Some Simple Tests of Voting and Agenda Setting
Sean Corcoran
New York University
Thomas Romer
Princeton University
Howard Rosenthal
New York University
Abstract*
We analyze a set of election data that permit simple tests of rational voting and agendasetting. The rational voting test is an analysis of whether aggregate election results are consistent
with single-peaked preferences. The prediction tested is that there is more opposition to the
second of two budget proposals that are voted on simultaneously. Unlike the standard binary
choice setting, not all voters have weakly undominated voting strategies. The game between the
voters can nonetheless be solved simply by the iterative application of weak dominance. The
agenda-setting prediction tested is that agenda setters should make one proposal rather than two
when making a single proposal is an option. The work also discloses a regularity with regard to
voter participation. There is typically less participation on the second proposal. The data for the
tests come from Oregon school financial elections in the years 1980 through 1983.
* We thank Alexander Ruder for very extensive and effective research assistance. We also thank
seminar participants at Columbia University for comments.
1
Introduction
We analyze a set of election data that permit simple tests of rational voting and agendasetting. For many years, school district operating budget referenda were an instance of
democracy in about half of the states. Oregon, which had such referenda for many years, until
the 1990s, held such elections and served as the quintessential case that motivated the RomerRosenthal (1978, 1979, 1982a, 1982b) model of agenda control by a budget-maximizing
bureaucrat, a.k.a. the school board.
For a brief time from 1980 to 1983, Oregon school elections had an institutional feature
that generated a useful natural experiment. 1 In some cases voters were asked to vote
simultaneously on two expenditure amounts that together comprised the locally funded portion
of the school budget. We use data from these referenda to test whether aggregate election results
are consistent with rational voter behavior under the assumption of single-peaked preferences.
Much research in political science explores the situation where voters make a simple binary
choice. Rationality in this instance is just voting for the preferred outcome. The “game” between
voters is uninteresting. Often, however, as in the literature on split-ticket voting, voters are asked
to make two or more choices. Testing rationality in such instances becomes complicated because
of both institutional complexities and data limitations as in Mebane (2000). In contrast, we
develop a prediction that has a straightforward, direct test.
The 1980-83 Oregon data also allow for a new test for agenda-setting behavior. In the
first two years of this period, school boards were required to split budget requests above a fixed
value into two expenditure proposals. In the latter two years, boards could elect to propose a
single expenditure amount. We assume the agenda setter is a budget maximizer (Niskanen, 1971;
Romer and Rosenthal, 1978, 1979). We show that a budget-maximizing agenda setter should
2
always make a single proposal. We test this prediction by examining whether referenda were
shifted to single proposals in the later period.
The election data also disclose an interesting regularity in the number of people who cast
votes on the two expenditure levels. We simply present the regularity. We briefly discuss
interpretations in light of the voter information models developed by Feddersen and Pesendorfer
(1997, 1999) and the non-voting from indifference model of Hinich and Ordeshook (1969).
Theory
We consider the following expenditure referendum. Voters are presented with a choice
between a reversion level of spending Q and a higher level A. At the option of the agenda setter,
there may also be a separate additional amount B to be voted on at the same time. Suppose both
A and B proposals are present. If both A and B receive majorities, actual expenditure becomes Z
ŁA+B. If only A receives a majority, the actual expenditure is just A. If neither receives a
majority or if only B receives a majority, the expenditure is Q. Thus, the outcome set is {Q,A,Z}.
Voter preferences are assumed to be single-peaked. We also assume for now that all voters vote
on both the A and B ballot (i.e., no abstention). Finally, the reversion amount Q in future years is
independent of current expenditure decisions. (This was the case in Oregon during the period of
our data, though the rule changed in later years.) Thus, we can limit our consideration to a oneshot game. 2
Rational voting
The pure strategy set of the voters can be described as {For A, For B},{For A, Against
B}, {Against A, For B}, {Against A, Against B}.
