Herein I try to show more technically that rational candidates are inclined to mobilize supporters to vote. Assume that election is a game with 2 players (candidateI, candidateII). Each has 2 strategies (to Mobilize supporters to vote, Not to mobilize supporters to vote) to choose from. The outcomes of the game are characterized by the winning probability of candidateI.

We need to make a strong assumption that the candidates in the election do not know the distribution of voters, that is, there are 3 situations — More support I, More support II, and they are equally supported– but no one knows who is more likely to win before voting results released. Note that, from my last post, we have shown that to make supporters regard the election as intense serves a good way to mobilize them to vote.

In turn, some remarks need to be made that if more support candidateI and if both candidates mobilize the supporters to vote, the winning probability of I is 1. If more support II and if only I mobilizes the supporters to vote, the winning probability of I is X and 0<X<1. If more support II and if no candidate mobilize the supporters, the winning probability of I is 0. And so on. To sum up, there are 3 kinds of outcomes {1, X, 0}. Moreover, for candidateI, 1>X>0. For candidateII, 1<X<0. Below is how the game tree looks:

Because for II, his preference is 0>X>1. Therefore, he will play “M" in every decision knot. Expecting this, I should choose a strategy to maximize his probability to win. Because he does not know the Nature, he compares the outcomes of each strategy. Without losing the generalization, we assume the probability of each Nature is equally 1/3. 1) Strategy M: 1/3*1+ 1/3*X +1/3*0 = 1/3(1+X) 2) Strategy N: 1/3*X + 1/3*0 + 1/3*0= 1/3X. Obviously, the payoff of “to Mobilize" is better than “Not to mobilize" (1/3(1+X) >1/3X). The same logic applies to II’s proces of decision making. Therefore, it is a dominant strategy to play “M" for both candidates.

In summary, judging from these 2 posts, I conclude that if the voters care about whether the candidate they support wins the election and if the election is close enough, every rational voter goes to vote, though it is inefficient. In turn, I show that the candidates tend to make their supporters think of the election as very close, therefore, to mobilize them to vote, if the distribution of the voters is unknown to both candidates and if the both candidates take step without succession. To sum up, the reason why rational people vote lies in that it is a dominant strategy for rational candidates to mobilize the supporters to vote by making them perceive the election is intense since rational people go to vote only if the election is intense. In short, going to vote is rational from the view of interaction among rational voters and rational candidates.

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