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Sunday, January 31, 2016

Rational Actors, Irrational Outcomes, and the GOP Nomination

Social scientists often use game theory in order to model real-world situations that involve cooperation between two or more parties. Perhaps the best known game is the "prisoner's dilemma," which illustrates how two individuals can act rationally but collectively reach an irrational outcome. Imagine a situation in which the police have two people in prison, but they don't have enough evidence to convict them on the principal charge. They do, however, have enough to sentence both to a year in prison on a lesser charge. Each prisoner is in solitary confinement and can't communicate with the other. The police decide to offer each prisoner the opportunity to get off scot free if they testify against the other.

The various outcomes are captured in the above matrix, which lists the "payoffs" for both prisoners (Prisoner #1's payoffs appear below each of the diagonals, while Prisoner #2's payoffs appear above). From the perspective of the prisoners, the best option is for both to keep their mouth shut. If they do, they'll only serve one year in prison (note the "1s" above and below the diagonal in the upper left cell of the table below). However, the rational thing for each prisoner to do individually is to betray the other so that they can go free. For example, if Prisoner #1 betrays Prisoner #2 and Prisoner #2 remains silent, the former will go free, while the latter will serve a three year sentence. The catch, of course, is that if both prisoners act "rationally," they'll both betray the other, and both will serve two-year sentences, which, at least from their perspective, is an irrational outcome.

The current race for the GOP presidential nomination is somewhat analogous to the rational/irrational dynamic captured by the prisoner's dilemma game. In an insightful analysis of the data ("Donald Trump’s Support In Iowa Is Narrow But Deep") Harry Enten of FiveThirtyEight shows why although Donald Trump is the candidate unacceptable to the most Iowa Republicans (according to the latest Des Moines Register poll, 37 percent said they would be “not OK” with Trump winning the Republican nomination), he will probably win the Iowa caucuses:
How does that make any sense? Trump isn’t liked by many Republicans, but he’s loved by a few, and in a 12-candidate field, that may be enough... Trump would almost certainly lose the Iowa caucuses if the field of candidates were smaller. Just 7 percent of Iowa Republicans list Trump as their second choice, while 17 percent list Cruz and 20 percent list Rubio. The Des Moines Register poll found that likely Republican caucus-goers preferred Cruz over Trump in a one-on-one matchup 53 percent to 35 percent. The problem for this majority is they’ll never get to vote in a two-man race. In a field of 12 candidates, it’s all about core support. You don’t get to cast a negative vote.
In other words, if there weren't so many candidates vying for the Republican nomination, then it's unlikely that Trump would win in Iowa. However, because most still believe they have a chance to win, they haven't dropped out of the race, and thus collectively they are handing Iowa to Trump. Put differently, by acting in their (rational) self-interest, collectively they are producing an irrational outcome.

The question is: after Monday will several of the candidates will have an epiphany, realize they can't win, and drop out? If they do, then someone like Marco Rubio might just have a chance of winning the nomination ("Don't Write Off Marco Rubio Just Yet"). For the general election, this could be good news for Republicans and bad news for Democrats ("It’s Rubio Or Bust For Republicans Who Want To Win"). It will be interesting to see if those who are running for President are able to set-aside their individual aspirations for the good of the GOP. Otherwise, they might be shut out of the White House again.

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