With single-peaked preferences, there are only four voter preference types (ignoring the
knife-edge cases of indifference). Denoting the strict preference relation by , these are
3
ZAQ, AZQ, AQZ, and QAZ. Any strategy is a best response if a voter is not
pivotal. We can study whether these types have weakly undominated voting strategies by
exhaustively considering their best responses in situations when they are pivotal. A voter can be
pivotal in one of three ways. First, his vote is decisive in both the A and B elections. Second, the
vote is decisive only in the A election. Third, the voter pivots only in the B election. The analysis
is summarized in Figure 1.
The situation for the low demand type, QAZ, is shown in the top table in the figure.
When an agent of this type is pivotal in both elections, a best response must include voting
against A since a vote against A leads to the most preferred outcome of Q. When the agent is
pivotal only in the B election, a best response must include voting against B, to obtain Q if A is
losing and A if A is winning. Voting against both A and B is a best response if the agent is
pivotal only in the A election. Consequently, voting against both A and B is uniquely a weakly
dominant strategy.
The situation for the high demand type, ZAQ, shown in the second table in the figure,
is simpler. When an agent of this type is pivotal in both elections, voting for A and for B is a
unique best response. It can be readily checked that voting for A and B is a best response when
the agent is pivotal in only one election. Hence, agents of this type have a weakly dominant
strategy of voting “Yes” in both elections.
The intermediate type AZQ, shown in the third table in Figure 1, has a unique best
response of voting for A and against B when the agent is pivotal in both elections. It can be
readily checked that this strategy is also a best response when the agent is pivotal in only one
election. Consequently, voting for A and against B is a weakly dominant strategy for this type.
4
Finally, the type AQZ does not have a weakly dominant strategy. This intermediate
type must also vote for A and against B when pivotal in both elections. This strategy is also a
best response when an agent of this type is pivotal in only the B election. But it is not a best
response when the agent is pivotal in only the A election. If, as shown in the bottom table of
Figure 1, B wins the B election, the agent must vote against A to obtain Q rather than the least
preferred outcome, Z.
The agent “knows” however that if the other three types use their weakly dominant
strategies, A will receive at least as many votes from these types as does B. Moreover, the agent
also “knows” that, for other AQZ agents, voting for B is weakly dominated since a vote for B
can only pivot to the least preferred outcome, Z. Thus, the type will never be in a position of
being a pivotal voter for A but not for B. The only instance in which B wins is one in which the
high demand types are a majority, and if the high demand types are pivotal for the B election
they will also be pivotal for A. By iteration of weak dominance, therefore, voting for A and
against B is a best response for the AQZ type when the type is pivotal.
In summary, ZAQ types are predicted to vote “Yes” on both the A and B votes,
QAZ types are predicted to vote “No” on both. The two intermediate types are predicted to
vote “Yes” on A and “No” on B.
Proposition 1. If there is at least one voter of either type A
QZ or AZQ, then the “No”
vote will be greater in the B election than in the A election. If there is no such voter, the “No”
vote in the B election will equal that in the A election.
Note that in standard one-election situations with two alternatives, weak dominance is
used to argue that all voters should vote sincerely. From the oodles of Nash equilibria in a voting
5
“game”, weak dominance selects the natural one based on sincere voting. In the two-election
case we model here, there is one type, AQZ that does not have a weakly dominant strategy.
We can, however, use iterated weak dominance to select a unique Nash equilibrium to the voting
game. 3 Note further that the strategies used by the voters do not depend on their knowledge of
the number of voters of each type.
Proposition 1 does depend on the assumption of single-peaked preference. In Figure 2 we
show the situation for a preference type that does not have single-peaked preferences. This
corresponds to individuals who prefer a high level of school expenditures but would rather not
have public education if the schools are mediocre. (See Stiglitz, 1974.) When an agent of this
type is pivotal in both elections, the agent must vote both for A and for B. If the agent is pivotal
in only the A election and B is losing, the agent’s best response is to vote against A. So there is
no weakly dominant best response. Moreover, the situation cannot be resolved by applying
further iteration. When this agent votes against A, voting for B remains a best response, so A
could get fewer votes than B,
Agenda setting
Suppose that the choices of the A and B amounts are made by a budget-maximizing
agenda setter. The agenda-setter is constrained, by law, as to the maximum amount of
expenditure that can be set in the A vote. Denote this as Amax. Anything greater requires a B vote.
