PhD Course
Voting and Political Debate
Lecture 6
Francesco Squintani
University of Warwick
email: f.squintani@warwick.ac.uk
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Leaders’ Judgment and Trustworthy Associates
“E la prima coniettura che si fa del cervello d’uno signore,
é vedere li uomini che lui ha d’intorno.”
[Transl.: The first opinion which one forms of a prince, and of his understanding,
is by observing the men he has around him.]
Niccoló Machiavelli, Il Principe, Ch. 22.
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Introduction
• We first ask: What makes a good leader?
• A leader’s valence corresponds to his wisdom, good judgment and competence.
• Valence is usually considered to be an innate characteristic of individual leaders.
• But good judgment also depends on the advice of the leader’s associates.
• Here, associates are trustworthy if they share similar views with the leader.
So, a leader’s judgment depends on the ideological distribution of his associates.
• We provide the first derivation from first principles of leadership and valence.
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• Further, we ask: Who will be elected as leader?
• The leader’s election is decided by the median politician in the group.
The median may delegate leadership, although this is not optimal.
• If politicians become more moderate, they may capture the control of the group, and
turn the group policy closer to their views.
• Finally, we explore leadership and electoral competition.
• A small but ideologically cohesive party may express the best candidate,
and win the election.
• If a candidate moves too close to the median, its party may wind up losing the
election.
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“Non era alcuno che conoscessi messer Antonio da Venafro per ministro di Pandolfo
Petrucci, principe di Siena che non iudicasse Pandolfo essere valentissimo uomo,
avendo quello per suo ministro. E perché sono di tre generazione cervelli, l’uno intende
da sé, l’altro discerne quello che altri intende, el terzo non intende né sé né altri, quel
primo é eccellentissimo, el secondo eccellente, el terzo inutile, conveniva per tanto di
necessitá, che, se Pandolfo non era nel primo grado, che fussi nel secondo: perché, ogni
volta che uno ha iudicio di conoscere el bene o il male che uno fa e dice, ancora che da
sé non abbia invenzione, conosce l’opere triste e le buone del ministro, e quelle esalta e
le altre corregge; et il ministro non puó sperare di ingannarlo, e mantiensi buono.”
Niccoló Machiavelli, Il Principe, Ch. 22.
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Model I
• A group N = {1, ..., n}, n odd, collectively selects a leader j ∈ N.
• Each politician i has ideology bi and payoff:
ui (ŷ, θ) = − (ŷ − θ − bi )2 ,
where θ is an unknown state, uniformly distributed on [0, 1].
• The ideology distribution b1 ≤ b2 ≤ ... ≤ bn is common knowledge.
• Each politician i has some private information on θ:
He observes a signal si
(Here, signals si , for i
∈ {0, 1} such that Pr(si = 1|θ) = θ.
= 1, ..., n, are independent conditional on θ.
We are working to allow signals of ideologically close politicians to be correlated.)
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• Each politician i sends a message m̂ij ∈ {0, 1} to the leader j;
then j makes decision ŷ ∈ R so as to maximize his payoff.
• A communication strategy mi of player i depends on si and on j.
• When talking to j, player i can either act as a “yes-man”
(if mij (si ) does not depend on si ), or as a “trustworthy associate”
(when mij (si ) = si for both si ∈ {0, 1}).
• Denoting a leader j ’s strategy as yj : {0, 1}N → R,
by sequential rationality, j chooses
yj (sj , m̂−j,j ) = bj + E[θ|sj , m̂−j,j ],
• Given a leader j, an equilibrium is a strategy pair (m, y);
we assume that players always play Pareto-dominant equilibria.
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• The optimally selected leader is the player j who induces the equilibria (m, y) with
the largest sum of expected payoffs:
W (m, y; j) = −
∑
E[(yj − θ − bi )2 ],
i∈N
and we denote by W ∗ (j) such maximal payoffs sum.
• Recall that the Condorcet winner is the player j who defeats any other player k in a
direct vote among the two alternatives j and k.
• The elected leader is the Condorcet winner of the election game in which each player
i’s payoff when j is the leader is:
Ui∗ (m, y; j) = −E[(yj − θ − bi )2 ],
where (m, y) is the top Pareto equilibrium when j is the leader.
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Trustworthy Advisers
Lemma 1 When player j is the leader, the profile (m, y) is an equilibrium if and only if,
whenever i is trustworthy to j,
1
|bi − bj | ≤
,
2[dj (m) + 3]
where dj (m) is the number of politicians who are trustworthy to j in m.
• i’s capability to be truthful with j declines with:
– their ideological difference and,
– the size of j ’s group of trustworthy advisers.
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• We introduce the function Nj : R → N. For any b ∈ R,
Nj (b) = max{i ∈ N : |bi − bj | ≤ b} − min{i ∈ N : |bi − bj | ≤ b}.
Nj (b) is the number of politicians whose ideology is within b of j ’s ideology bj .
Proposition 1 For any politician j, the maximal equilibrium number of trustworthy
associates d∗j is the unique d
∈ N which solves:
)
(
1
Nj
= d.
