## Game Theory in Voter Polarization

https://pennpoliticalreview.org/2018/01/disastrous-elections-predicted-by-game-theory/

A first-past-the-post voting system the type of voting system present in the United States. It’s simplest definition is one person, one vote. This seems logically fair; however, it is fundamentally flawed in voter satisfaction. The effects of a first-past-the-post voting system is the consolidation of the political system to be two relatively-polarized parties. The people most unhappy with the system are those who in the middle.

Assume that we are on a spectrum that contains, in order, far-left, left, center, right, and far-right, numbered 1-5. The amount of satisfaction felt is a quadratic equation that follows the formula 16-x^2, where x is the number of spaces away. So a right-leaning voter will have a satisfaction score of 15 should a far-right or center candidate be elected. This means that in an electorate made up of two far-left and three far-right voters, a center candidate would yield greater vote satisfaction (of 60) than a far-right candidate, (which yields a voter satisfaction of only 48). This seems relatively obvious, but this rewards voter polarization as illustrated in the next example.

Given a district with an electorate of two-far left, one center, one right, and one far-right voters, should everybody vote for their preferred candidate, this would result in the far-left candidate winning. This yields a total satisfaction of 51. In a separate election with the same electorate that occurs in another district at a later date, the right-wing voter will choose to vote for the far-right candidate, as they hope that they would be able to get some sort of payoff as they know voting for the right-wing candidate is practically “throwing away their vote.” Simultaneously, the two-far left and one far-right voters choose to vote for their candidates. This means that the total vote count is two for the far-right candidate and two for the far-left. The center voter is now indifferent to voting far-left or far-right and chooses to vote for the far-right one. This means that the far-right candidate wins and total voter satisfaction is 43. Although this voter satisfaction is lower than of the first district, it showcases how the right-leaning voter must vote for the far-right candidate for a payoff as 15 as opposed to 7.

This final point is essential in illustrating voter polarization. It shows why the U.S. electorate has moved to two-polarized parties that cater to extreme views but enjoy more moderate support. This also means that center voters experience a relatively low amount of satisfaction.  The principles of game theory and socially-optimal amounts that were covered in class apply extensively in this example.