We assume further that if a majority of the voters would not approve any expenditure greater
than Amax, the setter will make a single A proposal. If the setter makes an A proposal and a B
proposal, budget maximization implies the A proposal will be Amax.
Now suppose that a majority of the voters would approve expenditure at least equal to
Amax. Relax the requirement that the setter must have a separate B vote on amounts greater than
6
Amax, and assume the agenda-setter is permitted to make a single proposal C to the voters.
Assume further that there is at least one intermediate type voter who prefers Z (=Amax+B) to Q
but prefers Amax to Z.
Proposition 2. When given the option, the setter will make a single proposal C rather than
make separate proposals A and Z.
Corollary. C > (Amax+B) if a majority of voters support B.
The proof of Proposition 2 is simple. We outline it for the case of symmetric preferences.
First consider the vote for a single proposal C versus the reversion Q. With symmetric
preferences, those with ideal points above the cutpoint (C+Q)/2 will vote for C and those below
this cutpoint will vote for Q. Similarly, in the case of two separate elections, the cutpoint in a
vote over the proposal Amax versus the reversion Q will be (Amax+Q)/2, and the cutpoint in a vote
over the proposal Z versus Amax will be (Z+Amax)/2.
In a jurisdiction where the majority of voters would support the higher proposal Z, voters
would also support a single proposal C*=Z. (The cutpoint (Z+Q)/2 < (Z+Amax)/2 since Q <
Amax). Indeed, the proposal C* will receive more votes than B receives in a B election.
Consequently, for some C > C*, the setter can obtain a larger budget than C*.
In a nutshell, in the ultimatum game between the setter and the voters, the setter’s threat
is greater with one election than with two.
7
Empirical Context
For many years, Oregon’s school finance system was characterized by school district
“financial elections”. These elections were referenda in which school boards would propose a
local budget that required approval by a majority of the voters. Through 1979, the proposals
were simple all-or-none proposals to add additional expenditure to a local reversion expenditure
(Q) that was fixed exogenously. The reversion expenditure varied by district, and could be zero
or a strictly positive amount. The reversion could be sufficiently large that a board might not
hold a referendum. In the event a proposal failed to achieve majority support, the board had
opportunities to hold an additional election. If an additional election were held, the board could
alter the proposed amount of expenditure. While in most districts the first election proposal was
approved, in some districts multiple proposals (very rarely as many as six elections) were
required.
For the 1980-81 through 1983-84 school years, the traditional system was altered by
property tax rebates that depended on characteristics of the taxpayer, characteristics of the
district, and the amount of proposed expenditure (Hartman and Hwang, 1985). 4 For proposals at
or below an exogenously fixed amount, which we denote Amax, a rebate was provided to some
taxpayers in the school district. For expenditures above Amax, additional (B) expenditures
received no rebate. Therefore, some taxpayers in the district were subject to two tax prices—a
lower one for A expenditures and a higher one for B expenditures. The shift in tax prices justifies
our theoretical assumption that expenditure no greater than Amax will be made through a single A
election. 5 The property tax rebate system ended after the1983-84 school year.
For 1980-81 and 1981-82, districts had to hold separate votes for A and B. A district
could hold no election and operate at the reversion level, hold only an A election, or hold A and
8
B elections simultaneously. For 1982-83 and 1983-84, the school board could alternatively hold
a “Combination” election in which there was a single proposal that included both A and B
amounts. The board could, if it so chose, also hold separate A and B elections as in the two
earlier school years. Elections were held in the calendar year of the start of the school year.
Elections were held as early as the last week in March for the school year that would begin in
September.
