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Contributions and implicationsThe main contribution of this book is to show that the implications change considerably from past studies when electoral promises are explicitly analyzed in formal models. In particular, this book introduces two major characteristics of electoral promises, namely, partially binding platforms and political ambiguity, into the standard political competition model (Downs, 1957; Wittman, 1973). These new models can explain many aspects of real elections that cannot be predicted by previous frameworks. The findings confirm the importance of analyzing electoral promises explicitly using game theory. The remainder of this chapter summarizes these new findings and explains how they differ from those of previous models. Two voles of electoral promisesBecause of the cost of betrayal, electoral promises serve as a commitment device and as a signal (see Chapters 2 and 3, respectively). First, because of the cost of betrayal, voters may believe that politicians will not betray their promise so severely to avoid paying this cost, and hence platforms can be considered as partial commitment devices to restrict a candidate’s future policy choice. Second, because of the cost of betrayal, candidates do not have an incentive to choose a platform further away from their preferred policy. This is because the winner will betray the promise severely and pay large costs when his/ her platform differs substantially from his/her ideal policy. Therefore, voters may be able to predict the position of the candidate’s preferred policy through electoral promises. Thus, platforms can work as a signal about the candidate’s policy preference. The following subsections summarize the main implications of each chapter. Electoral promises as a commitment deviceChapter 2 mainly analyzes electoral promises as a commitment device by introducing the cost of betrayal into the Downsian electoral competition model with policymotivated candidates. This model is generally known as Wittman’s (1973) model. There is a onedimensional policy space, and voters’ preferred policies are distributed on this space. The preferred policies of 50% of voters are located to the left of the median policy and the remaining 50% of voters’ preferred policies are located to the right. A voter who prefers the median policy is called the median voter. One candidate prefers to implement a policy to the left of the median policy and the other candidate, to the right. Candidates announce their platforms before the election and the winner chooses a policy to be implemented thereafter. Politicians care about (1) the probability of winning, (2) the policy to be implemented, and (3) the cost of betrayal. 1 also analyze endogenous decisions to run on the basis of a simplified version of the citizencandidate model (Osborne and Slivinski, 1996). Partially binding platforms can explain the following observations from real elections, which cannot be explained by models of completely binding or nonbinding platforms. Usually, in real elections, candidates have asymmetric characteristics (e.g., their policy preferences, the importance of policy, and costs of betrayal differ). Moreover, we frequently observe asymmetric outcomes (i.e., one candidate has a higher probability of winning than the other). Some candidates may avoid compromising on their principles to please voters and accept a lower probability of winning than their opponent, even though their probability of winning would be higher by compromising. However, in existing frameworks, it is difficult to show asymmetric electoral outcomes. In models of completely binding platforms, both candidates propose the median voter’s ideal policy regardless of their characteristics; hence, they have the same probability of winning (50%). In models of nonbinding platforms, voters expect candidates’ ideal policies to be implemented if they win. Then, only the candidate whose ideal policy is closer to the median policy can win, and no other characteristics affect the electoral outcome. On the contrary, in models of partially binding platforms, candidates with asymmetric characteristics can and will choose different platforms and policies to be implemented, since if their characteristics differ, one candidate may have a greater incentive to win  and would actually win  the election. This results in an asymmetric electoral outcome. Chapter 2 shows that an electoral outcome is asymmetric in the equilibrium when two candidates have different characteristics. For example, a more moderate candidate whose ideal policy is closer to the median policy wins against a more extreme candidate. Although this implication is the same as in models of nonbinding platforms, this outcome is derived endogenously as opposed to exogenously as in those models. Similarly, if a candidate’s cost of betrayal is higher than that of his/her opponent with the same degree of betrayal, the former candidate wins. If the cost is lower with the same degree of betrayal, a candidate will betray his/her platform more severely such that the realized cost of betrayal is higher; hence, this candidate has a lower incentive to win. In addition, a less policymotivated candidate wins against a more policymotivated candidate since the candidate with higher policy motivation will betray his/her platform more severely and pay his/her cost of betrayal. In existing frameworks, it is also difficult to explain why a candidate runs even though he/she may lose in a twocandidate model. In models of completely binding platforms, both candidates have an equal probability of winning, and hence an explicit loser does not exist. In models of nonbinding platforms, the winner will implement his/her ideal policy after the election, which means that the loser’s decision to run does not affect the winner’s policy. Thus, the loser has no reason to run. On the contrary, models of partially binding platforms show that even though a candidate is aware that he/she will lose, he/she may not deviate by withdrawing; therefore, he/she runs to induce his/her opponent to approach the median policy and thus the loser’s ideal policy. For example, in the US 2010 primary elections of the Republican Party, one purpose of Tea Partyendorsed candidates was to induce Republican candidates or officeholders to be more conservative, which they succeeded in doing (Skocpol and Williamson, 2012). In obtaining this implication, the concept of partial bindingness is critical since the loser can change the winner’s policy simply by entering the race. 
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