Applied Game Theory in Politics
Game theory can be used to analyze the strategic behavior of candidates and voters in voting and elections. Two commonly used models in game theory for voting are the Downsian model and the Spatial model.
The Downsian model assumes that voters have a single-dimensional preference and choose a candidate who is closest to their own position on that dimension. Candidates, on the other hand, choose a policy position that maximizes their chances of winning. This results in a two-player game between the candidate and the voters.
In this game, the candidate is the first mover and chooses a policy position. The voters observe the candidate's choice and then choose whether to vote for the candidate or not. If the voters vote for the candidate, the candidate wins and implements their chosen policy. If the voters do not vote for the candidate, the candidate loses and does not get to implement their chosen policy.
The Spatial model assumes that voters have a multi-dimensional preference and choose the candidate who is closest to their position on all dimensions. In this model, candidates also choose a policy position that maximizes their chances of winning by taking into account the preferences of the voters.
These models can be used to analyze the effects of different voting systems and candidate strategies. For example, in a plurality voting system, where the candidate with the most votes wins, the Downsian model predicts that candidates will choose extreme policy positions to differentiate themselves from their opponents. In contrast, in a proportional representation system, where seats are allocated based on the percentage of votes received, the Spatial model predicts that candidates will choose more moderate policy positions to appeal to a broader range of voters.
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