2 (d + 3)
• We let a leader j ’s judgment be d∗j .
It is based on j ’s ideological position bj relative to the other politicians in N.
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Optimal Leaders and Elected Leaders
Proposition 2 The optimal leader j maximizes the expression
∑
W (j) = −
(bi − bj )2 − n
∗
i∈N
1
.
∗
6(dj + 3)
The first term is maximized by moderate leaders j whose ideology bj is close to the
average
∑
i∈N
bi /n.
The second term is maximized by leaders j who can rely on many like-minded
trustworthy associates, so that d∗j is large.
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Proposition 3 The Condorcet winner of the election game is the politician j who
maximizes the expected payoff of the median politician m
∗
Um
(j)
= (n + 1)/2:
1
= −(bm − bj ) −
.
∗
6(dj + 3)
2
The median politician m chooses the leader j (who can be m himself) on the basis of
j ’s ideological proximity with his own views and of j ’s judgment d∗j , determined by the
number of j ’s like-minded trustworthy associates.
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Moderation or Trustworthy Advice?
Consider an ideology distribution b symmetric around the median ideology bm .
We define b single-peaked if bi+1
− bi weakly increases in i, for i = m, ..., n − 1.
Proposition 4 When politicians’ ideologies are single-peaked and symmetric, the
median politician m also has the best judgment. He will always be elected, and should
always be selected, as leader.
• Hence, the only fighting chance at leadership for a non-moderate politician is when
ideologies are distributed with lumps away from the median.
• We now study an example in detail.
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Example 1 There are 5 politicians, with ideologies b1
= −(α + β), b2 = −β, b3 = 0,
b4 = γ, b5 = γ + δ.
1. Start from the case of evenly distributed bias, with bi+1
− bi ≤ 1/10, for all i.
By Proposition 4, the optimal leader is 3, and he is elected by majority.
Suppose that the centre-right politician 4 extremizes his views, so that
b4 − b3 = γ > 1/10.
= β ≤ 1/10 but γ > 1/10; so that the centre-left player 2 can rely on the
trustworthy advice of 1 and 3, whereas 3 can trust 2 but not 4.
Now, α
By Proposition 3, the centre-left politician 2 wins the election if β is sufficiently small.
By extremizing his views, the centre-right player 4 makes the centre-left player 2 win
the election instead of the median player 3.
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2. Alternatively, consider the equidistant bias case with bi+1
− bi = γ > 1/10, for all
i; and suppose that the leftist politicians 1 and 2 moderate their views, so as to
decrease b3 − b2 = β and b2 − b1 = α below 1/10.
By moderating their leftist views, 1 and 2 swing the election in favor of the centre-left
politician 2, against the median politician 3.
3. Finally, we compare the leader’s election with optimal selection.
When δ and γ are large relative to α, there is an interval of β such that the
Condorcet winner is player 2, although the optimal leader is the median player 3.
The median player 3 delegates leadership to 2 although it would be optimal for the
group that he retained leadership for himself!
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Example 1 allows us to draw the following conclusions:
1. When the ideology distribution is not single-peaked and symmetric, a politician other
than the most moderate one can win the election and be the optimal leader.
2. If politicians become more moderate (extremist), they swing the election in favor of a
leader with views closer to (away from) theirs.
3. Relative to the group of politicians, the median player weighs good judgment more
than moderation. He may delegate leadership in the election game to a less
moderate politician, even when this is suboptimal for the group.
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• Our findings overturn the view that only the opinion of the median committee member
matters for decisions in small committees.
• Empirical evidence on Supreme Court justice nomination (Rohde and Shepsle, 2007,
and Krehbiel, 2007) and Supreme Court decision (Clark, 2012) shows that the views
of non-median justices matter.
• In his review, Clark suggests that an explaination of this fact includes relaxing the
complete information assumption of extant models.
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• The leader’s election game can be interpreted as a form of ‘strategic delegation’ by
the median voter.
• In this context, our results overturn the “ally principle”: the supposition that a principal
will always delegate to the available agent who is ideologically closest to her.
• There is various evidence in political science and in management science against the
ally principle.
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• Our results overturn the usual interpretations of valence and leadership.
• Valence is defined as ‘the leader’s characteristics’ that influence approval
independently of the respondent’s ideology.’
• Here, valence (good judgement) is not orthogonal from ideology,
instead, the ideology distribution determines valence.
• Not only the ‘global’ ideology distribution matters (it defines the median politician),
but also the ‘local ideology distribution’ matters, as it determines good judgment.
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Model II
• There are two parties, A and B.
• The leading politicians in the two parties are NA = {1, ..., q} and
NB = {q + 1, ..., n}, with b1 < b2 < ... < bn .
• Each party i selects one candidate in Ni for a general election.
• There is a continuum of voters. The preferences of each voter k, including politicians,
are expressed by:
uk (ŷ, θ) = − (ŷ − θ − bk )2 ,
bk is the ideological bias of voter k relative to the median voter m, where bm = 0.
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• The winner of the general election j implements policy ŷ ∈ R.
• Candidates cannot credibly commit to electoral promises, so that the winner
implements his preferred policy.
