Game theory for the average voter
The United States has always had a two party system. Every election year, both parties rile up their respective bases to motivate them to vote and attempt to hold majority control over state and national offices. Every election cycle, the same story is told that if the other candidate wins, then the country as people love it, will end. This usage of scare tactics served its purpose and polarized the public continuously, and through the years, it has led to this current election year, where the two candidates of the major parties are the most disliked in history. Trump currently stands at a 57.3% disapproval rating while Clinton is only slightly behind at 54.9%(both numbers have been averaged from several polls). These ratings imply that there is a good portion of Americans who dislike both candidates, and who would rather vote for anyone else. Although each voter would prefer to vote for a person they admire, they often feel that they have no other option. This is because they know that if they vote for a third candidate, they increase the chances that the person they like even less will win. Here is where game theory comes into play.
This is called “The Coordination problem”, and it is a variation of the Prisoner’s Dilemma. Whereas the Prisoner’s Dilemma involves the choice that two criminals have to individually make about whether or not to confess, this general coordination problem simply relates to the fact that voters don’t know whether or not to vote for someone that they actually like. To extend the similarity further, in the prisoner’s dilemma, even though the ideal strategy is for both to not confess, they know that they risk a worse payoff should they withhold a confession, while the other confesses. Likewise, a reasonably large demographic of voters want to avoid both Trump and Clinton, but they don’t want to risk their payoff being worse should the candidate they like less get elected.
To attempt to illustrate this problem, consider two players, one conservative, one liberal, who dislike both candidates but dislike the Democratic and Republican candidate more respectively. Additionally, both players can opt to vote for a third party that they both like.
| Conservative Voter | ||||
| Liberal Voter | Trump | Clinton | Third Party | |
| Trump | -1, 0 | -1, -1 | -1,1 | |
| Clinton | 0, 0 | 0, -1 | 0,1 | |
| Third Party | 1,0 | 1, -1 | 1,1 | |
As can be seen in the above table, the Nash Equilibrium is at Clinton, Trump for the (Liberal, Conservative). This is because voting for a major party candidate is the safest response against the voting tendencies of other people. Ideally both voters would vote third party, but both know they can’t win unless both agree previously to vote third party. However, when extending this model to millions of voters, it can be seen that it is hard for a majority of Americans to vote agree to vote third party.
Sources:
http://www.realclearpolitics.com/epolls/other/trump_favorableunfavorable-5493.html
http://www.realclearpolitics.com/epolls/other/clinton_favorableunfavorable-1131.html