Summary statistics on elections are provided in Table 1. In the table, we place all school
districts in one of five mutually exclusive categories.
1. School districts that had at least one simultaneous A and B election. Some of these
districts had multiple such elections in a given school year. Others could have later held
an A election only after defeat of both an A and B proposal. They might also have held a
B election only if an A proposal had passed and a B proposal failed. In the last two years,
some districts in the first category could have held combination ballots that failed and
then went to an A, B setup.
2. Districts that held only A elections. These were districts where the entire proposed
operating budget qualified for the property tax rebate.
3. Districts that held only B elections. In these districts, few in number, any increase
beyond Q would not have qualified for the rebate program.
4. Districts that held only combination elections. Combination elections were permitted
only for the last two school years of this period.
5. Districts not holding elections. The board in these districts chose to operate with Q (or
less).
In each of the four years, Oregon had just over 300 school districts.
9
Table 2 provides additional details for districts holding A and B, and/or Combination
elections. The categories in this case are no longer mutually exclusive. The first row, carried over
from Table 1, shows the total number of school districts holding at least one election with both A
and B ballots. The second row shows the number of districts that held at least one Combination
election. (Some of these districts also held simultaneous A and B elections at a later date, so the
numbers in row 2 differ from the numbers in row 4 of Table 1.) The third row shows the total
number of instances where A and B votes were held on the same day. The numbers in this row
exceed those in the first row because of multiple elections held by some school districts. Some
districts held two or three simultaneous A and B elections in the same year. 6
School districts were able to split the B vote into two (typical) or more (rare) votes,
presumably to offer a menu of add-ons, such as kindergarten. These votes are not covered by our
formal model. Therefore in the fourth row of Table 2 we show the number of observations with
an A election and a single B election on the same day. These elections constitute our population
of interest. As a comparison of the third and fourth rows indicates, multiple B elections were
infrequent. Our main results are presented in the remaining rows of the table.
Results
Proposition 1
We focus on differences in the percentage voting “No” on the B and A votes because
there are variations in the number of voters casting A ballots and B ballots. These variations are
relatively small. We report on abstention in a later section. The fifth row in Table 1 shows the
number of observations with an increase in the percentage voting “No” on the B as compared to
the A ballot. The sixth row reports observations with an increase in the subset of observations
with a single B election. No change in the votes against is also consistent with the model. This
10
could arise if there were no voters of preference type AQZ or AZQ. There are one or two
observations of this type in each of the first three years. There are none in the fourth year. The
seventh and eighth rows report the number of cases in which there was no change in the votes
against.
The errors to the prediction of Proposition 1 are shown in rows nine and ten. If we focus
on districts with single B elections, there was only one violation of Proposition 1 in 1980. The
district with a decrease in the “No” vote had a decrease of 1.64 percentage points, quite small in
comparison to the average increase of 9.74 percentage points in that year. There was also a
single, somewhat uncertain, violation in 1981. 7 There were no violations in either 1982 or 1983.
In summary, the evidence in support of Proposition 1 is overwhelming. In a total of 295
observations, there were only two violations, with one of the two being suspect.8 It is delightful
to find a result where reporting a statistical test would be absurd. In those districts where there
was an increase in the percent No, the increase was substantial, as reported in the eleventh row.
The average increase ranged from 6.75 percentage points in the 1981 elections to 9.74 in the
1980 elections
Proposition 2
Proposition 2 predicts that school boards should prefer to conduct Combination ballot
elections rather than separate A and B elections. Thus, when the state permitted Combination
ballots, there should be a substantial shift away from A and B elections to Combination ballots.
The shift is supported by the data. Table 1 shows that the number of school districts holding A
and B votes decreased from 116 in 1981 (and 77 in 1980) to only 23 in 1982, before increasing
back to 35 in 1983. Moreover, of the 23 districts that held A and B votes in 1982, 12 had
previously tried a Combination ballot in the same year; in 1983, 27 of 35 districts tried a
11
Combination ballot first. Districts holding at least one combination ballot numbered 77 in 1982
and 78 in 1983.
