Endogenous candidates

Osborne and Slivinski (1996) explain why some candidates run forelection even though they might lose. They assume non-binding platforms; hence, a candidate cannot induce his/her opponent to compromise more because the policy to be implemented is given as an ideal policy. Thus, the reason a candidate runs to lose is different in their study and my model. According to Osborne and Slivinski (1996), the loser runs to change the identity of the winner (i.e., decrease an undesirable candidate’s probability of winning). On the contrary, in the model presented in Chapter 2, the loser runs to induce the winner to approach the loser’s ideal policy. Moreover, in Osborne and Slivinski (1996), a candidate who runs and is certain to lose never appears in a two-candidate competition. Wada (1996, Ch. 2) also shows that some candidates may run even though they will lose using a different model framework. Ishiha- ra’s (2020) result using a repeated two-candidate competition model is similar to that of my model, which analyzes a one-shot game.

Valence

The models in Chapters 2 and 3 also relate to models of “valence” since they show asymmetric electoral outcomes in the equilibrium. Several studies such as Ansolabehere and Snyder (2000), Aragones and Palfrey (2002), Groseclose (2001), Kartik and McAfee (2007), and Callander (2008) consider the effects of a candidate’s character or personality, as indicated by Stokes (1963) as valence, and show an asymmetric probability of winning in a political competition. These studies assume that there are advantaged and disadvantaged candidates, and an advantage is given exogenously as valence. Voters care not only about policy but also about valence, suggesting that an advantaged candidate with good valence has a higher probability of winning an election. Therefore, an extreme candidate may win against a moderate candidate if he/she has good valence, as shown by Kartik and McAfee (2007) and Callander (2008).³ On the contrary, I derive an asymmetric probability of winning endogenously in Chapter 2 and show that an extreme candidate wins against a moderate candidate without such exogenous valence in Chapter 3.

Political ambiguity

Causes of political ambiguity

Prior studies use formal models to indicate various mechanisms that generate political ambiguity. There are two main types of models: voter-centered and candidate-centered models. Voter-centered models suppose that voters prefer a higher degree of ambiguity and that candidates choose an ambiguous promise to win an election. This category includes models in which voters have convex utility functions. Callander and Wilson (2008) indicate that voters may develop a taste for ambiguity using the notion of context-dependent voting, as introduced by Callander and Wilson (2006).⁴ Kartik et al. (2017) suppose that voters are uncertain about their own ideal policy and that only politicians receive policy-relevant information after an election. In this case, voters prefer a politician who announces a vague promise when he/she shares voters’ policy preferences, because they prefer to allow the politician the discretion to adopt policies. Moreover, if voters are boundedly rational, candidates who make ambiguous promises may win the election. For example, voters believe incorrectly that their favored candidate’s position is closer to their preferred policy than it actually is (Jensen, 2009), voters are not expected utility maximizers and have Knightian uncertainty (Berliant and Konishi, 2005), or voters take at face value the campaign promise announced by candidates without being able to decipher their strategy (Demange and Van der Straeten, 2017; Szembrot, 2017).

On the contrary, candidate-centered models suppose that voters dislike ambiguity, but that candidates prefer ambiguity. First, candidates may prefer political ambiguity because of its direct (non-electoral) benefits. For example, they may not know which policy is most expedient (Aragones and Neernan, 2000) and may want the flexibility to implement their own preferred policy (Alesina and Cukierman, 1990). Furthermore, a party may be able to recruit a greater number of elites by allowing for ideological diversity (Jensen and Lee, 2017). Second, candidates may be able to obtain indirect (electoral) benefits from political ambiguity even though voters prefer a less ambiguous policy. For example, when candidates are uncertain about the position of the median policy, they may prefer to maintain ambiguity (Glazer, 1990). This is especially true in primary elections because candidates have less information about voters’ preferences (Meirowitz, 2005). Moreover, if campaign platforms are decided sequentially, the follower, who makes policy decisions later than his/her opponent, has a significant advantage when a Condorcet winner does not exist. As a result, candidates prefer to retain political ambiguity (Kamada and Sugaya, 2020).

Definitions of political ambiguity

This book interprets political ambiguity as a lottery that includes several policies; however, it has alternative definitions. Some studies interpret a set of policies as an ambiguous policy and do not consider a candidate’s decision-making on a probability distribution in this set (Glazer, 1990; Aragones and Neeman, 2000; Jensen, 2009; Kartik et al., 2017; Kamada and Sugaya, 2020). Meirowitz (2005), Berliant and Konishi (2005), and Szembrot (2017) suppose that ambiguity exists when candidates do not announce anything in their campaigns.⁵ Most of these studies suppose that candidates do not have the discretion to decide the probability distribution on policies, which is given exogenously in the model. That is, candidates cannot change the degree of ambiguity completely. On the contrary, studies that suppose political ambiguity as a lottery assume that candidates can choose any probability distribution freely. The reality should be between these two definitions; candidates have some (but not perfect) discretion to decide a probability distribution. However, I suppose political ambiguity as a lottery in Chapter 4 to investigate the strategic choices of candidates on the degree of ambiguity.

There are two justifications to suppose that candidates announce a specific probability distribution on policies in their campaign. First, using words, candidates may induce voters to have specific expectations. For example, in Japan, Prime Minister Shinzo Abe made an ambiguous announcement stating that he will increase the consumption tax rate in 2019 if a severe financial crisis (or a similar event) does not occur. Thus, voters may think that although the probability of such an event is high since financial crises do not occur frequently, it is not 100% certain. (If COV1D-19 was spreading in early 2019, it might not be increased.) Second, candidates may induce voters to have specific expectations by allocating weights to each policy (Page, 1976).⁶ Voters believe that a policy with a higher weight is more likely to be implemented. These interpretations suppose a probability distribution of an ambiguous promise as the beliefs held by voters. In other words, a candidate can use weights or words to induce voters to form specific beliefs.