Strategic Ambiguity with Probabilistic Voting
| Author | Yasushi Asako |
| Published date | 01 October 2019 |
| DOI | 10.1177/0951629819875516 |
| Date | 01 October 2019 |
| Subject Matter | Articles |
Article
Journal of Theoretical Politics
2019, Vol.31(4) 626–641
ÓThe Author(s) 2019
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DOI: 10.1177/0951629819875516
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Strategic Ambiguity with
Probabilistic Voting
Yasushi Asako
Faculty of PoliticalScience and Economics, Waseda University, Japan
Abstract
Political parties and candidates usually prefer making ambiguous promises. This study identifies
the conditions under which candidates choose ambiguous promises in equilibrium, given convex
utility functions of voters. The results show that in a deterministic model, no equilibrium exists
when voters have convex utility functions. However, in a probabilistic voting model, candidates
make ambiguous promisesin equilibrium when (i) voters have convex utility functions, and (ii) the
distribution of voters’ most preferredpolicies is polarized.
JEL Classification: D71, D72
Keywords
Elections; Political ambiguity; Public promise; Campaignplatform; Probabilistic voting; Polarization
I. Introduction
Politicians prefer using vague words and announce several policies in their electoral
promises, a practice referred to as ‘‘political ambiguity.’’ A standard and classical
interpretation of political ambiguity is a lottery, that is, a probability distribution
on policies. This can be explained in the following manner: candidates announce a
lottery, and voters choose the candidate who announces the better lottery
(Zeckhauser, 1969; Shepsle, 1972; Aragones and Postlewaite, 2002; Callander and
Wilson, 2008). One possible reason why candidates make such vague promises is
because voters have convex utility functions. Zeckhauser (1969) was the first to
Corresponding author:
YasushiAsako, Faculty of Political Scienceand Economics, Waseda University,1-6-1 Nishi-Waseda,
Shinjuku-ku, Tokyo 169-8050,Japan.
Email: yasushi.asako@waseda.jp
interpret political ambiguity as a lottery, and showed that the median policy, which
is most preferred by the median voter, can be defeated by a risky lottery when the
voter’s utility function is convex. Shepsle (1972) generalizes the findings of
Zeckhauser (1969) and shows that a Condorcet winner does not exist when voters
have convex utility functions. However, they do not establish the existence of equili-
bria in which candidates announce ambiguous promises. Aragones and Postlewaite
(2002) show political ambiguity as an equilibrium phenomenon using voters’ convex
utility functions. However, they assume that candidates need to provide a positive
probability for their most preferred policy. Thus, a campaign promise is always
ambiguous when candidates commit to implementing a policy other than their own
most preferred policy. To the best of my knowledge, no existing studies show that a
candidate chooses to make an ambiguous promise in equilibrium because of the
convex utility functions of voters, without any restriction on the candidate’s
choices.
This study identifies the conditions under which candidates choose ambiguous
promises in equilibrium when voters have convex utility functions, and there is no
restriction on the candidate’s choices. It extends the standard Downsian model with
fully office-motivated candidates to allow a candidatechooses a lottery. Voters vote
sincerely, and two candidates announce a binding promise before an election: a
candidate will implement a policy according to the probability distribution of the
announced promise after s/he wins the election.
1
The findings are as follows. First,
in a deterministic model without any uncertainty, the unique Condorcet winner is
the median policy when voters have concave or linear utility functions. However,
no Condorcet winner exists when voters have convex utility functions. Therefore,
two candidates choose the median policy in equilibrium when voters have concave
or linear utility functions, but no equilibrium exists in the case of convex utility
functions. On the other hand, in a probabilistic voting model, where candidates are
uncertain about voters’ preferences, they choose ambiguous promises in equili-
brium when (i) voters have convex utility functions, and (ii) the distribution of vot-
ers’ most preferred policies is polarized. Therefore, for political ambiguity to be
considered as an equilibrium phenomenon with convex utility functions, voters
must be polarized, and voting must be probabilistic.
Most prior studies assume that voters are risk-averse. However, there is no
robust and clear evidence that voters have concave utility functions for all political
issues. Osborne (1995) states that, ‘‘I am uncomfortable with the implication of
concavity that extremists are highly sensitive to differences between moderate can-
didates’’ (p. 275), and ‘‘it is not clear that evidence that people are risk-averse in
economic decision-making has any relevance here’’ (p. 276). Furthermore, Kamada
and Kojima (2014) state that, ‘‘(e)conomic policy is arguably a concave issue, given
the evidence that individuals are risk-averse in financial decisions. By contrast, vot-
ers may have convex utility functions on moral or religious issues’’ (p. 204). Their
findings imply that an ambiguous promise tends to be used for non-economic
issues, which may be a convex issue. Shepsle (1972) states the following:
Asako 627
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