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The Centrists’ Prisoner’s Dilemma

In the article Political tribalism and the prisoner’s dilemma, author Richard J. Shinder discusses the idea of a prisoner’s dilemma that exists for centrist voters. A centrist voter is a voter whose political views lie somewhere in the middle of the two party system, the article is strictly concerned with the centrist voter who does identify with a specific party (left-wing or right-wing), and how these voters face an ever growing problem: as political parties increasing skew toward fringe party beliefs, the centrist voter is left with little recourse. Shinder explains that these centrist voters really only have three choices: sit out the election, stay with their party, or crossover to the opposing party. And within this framework, Shinder imagines a prisoner’s dilemma that exists between these centrist voters and the opposing political party; The opposing party can either cater to centrist voters or to their own party, while the centrist voter can sit out, crossover, or stay with their original party. Shinder comes to the conclusion that the opposing political party will always cater to their party beliefs, while the centrist voter will always remain with their original party; as such, I wanted to see if I could reconstruct and dissect this prisoner’s dilemma using game theory.

First lets make sense of the graph for the centrist voter: 

1. A payoff of 1 means you voted for something that you wanted ( i.e. I crossed-over to the opposing political party and the opposing political party catered to my views)
2. A  payoff of 0 means you voted for something that you didn’t want, but you wouldn’t change your action if you could (i.e. I stayed with my political party and voted for fringe beliefs I don’t necessarily like, but at least I didn’t crossover and vote for beliefs I definitely don’t like).
3. A payoff of -1 means you didn’t vote when you wish you had (i.e if the opposing party caters to you and you don’t vote, you’ll wish you had voted for the opposing party or if the opposing party caters to their party, you’ll wish you would’ve supported your own party instead of sitting out).
4. A payoff of -2 means you voted for something when you wish you’d voted the opposite (i.e. I crossed over, and the opposing party didn’t cater towards my beliefs or I stayed with my party and the opposing party catered to my beliefs; in either case, you’ll wish you’d voted for the opposite party).

 

For the opposing party, the payoff is an equation: (centrist vote + party vote) – (opponent vote). 

1. If the opposing party caters to centrists and the centrist voters sit out: the opposing party doesn’t get the centrist vote, doesn’t get votes from their party because they compromised, but the opponent also doesn’t get the centrist vote [(0 centrist vote + 0 party vote)-(0 opponent) =  0]. Payoff is 0.
2. If the opposing party caters to centrists and the centrists crossover: The opposing party gets the centrist votes the opponent would’ve gotten, but doesn’t get votes from their own party. Payoff is 1.
3. If the opposing party caters to centrists and the centrists stay with their original party: the opposing party gets neither centrist, nor their party votes, and the opponent gets the centrist votes. Payoff is -1
4. If the opposing party caters to their party and the centrist voters sit out: Neither they nor the opponent gets the centrist vote, but they get their party’s votes. Payoff is 1.
5. If the opposing party caters to their party and the centrists crossover: The opposing party gets both the votes from their party and the centrists, while the opponent doesn’t get centrist votes. Payoff is 2.
6. If the opposing party caters to their party and the centrists stay with their original party: The opposing party gets their party’s vote, but doesn’t get the centrist vote and the opponent gets the centrist vote. Payoff is 0.

 

It immediately becomes apparent that the opposing party has a dominant strategy to cater to their own party, the best case scenario being the centrists crossover and they keep their own party happy; even if the centrists remain in their original party, the opposing party can get votes from their own party if they cater to them. And because the centrists know the price of crossing over is betrayal by the opposing party, they will always choose to stay in their original party; the opposing party will never cater to centrists, so centrists should stick with their own side. This scenario is best embodied by the saying “better the devil you know, than the one you don’t”. But as party politics becomes more and more extreme, it’s interesting to see if the future holds any surprises.

Article:

https://thehill.com/opinion/campaign/3550198-political-tribalism-and-the-prisoners-dilemma/

 

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