Proposition 2 is not supported as strongly as Proposition 1. A few districts continued to
go directly to A and B ballots. Somewhat more reverted to A and B after Combination ballots
failed. Romer and Rosenthal (1979) argue that, were Combination ballots available, budgetmaximizing agenda setters would make a relatively high proposal initially and then cut it after a
failure. Perhaps switching from Combination to A and B represents a concession expected by
voters in the new institutional framework established by the property tax rebate system. 9 In any
event, even though Combination ballots were not adopted uniformly, there was a strong tendency
to substitute Combination ballots for A and B ballots. This tendency was especially strong on the
first annual election in the district. Proposition 2 is consistent with the drop in A and B elections
between the first two years and the second two years.
Abstention when A and B proposals are both on the ballot
As we have noted, voters did not always vote on both the A proposal and the B proposal
when these were both on the ballot. Although the differences in votes cast in the two elections
are small, the differences are systematic.
The differences do not appear to have an explanation in the purely random turnout model
of Romer and Rosenthal (1979). The voters have taken the trouble to vote; they should be no
more likely to “forget” to vote on one of the two proposals than the other or to make a “mistake”
and omit voting. Consequently, differences in turnout should not be systematic. The number
voting on the A amount should exceed those voting on the B amount about half the time, and
vice versa. The differences would also seem unrelated to the strategic turnout models based on
12
the cost of voting (Palfrey and Rosenthal, 1985). The voters, by getting a ballot, have paid the
cost of voting.
What might be relevant to the differences is informational uncertainty about preferences
(Feddersen and Pesendorfer, 1997, 1999). A voter might not be sufficiently informed, say, to
know whether he has preference ZAQ or AZQ. This voter knows he should vote for A,
but is unsure about whether to vote for B. Such a voter might abstain strategically and leave the
decision to informed voters. Alternatively, the voter might be close to indifferent between A and
Z. In such a case, the voter might abstain due to indifference (Hinich and Ordeshook, 1969).
What we have in mind here is not “I’m close to indifferent, so I do not want to pay the cost of
voting”, as in Riker and Ordeshook’s seminal 1968 paper. It is more “I’m close to indifferent,
and I can’t make up my mind, so I’ll just pass on this one”.
A strong empirical relationship with regard to votes cast is shown in Table 3. In all four
years, the number of districts where there are fewer votes on the B proposal than on the A far
exceeds the number of districts where the opposite is true. The last row of the Table presents a
simple binomial test of the null hypothesis that votes in the B election are fewer than those in A
elections with probability 0.5. That is, fewer votes is a “success” and more votes or no change is
a “failure.” The test is run for single B election districts only. For each year, the null is rejected
with p-values lower than 0.001.
Conclusion
We have presented evidence that voters, at least in the aggregate, respond rationally when
presented with a budget proposal and an “add on” second proposal. Under the assumption that
voters have single peaked-preferences over spending, we should systematically find more votes
against the second proposal than against the first. This proposition is verified. Another
13
observation pointed to systematic behavior by budget-maximizing agenda setters. When given
the option of not having two proposals and proposing just a single budget, the setters should opt
for the single proposal. Setters did opt for a single proposal, with relatively few exceptions.
Voters do vary in their participation when voting on two proposals. Second proposals
typically have fewer voters than first proposals, at high levels of statistical significance.
The results in this paper are in the spirit of Romer and Rosenthal (1979), who presented a
theoretical model of budget-maximizing agenda setting and then presented qualitative evidence
that was consistent with the model. Their model also made quantitative predictions about the
amounts of the proposals and about the percentage of voters that should support a proposal.
These predictions were then tested in a series of later papers (Romer and Rosenthal, 1982a,
1982b; Filimon, Romer, and Rosenthal, 1982). The two-proposal scenario will similarly generate
a set of quantitative predictions about budget proposals and voting. These predictions will have
to account for the endogeneity of tax price (see Romer, Rosenthal, and Munley, 1992) induced
by the A and B setup. The various predictions generated by the A and B setup can be pursued in
further research.
