players increase in aversion to both advantageous and disadvantageous inequity proportionally.
Then, it is straightforward but tedious to show that
∂sIA
δ(k − 1)(1 + δ)N 3
min
=−
M < 0.
∂β
[δ(α + N − αN ) + N (β + N − βN )]2
A.2
Additional figures
Figure 7 reports salary choice frequencies analogously to Figure 2, but disaggregated not only by cell (as
Figure 2 was) but also by group size. As noted in Section 2.1, the benevolent–equilibrium salary (as a proportion
of the endowment) decreases as the group size increases. Some evidence for this in the data is seen in the mode
in the interval (18,27] when the group size is 5, versus (9,18] for the other group sizes. Such salary choices are
inconsistent with equilibrium under expected–payoff maximisation, but can be equilibrium choices under risk–
or inequity–aversion.
Figure 8 illustrates the predicted incumbent vote share and re–election probability for various combinations
of treatment and official salary choice, based on the regression results reported in Table 4. The difference in
incumbent vote share between the BASE–0.8 and BASE–0.9 curves is never significant at the 5% level. Re–
election probability is significantly lower in BASE–0.9 than BASE–0.8 at the 5% level for salaries between
20 and 80 percent of the endowment. The effect of the COMM–0.8 indicator on vote share is negative at low
salaries but never significantly so, while there is a significant positive effect at the 5% level for salaries of
at least 30 percent of the endowment. Re–election probability is significantly lower (at the 5% level) in the
COMM–0.8 treatment than the BASE–0.8 treatment for low salaries (20 percent of the endowment or less),
and significantly higher for salaries at least 30 percent of the endowment.
Figure 7: Salary choice frequencies for each cell and group size
BASE–0.8
BASE–0.9
5 voters
c 6 voters
s 7 voters
8 voters
* 9 voters
p
p` ppp ppp pppp ppp ppp pppp ppp ppp ppp pp
0.6 pp ppp ppp pppp*ppppppppp ppp ppppp
pp ppp pp ppp
p p
pp pppp pp pppp
Frequency
ppp pdpppp ppp pppp
p p pp pp p pp
0.4 pp ppp ppp pppppppp pppppppppppp ppppp pppppppppppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pp
pp pp ppppppppp ppp
*ppp
p p t pppppp pp
ppppppp ppppppp ppppppppppp ppppp
pp p ppt
ppp p
pp pp pp pp ppppp pp pppppppppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppppppppp ppp pp
p`
0.2 pp ppp ppppppp pppppp ppppp ppppppppppppppppppp
dp p
pp p p p pptppppppp ppp
ppppp ppppp
ppppppppp ppp ppppp pppppppppppppppp ppp`ppp
pppppp ppppppppd
p pp p p
p ptppp ppp pp
pppp pp ppp pppppppppdpppppppppppppptppppp
d pppppppp ppppp ppppppp ppdpppppp
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0 *
*
* * * * * *
tp
pppp ppp ppp pppp
ppp ppp pppp`pp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp
*ppppppp pp pppp
p pp p
pp pppp pp ppp
pppp pdpppppppppp ppp ppppp
p pppppppppppp ppp pppppppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp
pppp ppp pppppp pppppp
p
p
pp pp pppppppp pppp
pp ppp pppppppppp ppp
p p p ppp ppdp ppp
ppppp ppp pppp pppp ppppp
*ppp ppp
p
p pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp
pppp pppp pppp ppppp ppppppppp pppp
pp pp pp ppp ppppp pppp
ppppppppptd`
pp
p p p
pppp pp pppp ppp `pppp
pppppppppp
ppppp `pppp pptpppppppppp ppppp ppppp
pp pppppppp p
p p ppppp * ppppppp*ppppdpppppppppppppppppptdppppp pppppppppt`ppppppppppppdppp p p ppppppt`pppppppppppptppppppppppppppppppptdppp
ptpppp *`ppppp pp pp*ppdpppppp ppt` p p ppppppdppppppppppp*ppd`pp p`
d`ppp ppp
*t
COMM–0.8
pp pppp ppp pppp ppp pppppp`ppppp ppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp p
pp
pppppp pp ppp
ppp ppppp ppp ppppp
p p
pp*pppp ppp ppp ppppp
pp pppp pppppppppppppptpppppppppppppp ppppp
p ppppppppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp pppp p
p
dpp p
ppppppppppppppppppppppp ppppp
pp pppppp pppppppppppppdp ppp
p pp p p
pppppp pp ppppppppppptp ppppp ppppp
p p ppppp pppp pppp ppp ppp pppp ppp ppp pppp ppp ppp ppp pppp ppp ppp pppp ppp ppp*ppppp p
pp pppp pppppppppp ppp ppppp pppp
ppp p ppp*ppppppp ppp ppp
pt
pppppppp ppp ppppp pppppppppppppppppppp
pppppppppd`
p
p
p
p p p p`p ppppp
pp pp
ppppp pp pp`p ppppppp pp pppppppppppd
tpp ppp pppppp ppppptppppp ppd
pp pp
ppppppppppppppppppppppp*pppppppt
pdppppppppppppppppppppp`pppppppppppppppppppppppppppppppppppppppp`ppppppppppppptpppppppppppptd`ppppppppppp
pppppp ppp p
d`p
* ` *pd
ppp *pt`pppp p p p*pptdp pppppppp*ppd`pppppppppppppppp
*t
* *
*
*
0 9 18 27 36 45 54 63 72 81 90 100 0 9 18 27 36 45 54 63 72 81 90 100 0 9 18 27 36 45 54 63 72 81 90 100
Salary (% of endowment)
Figure 8: Point estimates for incumbent vote share and re–election probability based on Table 4 models
Incumbent vote share (from [1])
Re–election probability (from [2])
cpppppppppc
BASE–0.8 1.0 pppppppppppppppppppcpp
ppppppp ppp
c BASE–0.9
pppppp
p
s
p
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ppppppspp pppcpppp
s COMM–0.8
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0.5
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p
p
p
p
pppppcppppppppcppppppppcpppppppppcpppppppppcs
c
c
c
c
c
c
0.0
0.0
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
