The Game Theory of Politics
This article describes the idea of game theory in political elections. Though the examples given in this article are old, they are still relevant to current elections. With time running out and Election Day getting closer and closer, campaigners are often faced with difficult decisions. They often face the choice of what states to visit in a last attempt to win the election. These decisions often depend on the choices one’s opponent makes as well as the reward gained from visiting certain states. To make such decisions author, Jordan Ellenberg, discusses how game theory, a concept we learned in class, comes into play for these presidential candidates.
This article mainly discusses the Bush vs. Kerry election. During this election, some states were clearly leaning towards either Democratic or Republican while others were on the fence. These states that were in the middle were the important ones for Kerry and Bush to sway. States such as Florida, Ohio and Pennsylvania were the most sought after states for their large number of electoral votes. Winning these would help secure either Bush or Kerry the presidential spot. The best thing to do for either contenders was however dependent on the other candidates move. For example, suppose the weekend before Election Day both candidates were allowed to make one last visit. The author allows Pennsylvania to go to Kerry and figures out what Bush needs to do from there to win the election. Given Bush has a 30% chance of winning Ohio and 70% chance of winning Florida and visiting a state gives both contenders a 10% increase, Bush clearly has a dominant strategy. If both visit Ohio, the chances of winning the election for Bush is 0.3*0.7= 21%. If Bush goes to Ohio and Kerry goes to Florida, the chances of Bush winning the election rose to 0.4*0.6=24%. However if Bush went to Florida and Kerry visited Ohio his chances dropped to 0.2*0.8=16%. Therefore his dominant strategy was visiting Ohio. If the opposite was done with Kerry’s chances of winning the election, his dominant strategy also turns out to be Ohio making this a Nash Equilibrium.
However if the game was changes slightly to make Bush have a 50-50% chance in each state, a mixed strategy emerges. Bush would always want to go to the same state as Kerry while Kerry would want the opposite. By both candidates flipping a coin to determine where they would want to go, it makes the game fair since neither opponent knows the other’s decision. This is a more subtle Nash equilibrium where chance plays a role in determining one’s actions. Therefore it is evident that elections have both mixed and dominant strategies depending on each candidate’s chance of winning a given state.
The author makes in interesting note here about predictability. He says that rational behavior tends to be predictable, and in a game of strategy, predictability leaves one with a disadvantage. Therefore since each opponent decides their choice with a coin toss, they remove the element of being predictable and make the game more difficult for the opponent. This also applies to a game of rock, paper, and scissors. If your opponent could predict your next move, you would be doomed to fail from the start. This article helps expand beyond the material learned in class by showing how game theory applies to real world situations. In this upcoming election, chances are both presidential candidates will be weighing out their options and choose their dominant strategy. However, the chances of winning are never set in stone and can only be estimated based on prior knowledge and a general sense of how each candidate believes a state will vote. Keeping all this in mind, game theory is clearly evident in daily life from the most basic of games like rock paper scissors to the future of the country by means of picking a leader to represent you.
– Nameless
Source: http://www.slate.com/articles/life/do_the_math/2004/10/game_theory_for_swingers.html