14
Table 1. Summary Statistics, Oregon School Referenda 1980-83
Election Law
Election Law
A, B Mandatory Combination O.K.
Districts with:
1980
1981
1982
1983
1. At least one A, B election
77
116
23
35
2. A election only
133
59
80
58
3. B election only
4
2
5
20
4. Combination only
n.a.
n.a.
65
53
5. No election
93
129
134
144
307
306
307
310
Total School Districts
15
Table 2: Oregon school budget elections by type, 1980 - 1983
1980
1981
1982
1983
1. Unique districts holding A & B elections
77
116
23
35
2. Unique districts holding Combination elections
n.a.
n.a.
77
78
3. Observations with A & B votes on same day.
92
163
32
39
4. Observations with A & single B election on same day
84
159
23
39
5. Observations with increase in %No vote
87
161
31
39
6. Observations with increase in %No, A & single B election
81
157
22
39
7. Observations with no change in %No vote
2
1
1
0
8. Observations with no change in %No, A & single B election
2
1
1
0
9. Observations with decrease in % No vote
3
1
0
0
10. Observations with decrease in % No, A & single B election.
1
1
0
0
9.74
6.75
9.54
7.06
11. Average increase in %No vote if increase > 0
Notes to Table 2:
1. Lake Oswego 7J in Clackamas County was the only observation in 1980 that had a single B
election and had a percentage decrease in the percentage No. The decrease was 1.64%.
2. The two observations with no change in the No vote in 1980 were both very small districts. Ash
Valley 125 in Douglas County had a total of 52 voters and passed both ballots by a vote of 43-9.
Pine Creek in Harney County had a total of 17 voters and passed both ballots by a vote of 16-1.
They both would appear to be homogeneous rural communities where the setter model is
inappropriate.
3. Tygh Valley 40 in Wasco County is the only observation in 1981 that had a percentage decrease
in the percentage no. The decrease was 8.81%. This observation may not be a model error. The B
election was reported as an A election in the official document. It may have been that the A
amounts were broken up into a menu of two pieces. In this case, the model does not apply.
4. Carlton 11 in Yamhill County is the only observation in 1981 with no change in the No vote.
Both A and B passed by a margin of 187-157. In this case, the A amount was very small, only
$11,213, while the more important amount, $126,291, was in the B election.
5. The number of simultaneous A, B elections drops in 1982 as a result of the use of Combination
ballots. In fact, of the 23 school districts that held at least one simultaneous A, B election in
1982, 12 had first tried a Combination ballot.
6. The single observation in 1982 with no change in the No vote between the A and B ballots was
Alsea 7J in Benton country. The vote was 148-277 on both ballots. The A ballot was for $519,268
as against only $25,629 on the B ballot.