Official’s salary (fraction of endowment)
1.0
A.3
Instructions from the experiment
Below is the text of the instructions from the COMM-0.8 cell of the experiment. The passages in square brackets
were removed, and the “Sequence of events…” section re-numbered, for the BASE-0.8 cell; from there, the only
change for the BASE-0.9 cell is the replacement of “20%” and “80%” with “10%” and “90%” in the “Continuing
or ending…” section.
Instructions
You are about to participate in a study of decision making. Please read these instructions carefully, as the money
you earn may depend on how well you understand them. If you have a question at any time, please feel free to ask
the experimenter. We ask that you not talk with the other participants – or anyone else – during the experiment.
In this experiment, your decisions will take place within a series of fictional “economies”. Each economy lasts for
a number of periods, which will be called “years”. An economy contains the same population of 5-9 participants
for all years of its existence. In each year, you can have one of two roles: citizen and official. There is always
exactly one official in each economy; the other group members are citizens. In the economy’s first year, the
official is chosen randomly by the computer; in every later year, the official is chosen by an election.
At the beginning of a year, your economy receives a sum of money, to be allocated amongst its population. The
amount of money received depends only on the economy’s population, and is the same in each year. This
allocation is made by the official, who chooses how much to take as his/her salary; the remainder (if any) is
divided evenly amongst the citizens. The official’s salary can be any whole number of cents (i.e., multiple of
$0.01), between zero and the total amount inclusive. After this decision is made, everyone in the economy is
informed of the salary the official chose, along with their own income.
Elections: After the elected official’s salary choice is announced, there is an election. There are two candidates.
One of the citizens is randomly chosen by the computer to be nominated as the challenger, and the official is the
incumbent. Each person in the economy (all citizens and the official) casts a vote for one of the two candidates.
If the challenger receives more votes than the incumbent, then the challenger wins the election. Otherwise, the
incumbent wins the election.
[Campaign announcements: Before the election, both incumbent and challenger have the opportunity to
announce – to everyone in their economy – the salary they would choose next year if they win the election. An
announcement can be any whole number of cents between zero and the amount the economy gets, inclusive. A
candidate can also choose to make no announcement. After both candidates have made their choices, the
announcements are seen by everyone in the economy before they vote. The announcements are non-binding –
they do not restrict the election winner’s future salary choices.]
Continuing or ending the economy: The number of years an economy exists is determined randomly. At the end
of each year, there is a 20% chance that the economy ends, and an 80% chance that it continues for at least another
year. If the economy ends, then a new one begins, with a new – randomly chosen – set of participants. If the
economy continues to the next year, the election winner becomes the official, and the loser becomes a regular
citizen.
Sequence of events: The sequence of events in a year is as follows.
(1) Your computer screen displays the population of your economy, and the amount of money it received. The
official in your economy chooses his/her salary.
(2) Your computer screen displays the salary the official chose, and your income for the year.
(3) One of the citizens in your economy is designated as the challenger. [The incumbent and challenger each
choose their campaign announcements, or to not make an announcement.]
(4) [Your computer screen displays both candidates’ announcements.] Everyone votes for either the incumbent or
the challenger.
(5) The computer screen displays the number of votes for each candidate, and the election winner.
(6) The year ends. The computer determines whether the economy ends or continues.
Payments: Your payment depends on the results of the experiment. At the end of each economy, one of the
years is chosen randomly by the computer, and you will be paid your income from that year. So, your total
earnings for the experiment will be the sum of your incomes in these randomly chosen years, rounded to the
nearest $0.05. Payments are made privately and in cash at the end of the session.
A.4
Sample screen-shots from the experiment
Below are sample screen-shots, typical of those that would have been seen in the COMM-0.8 cell of the
experiment. Screen-shots from other cells are available from the corresponding author upon request.
Official’s salary choice:
Announcement of salary choice to citizens:
Challenger campaign promise decision:
Election screen:
Election result:
End of round, continue/end announcement: