The Game Theory of Politics

[Mr Skeptic]

This actually seems like it would be good material for a book.

 

Some definitions in game theory:

scoring

: although we can "play" with an abstract score, it could also be a significant thing, such as money, years in prison, suffering, happiness, honor, chance of dying, or whatever else the players value, so long as it can be quantified.

Dummy

: a player who's input cannot affect the outcome is a dummy.

Dominant Strategy

: a strategy that is always equal to or superior to any other strategy.

Nash Equilibrium

: a set of strategies, one for each player, such that no player has incentive to unilaterally change her action.

Pareto Efficiency

: an outcome is more Pareto efficient if at least one person is made better off and nobody is made worse off.

Kaldor-Hicks Efficiency

: an outcome is more Hicks efficient if those that are made better off could

in theory

compensate those that are made worse off, so that a Pareto improving outcome results.

 

Game Types:

Constant (or Zero) Sum Game

: a game where the overall score is limited, so you can only increase your score at the expense of other players. If there are only two players, than your opponent's loss is directly your gain. A Zero Sum Game is a subcategory, where the overall score is zero, although what actually matters is differences in score rather than overall score.

Variable Sum Game

: a game where the overall score depends on the choices of the players. This usually results in more cooperation than a zero sum game.

Simultaneous Game

: A game type where each player's choice is made without knowledge of other player's choices (regardless of whether it is time-simultaneous or not).

Iterated Game

: if the same game is played repeatedly, reputation and retribution often become possible if they were not before, which can facilitate cooperation.

Cooperative Game

: a game type where binding agreements can be made, that can be enforced outside the usual game rules. This in no way guarantees actual cooperation, although it often will.

 

Some Games:

Prisoner's Dilemma

: a game where defecting is a dominant strategy, and cooperating a dominated strategy. Although both would be better off overall (Pareto Optimal) cooperating with each other, each would be better off betraying the other regardless of what the other does.

Volunteer's Dilemma

: a game with many players, such that each player is better off if someone volunteers and they don't, but far worse off if no one volunteers.

Bargaining Problem

: a game where players are better off if they can reach an agreement, and worst off if they cannot agree, but have different preferred outcome.

Ultimatum Game

: a game where one player makes and offer division of score and the other player can reject the offer or accept it. The rejection results in zero score for both.

 

Hm, enough of that. There's plenty more games and game types. Game theory is intriguing, but for this thread I'd like to consider it's application to politics. This is significant as game theory gives us a good idea as to what to expect given a certain game. Since we can in theory design the game played in politics, the objective of this thread would be to identify the games currently played in politics, whether they have bad outcomes, and whether the game could be changed to one with a better outcome.

 

For politics, we can consider two sets of players: the politicians, and the public. Both are playing different games. While doing some of the below, I have noticed that the scoring rules are rather complicated (except for the election game).

 

Let's see:

Elections

:

For the politicians, elections are a constant sum game, where the score is the office(s) that is being run for, or votes. If there is no more than two strong contenders, it is essentially a two player constant sum game, so that sabotaging the main opponent directly scores you votes so long as it makes people dislike your opponent more than they dislike your badmouthing him, and any minor contenders can be safely ignored. Sabotaging the opponent is also an option, so long as the public doesn't care or doesn't find out. With more credible contestants, badmouthing an opponent scores you less votes, so that the choice to badmouth is less desirable. I don't think we can change this game, although it seems that we would get a better outcome with more players.

 

For the voters given the current voting system (only one vote for only one candidate), elections are a form of simultaneous bargaining/coordination game, with the score the "value" of the candidate. However, given polling and public announcements of support, it is no longer simultaneous. Since people know which are the two most popular candidates, coordination efforts focus on the favorite of these two (this is called strategic voting). The result is to essentially make the election game an essentially two player constant sum game for the politicians involved, with nasty results.

 

For election we can change the game played by the voters. By using, for example, approval voting, we remove the coordination aspect of the game almost entirely. Then voters can vote according to their own preference rather than focusing on coordination (ie the top two candidates). Concerns over coordination would focus on how acceptable a candidate would have to be for them to approve of that one. The result is that there can be more than two credible candidates.

 

 

Raising Taxes or Lowering Spending

:

This one is a game of Prisoner's Dilemma: both raising taxes and lowering spending are inherently unpopular, but someone has to keep the budget in check. Eventually. Or bad things will happen. Although many people pretend they would like to lower spending, when it comes down to actually having less services or getting less aid people get rather upset, for the most part moreso than the general population is pleased at the saving of some money. The score seems to be largely voter approval, although some congresscritters may actually care about the outcome for other reasons. Here our politicians have split into two teams, one focused on lowering taxes and the other focused on increasing spending (rather the services and aid from that spending). In this game, bluster is an effective strategy, as it is much less complicated than actual changes to the budget.

 

I suppose the ideal here would be some way to balance the budget over the long term. Since the long term budget might be decided by other players, however, in practice balancing the budget in the short term would be more likely. The other problem is that the public (as evidenced by our debt) likes spending now rather than later, and politicians will happily indulge us. I guess game theory is of limited use to this one: for the most part, we just need to pull our heads out of our collective asses and demand a balanced budget.

 

Another potential problem is that the public is essentially a dummy player in this, in that for all our complaining, these decisions are made by the congresscritters, although we can influence them somewhat.

 

 

Dividing the Budget

:

This is another game played for voter approval, although again in a few instances the congresscritters may care about the outcome. The actual money available is limited for a given budget, making this somewhat of a constant sum game. Congresscritters get a better score if they can draw money into their district, even if it is not needed there or can be used more efficiently elsewhere, so long as they don't look silly doing so. Bluster is again very important, both to distract from one's pork barrel projects or to lower support for enemy projects.

 

Again the public are dummy players. The contenders for the congresscritters' seats are also dummy players, though of course may offer their opinion on the budget, but they are playing a different game anyways (the election game). The public's interest in the game is that it decides what they get, and they prefer money that goes to their area to money that goes elsewhere. The public can attempt to influence the game by approving or disapproving of what the congresscritters do, although they have more influence on their own congresscritter.

 

While we can't change the nature of the game itself, we can certainly change the scoring rules. For example, we could require a cost/benefit analysis of each item on the budget, and then question why people choose an item with a lower cost/benefit just because it is in their district. Likewise, we can ridicule people who support such a project just because it is in their district. Since the money only very indirectly reaches most people in the district, such ridicule will be a significant aspect of their score.

 

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Well, what do you think? Does this seem like an interesting idea to explore? Any other aspects of politics that fall under game theory? Perhaps you can suggest a way to improve the games played by our politicians?

[bob000555]

One of the most important applications of game theory to politics is the median voter theorem.

http://en.wikipedia.org/wiki/Median_voter_theorem

Here is a great lecture from Yale on the subject:

[Pangloss]

It's a good idea. There are a lot of payoff matrices (e.g. Prisoner's Dilemma) in politics. We had one on global warming pass through here a while back, where a guy in a YouTube video basically shows how the only logical choice is to act to stop GW because only that choice doesn't have a chance of resulting in destruction, etc. Lots of fertile ground in this area.

 

It might be interesting to look at potential for equilibria with regard to creating legislation. Creative gameplay on the part of a bill's "sponsor" could result in a situation in which players who are normally in "ideological opposition" would be motivated to support a bill they would normally oppose. The dynamic variable there would be ideological compromise, I suppose, on some sort of sliding scale, or perhaps external inputs of some kind (tit-for-tat deals). Lots of variables here, though!

 

You should give Steve Jackson Games a call, Skep.