16
Table 3: Oregon school budget elections by type, 1980 - 1983
1980
1981
1982
1983
1. Unique districts holding A & B votes
77
116
23
35
2. Observations with A & B votes on same day.
92
163
32
39
3. Observations with #voting on B < #voting on A
64
103
24
39
4. Observations with #voting on B = #voting on A
7
8
2
1
5. Observations with #voting on B > #voting on A
21
52
6
8
6. Observations with A & single B election on same day
84
159
23
39
7. Observations with #voting on B < #voting on A
61
103
20
30
8. Observations with #voting on B = #voting on A
7
8
1
1
9. Observations with #voting on B > #voting on A
16
48
3
8
0.00009
0.00016
0.00077
0.00053
Districts with A and single B
p-level, Null: Prob(increase) = 0.5, single B elections
17
Figure 1. Best Responses of the Voter Types (Single-Peaked Preferences)
Q
A
Z (Low demand)
When Pivotal
Pivotal for A
Pivotal for B
Non-pivotal outcome
B wins
B loses
A wins
A loses
Pivotal for both
Best Response for Agent
Against A
Against A
Against B
Against B
Against both A and B
Z
A
Q (High demand)
When Pivotal
Pivotal for A
Pivotal for B
Non-pivotal outcome
B wins
B loses
A wins
A loses
Pivotal for both
Best Response for Agent
For A
For A
For B
For B
For A and B
A
Z
Q (Intermediate)
When Pivotal
Pivotal for A
Pivotal for B
Non-pivotal outcome
B wins
B loses
A wins
A loses
Pivotal for both
Best Response for Agent
For A
For A
Against B
Against B
For A, Against B
A
Q
Z (Intermediate)
When Pivotal
Pivotal for A
Pivotal for B
Pivotal for both
18
Non-pivotal outcome
B wins
B loses
A wins
A loses
Best Response for Agent
Against A
For A
Against B
Against B
For A, Against B
Figure 2. Best Responses of a Voter with Non-Single-Peaked Preference
Z
Q
A
When Pivotal
Pivotal for A
Pivotal for B
Pivotal for both
19
Non-pivotal outcome
B wins
B loses
A wins
A loses
Best Response for Agent
For A
Against A
For B
For B
For A, For B
References
Feddersen, Timothy, and Wolfgang Pesendorfer. 1997. Voting Behavior and Information
Aggregation in Elections with Private Information. Econometrica 65: 1029-1058.
Feddersen, Timothy, and Wolfgang Pesendorfer. 1999. Abstention in Elections with Asymmetric
Information and Diverse Preferences. American Political Science Review 93: 381-398.
Filimon, Radu, Thomas Romer, and Howard Rosenthal. 1982. Asymmetric Information and
Agenda Control: The Bases of Monopoly Power in Public Spending. Journal of Public
Economics 17: 51-70.
Fudenberg, Drew, and Jean Tirole. 1991. Game Theory. Cambridge, Mass.: MIT Press.
Gramlich, Edward, and Daniel Rubinfeld. 1982. Micro Estimates of Public Spending: Demand
Functions and Tests of the Tiebout and Median-voter Hypotheses. Journal of Political
Economy 90: 536-60.
Hartman, William T., and C.S. Hwang. 1985. Effectiveness of Property Tax Relief in Oregon.
Journal of Education Finance 10: 339-359
Hinich, Melvin J., and Peter C. Ordeshook. 1969. Abstention and Equilibrium in the Electoral
Process. Public Choice 7: 81-106.
Mebane, Walter R., Jr. 2000. Coordination, Moderation, and Institutional Balancing in American
Presidential and House Elections. American Political Science Review 94: 37-57
Niskanen, William. 1971. Bureaucracy and Representative Government. Chicago: AldineAtherton.
20
Palfrey, Thomas R., and Howard Rosenthal. 1985. Voter Participation and Strategic Uncertainty.
American Political Science Review 79: 62-78.
Riker, William, and Peter C. Ordeshook. 1968. A Theory of the Calculus of Voting. American
Political Science Review 62: 25–42.
Romer, Thomas, and Howard Rosenthal. 1978. Political Resource Allocation, Controlled
Agendas, and the Status Quo. Public Choice 33: 27-43.
Romer, Thomas, and Howard Rosenthal. 1979. Bureaucrats vs. Voters. Quarterly Journal of
Economics 93:563-87.
Romer, Thomas, and Howard Rosenthal. 1982a. Median Voters or Budget Maximizers:
Evidence from School Expenditure Referenda. Economic Inquiry 20: 556-578.
Romer, Thomas, and Howard Rosenthal. 1982b. An Exploration in the Politics and Economics
of Local Public Services. In Public Production, ed. Dieter Bös, Richard A. Musgrave,
and Jack Wiseman. New York: Springer, 105-126.
Romer, Thomas, Howard Rosenthal, and Vincent Munley. 1992. Economic Incentives and
Political Institutions: Spending and Voting in School Budget Referenda. Journal of
Public Economics 49: 1-33.