• Unlike citizens, each politician i observes a private signal si ∈ {0, 1} such that
Pr(si = 1|θ) = θ, after the election.
• Before choosing ŷ, the winner of the election j gathers the advice of politicians in his
party: each sends a message m̂ij ∈ {0, 1}.
• We select the equilibria in which both parties i choose a candidate who wins againts
the largest set of candidates from the opposite party (a form of weak dominance).
• We focus on parametrizations in which such a candidate is unique for both parties.
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Results
We build on the following benchmark, which deals with the case in which politicians do
not communicate.
Proposition 6 Suppose that the politicians cannot communicate to the elected policy
maker j. Then the winner of the general election is always the politician ideologically
closest to the median voter.
We explore how strategic advice changes the picture, by studying 2 examples in details.
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Example 2 Suppose that there are 6 politicians, with evenly distributed ideologies,
symmetric to the median ideology.
= −2β − β/2, b2 = −β − β/2, b3 = −β/2, b4 = β/2,
b5 = β + β/2 and b6 = 2β + β/2.
Specifically, b1
The leftist politicians belong to party A and the rightwing ones to B.
The median voter has bias zero, and decides the general election.
His utility for electing candidate j is:
U0 (j) =
−b2j
1
−
.
∗
6(dj + 3)
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Unless 2 and 5 have more trustworthy associates than 3 and 4, the latter are selected
as candidates and tie the general election, in equilibrium.
But when 2β
> 1/10, politician 3 can only rely on the truthful advice of 2, if he is
elected.
Further, when β is not too much bigger than 1/20, politician 2 can rely on both 1 and 3,
and his ideology is not too far from the median.
Hence, players 2 and 5 are chosen as candidates and tie the general election.
Conclusion: Even if the ideology configuration b is evenly distributed, the winner(s) of
the general election need not be the player(s) ideologically closest to the median.
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Example 3. Suppose that there are 5 politicians, with ideologies b1
= −α, b2 = −β,
b3 = −γ, b4 = −γ + δ and b5 = −γ + 2δ.
Politicians 1 and 2 are in party A; 3, 4, and 5 are in party B.
Party B is ‘larger’ in two ways:
1. the politician ideologically closer to the median, player 3, is in party B.
2. there are more leading politicians in party B : potentially, a candidate from party B
has access to more information.
If there were no communication, party B would always win the general election by
selecting player 3 as its candidate.
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But when α − β
≤ 1/8 and δ > 1/8, party A is more ‘ideologically cohesive’ than
party B : party A’s politicians are ideologically closer.
As a result, party A’s most moderate candidate, player 2, can trust the advice of his
party fellow, player 1, if elected.
Instead, party B ’s candidate, player 3, must decide on his own.
So, when β is not too large, party A wins the general election with 2.
Importantly, however, if 2 moves too close to the median, then α − β
> 1/8,
so that 2 loses the informational advantage over 3, and loses the election.
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Example 3 allows us to draw the following conclusions.
1. A small party can win elections if it is more ideologically cohesive than a larger party.
This is because the small, cohesive party can express candidates who rely on a larger
group of trustworthy associates.
2. If a candidate moves too close to median, he may lose the cooperation and advice of
the other leaders of his own party.
As a result, the party may lose the election even if its candidate is closest to the median.
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• Our results can be related to cases and instances of party success or failure.
• One case-story is ‘New Labour’: the successful transformation of the British Labour
party during the 1990s.
Tony Blair was always a moderate. His success much depended on the advice of
politicians such as Gordon Brown, John Reid, and David Blunkett whose views
moved to the centre during the 1990’s. (See Blair’s memories,).
• The poor electoral performance of the Italian Democratic Party in the 00’s is partly
explained by lack of cohesion and ideological proximity among its leaders (Massimo
D’Alema, Massimo Veltroni, Romano Prodi, and Luigi Bersani).
Romano Prodi, in particular, was more much moderate than PD party’s leaders.
His two Governments were poorly supported, and unstable.
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Literature Review
• Theoretical Studies of Leadership: Dewan and Myatt (2008, 2012), Bolton,
Brunnermeier, Velkamp (2010), Egorov and Sonin (2010).
• Empirical Studies on Leaders’ Competence: Besley and Reynal- Querol (2011),
Galasso and Nannicini (2011).
• Empirical Studies on Valence in Elections: Stokes (1963), McCurley and Mondak
(1995), Ansolabehere, Snyder and Stewart (2001), Burden (2004), Stone and Simas
(2010).
• Theoretical Studies on Valence: Aragones and Palfrey (2002), Kartik and McAfee
(2006), Callander and Wilkie (1997), Bernhardt, Camara, and Squintani (2011).
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• Multi-Player Communication: Morgan and Stocken (2008), Galeotti, Ghiglino and
Squintani (2009), Ivanov, (2010), Patty and Penn (2013).
• Communication and Optimal Executives: Dewan, Galeotti, Ghiglino and Squintani
(2013), Patty (2013).
• Delegation and Communication: Dewan and Squintani (2012), Gailmard and Patty
(2013), Penn (2014).
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