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Strategies and Game Theory in Republican Primaries

Image from http://www.businessinsider.com/perry-romney-social-security-fight-explodes-2011-9

Image from http://www.businessinsider.com/perry-romney-social-security-fight-explodes-2011-9

After a recent Republican Presidential Primary Debate, a Politico article (http://www.politico.com/news/stories/0911/62964.html) looked at Rick Perry’s more conservative strategy, and Mitt Romney’s more moderate strategy. Polling data that shows Rick Perry leading the Republican primary race can be explained using game theory analyzing these strategies.

There is also a belief that political primaries cause greater political polarization. Primaries tend to draw out voters who have stronger beliefs at further ideological extremes.  To win their primaries, candidates need to appeal to these ideological extremes. Game theory can also be used to understand this shift toward polarization.

Data from 500 Republican primary voters across the country in September 2011 gathered by Public Policy Polling shows the following breakdown of ideological self-identification:

Very liberal ……………………………………………… 1%
Somewhat liberal …………………………………….. 4%
Moderate………………………………………………… 19%
Somewhat conservative……………………………. 43%
Very conservative ……………………………………. 33%

We can simplify the game setting to have 2 candidates running against each other for the Republican Nomination. They can choose to play a moderate or conservative strategy. We will also assume that liberal to moderate voters (24% in total) would vote for the moderate strategy, and somewhat and very conservative voters (76% in total) will vote for the conservative strategy. When both candidates play the same strategy, it is assumed that voters will split evenly.

Candidate 1\2 Moderate Strategy Conservative Strategy
Moderate
Strategy
12, 12 (Box A) 24, 76 (Box B)
Conservative
Strategy
76, 24 (Box C) 38, 38 (Box D)

For both candidates, employing a conservative strategy is a strict dominant strategy, because it is the best response to any of the other candidate’s strategies.  Box D, where both candidates use a conservative strategy is the pure strategy Nash Equilibrium. Thus, if both candidates use conservative strategies, the political discourse in the primary moves in a more conservative direction.  However, the Politico article implies that as of now, Rick Perry uses a more conservative strategy, and Mitt Romney has a more moderate one. These strategies would match Box B in the payoff matrix, which predicts a higher payoff to the more conservative candidate, which is seen in the polling data from Public Policy Polling – in a 2 person race, Perry leads at 49% to Romney’s 37%. In the future, the matrix would predict that Mitt Romney will shift toward a more conservative strategy to maximize his payoff.

However, it is important to realize the constraints of the game played above (besides the assumptions already mentioned). The game created only looks at 2 different strategies, while in reality there is not such a clear distinction; there are positions in between that could be taken. The payoff structure does not take the general election into account, which is one of the points made in the Politico article, that Mitt Romney may be using a more moderate strategy to have a wider appeal in the general election. However, this matrix does provide a nice way of looking at strategies for political primaries.

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