Rosenthal, Howard. 1990. The Setter Model. In Advances in the Spatial Theory of Voting, ed.
James Enelow and Melvin Hinich. New York: Cambridge University Press.
Stiglitz, Joseph E. 1974. The Demand for Education in Public and Private School Systems.
Journal of Public Economics 3: 349-395.
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Endnotes
1
All data on elections come from Oregon Department of Education, “1980 Summary of School
District Financial Elections”, Jan. 1981; “1981 Summary of School District Financial Elections”,
Dec. 1981; “1982 Summary of School District Financial Elections”, Mar. 1983; “1983 Summary
of School District Financial Elections”, May 1983. Copies were obtained from the Oregon State
Library. A pdf that contains the documents is available through Google Docs at:
https://docs.google.com/open?id=0B18lDjY36mjqZjY2NWZhNDUtNTIxOS00OWNlLWJlZTgt
N2JkMWRiOWRlYzIy
2
Our formal model is one of complete information. We therefore ignore the strategic
implications of the fact that, in practice, the setter could hold additional elections if a given A or
B proposal failed. Strategic behavior by the setter was explored theoretically in Romer and
Rosenthal (1979). Strategic behavior by the voters, discussed in Rosenthal (1990) is an open
research question.
3
The concept of iterated weak dominance is presented in Fudenberg and Tirole (1991), chapter
11.
4
The Oregon Education Association’s summary states, “The Property Tax Relief Program
limited growth of assessed value of all property in the state to no more than five percent per year
and provided that the state General Fund pay up to 30% of local residential property taxes –
capped at $800 per low-income homeowner and $400 per low-income renter.”
(http://www.oregoned.org/site/pp.asp?c=9dKKKYMDH&b=4955821, accessed Oct. 14, 2011.)
The $800 amount for 1980 was reduced to $425 in 1981, $192 in 1982, $170 in 1983 and 1984,
and $100 in 1985 before the program was ended. No A, B elections took place for the 1984-85
and 1985-86 school years. The description of the dollar amounts is contained in “Appendix B: A
22
Recent History of Oregon Property Taxation,” downloadable at
http://www.oregon.gov/DOR/STATS/303-405-01-toc.shtml, accessed Oct. 15, 2011
5
It is always true that for any expenditure less than or equal to Amax, taxes for a strictly A
expenditure are weakly less for all voters than taxes for a mixture of A and B expenditure of the
same amount. Hence, raising an amount no greater than Amax through an A election is weakly
Pareto superior for both voters and the setter compared to raising the same amount through a
mixture of A and B.
6
There was one case, Prairie City in Grant County, where four A and B elections were held from
May through November 1981. Both A and B ballots failed all four times. The A ballot was for
$31,600. The B ballot was cut from an initial $402,167 on the first try to $68,300 on the last two.
A single A ballot election had failed in 1980. Prairie City was unable to pass a school budget
until September 1982.
7
The violation occurred in Tygh Valley in Wasco County with a decrease of 8.81 percent. The
observation may not have been a violation. The official election document reported that there
were two A elections rather than an A and a B. We have conservatively treated the second
election as a misreported B election. It may have been, though, that the district split the A ballot
into two pieces. If that were the case, Proposition 1 would not apply.
8
Of course, not all the observations are independent, since some school districts appear in more
than one year and others hold more than one A and B elections. Gervais UH1 also proposed two
A ballots in 1982.
9
Prairie City (see note 6) made such a concession. After failing a Combination ballot in May, it
succeeded with A and B ballots on September 21, 1982. The total budget was the same in both
May and September. Romer and Rosenthal (1979) report that budgets not infrequently had zero
23
or very small cuts in later elections. The result is consistent with work by Gramlich and
Rubinfeld (1982) who report that participation changes as the impact of losing the custodial
value of the schools becomes apparent to parents. In this case, the May election took place on a
general primary ballot. The September election was a special school election.
24