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Electoral promises with vague words

Chapter 4 analyzes a possible cause of political ambiguity by allowing candidates to choose not only a single policy but also an ambiguous promise. A standard and classical interpretation of political ambiguity is a lottery (i.e., a probability distribution on single policies): candidates announce a lottery and voters choose the candidate who announces the better of the alternatives (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 interpret political ambiguity as a lottery, showing that the median policy 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, neither study establishes the existence of equilibria 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 preferred policy. Thus, a campaign promise is always ambiguous when candidates commit to implementing a policy other than their own preferred policy. To the best of my knowledge, no existing studies show that a candidate chooses to make an ambiguous promise in the equilibrium because of the convex utility functions of voters, without any restriction on the candidate’s choices.

Chapter 4 identifies the conditions under which candidates choose ambiguous promises in the equilibrium when voters have convex utility functions and candidates’ choices are unrestricted. It extends the standard Downsian model with fully office-motivated candidates to allow a candidate to choose a lottery. Voters vote sincerely, and a candidate will implement a policy according to the probability distribution of the announced promise after he/she wins the election.

The findings are as follows. First, in a deterministic model without 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 the equilibrium when voters have concave or linear utility functions, whereas no equilibrium exists in the case of convex utility functions. On the contrary, in a probabilistic voting model, where candidates are uncertain about voters’ preferences, they choose ambiguous promises in the equilibrium when voters have convex utility functions and the distribution of voters’ 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, ‘T am uncomfortable with the implication of concavity that extremists are highly sensitive to differences between moderate candidates” (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 Kojirna (2014) state that “(e)conomic policy is arguably a concave issue, given the evidence that individuals are risk-averse in financial decisions. By contrast, voters may have convex utility functions on moral or religious issues” (p. 204). They claim that an ambiguous promise tends to be used for non-economic issues, which may be a convex issue.

For example, suppose a voter who is conservative and is against introducing regulation on gun ownership. Thus, this voter’s preferred policy is no regulation on gun ownership and his/her ideal policy can be located at the right end when the policy space represents the degree of regulation on gun ownership, as shown in Figure 1.3. When this voter has concave preferences as in Figure 1.3(a), it means that his/her utility decreases little when a weak regulation is introduced, whereas he/she cares a lot about a small difference in strict regulations since his/her utility changes greatly with a marginal difference. On the contrary, when this voter has convex preferences as in Figure 1.3(b), a small change in strict regulations changes his/her utility little since it is already very low'. Rather, the utility of this voter decreases considerably by introducing any type of regulation - even a weak one. To represent the conservative voter’s preference, the latter should thus be more appropriate than the former.

Concave and Convex Preferences

Figure 1.3 Concave and Convex Preferences.

Electoral promises in forma! models 11 Shepsle (1972) states the following:

In the 1968 presidential campaign, both Nixon’s “1 have a plan” statements on the Vietnam issue and Humphrey’s “law and order with justice” slogan on “the social issue” suggest that equivocal pronouncements during the course of campaign are a common and recurrent theme in American electoral politics.

(p. 555)

These are examples of ambiguity regarding non-economic issues, and public opinion on the Vietnam war was almost equally divided and polarized between pro-escalation and anti-escalation (Verba et al., 1967). Therefore, the model in Chapter 4 provides one possible explanation for why Nixon chose an ambiguous promise.


Table 1.1 highlights the contributions and implications of each chapter. This table shows the new settings and novel implications that extend the findings of past studies. To clarify the novelty of my implications, the next section summarizes previous studies and explains how they differ from my model.

Table 1.1 New Settings and Implications of Each Chapter

New Setting(s)

New Implication^)

Chapter 2

• Partially binding

• Asymmetric electoral



• The reason why a loser runs an election

Chapter 3

  • • Partially binding platform
  • • Uncertainty about a candidate’s policy preference

• Political polarization (the reason why an extreme candidate wins an election)

Chapter 4

  • • Allowing candidates to choose a lottery as a promise
  • • Uncertainty about voters’ policy preference

• Political ambiguity with a convex policy preference

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