Monday, September 17, 2007

Free Riders, Game Theory, and Morality

Yesterday, I described what economists call the Free Rider Problem in terms of one of game theory’s favorite devices, the Prisoners’ Dilemma.

When I write a post, and I refer to an earlier post, my rule has been to bring all relevant information forward so that a reader does not have to go back. However, in this case, the previous post contains a lot of relevant detail. I must refer a reader back to that post for the detail.

For those who have read yesterday’s post, I attempted to show how a ‘free rider’ situation means that people end up worse off than they could have been. This is the benefits of a public good cannot be assigned to any specific person. The payoff gets distributed among the population, with the donor getting such a small percentage of the total that it is not in his interests to donate. However, if everybody were to contribute to these public goods, everybody would benefit.

I created an example where a ‘public good’ produces a 50% return on investment that is distributed evenly among the population. Each person has an option of contributing $1000 to this public good. This will return $1500 in ‘public good’ for each person who contributes. However, because the return is distributed evenly, the person who makes the $1000 investment only gets (1/population) of the return. In my two-person case, this was one-half of the return, or $750. If everybody were to donate to this public good, in this hypothetical case, everybody would get $1500 out of the public good. However, no individual has an incentive to contribute, so everybody misses out on an opportunity to become $500 better off than they would have been.

Yesterday, I also looked at a political solution to this problem. The political solution is to force everybody to contribute $1000 by taxing them, or passing a law forcing them to prove that they have made the required contribution. Unfortunately, each ‘faction’ still has an incentive to lobby for laws in which others are required to contribute, but they obtain special immunities and exceptions.

This sets up a ‘political auction’ where everybody must pay what they bid whether they win or lose, and everybody must play. The penalty for not playing is being made the loser in the political options. Losers must contribute to public goods that benefit others, while those others do not contribute to the public goods that benefit the loser.

Morality and Free Riders

Today, I want to present a moral response to the free rider problem.

The moral response is not a solution to the free-rider problem. It is, instead, a way of avoiding the free-rider problem and all of the implications that follow from it.

The moral solution avoids this problem by altering the payoffs. Specifically, in this case we are going to introduce $300 worth of social (and, potentially, criminal) sanctions against those who do not contribute to the public good.

In the original situation, if I contribute and you do not, then your return will be $1750 (The $1000 you kept, and the $750 that is your share of the public return on my $1000 contribution). This is opposed to $1500 if you do contribute. You have an incentive not to contribute.

However, if I threaten you with $300 in sanctions, then you get $1500 if you invest and $1450 if you do not. Now, you have an incentive to invest. As a result of your investing your return goes up to $1500 and my return goes from $750 (my share of the return from my $750 investment) to $1500.

Checks and Balances

There is still a problem with this option. It assumes (1) that I have the power to impose $300 in social sanctions on you, and (2) I will not use that power to force you to pay while I refrain from paying. If either of these assumptions are violated, then the person with power can harvest the profits from failing to contribute with impunity.

This problem disappears as soon as we add one more player. Now, if Player 1 wishes to impose sanctions on Player 2, he has Player to back him up. On the other hand, if Player 1 wishes not to contribute, then Player 3 can work with Player 2 to impose sanctions on him. If Player 3 decide not to contribute, Players 1 and 2 have the power to impose sanctions on him. As long as we have at least a three-ways system of checks and balances, and nobody has more power than the other two combined, we have a method of forcing cooperation and imposing sanctions on refusing to contribute.

Anonymous Defection

Another problem with this solution rests with the possibility of anonymous defection. Game theory often works under the assumption that all defections are public knowledge, so that everybody knows who contributed and who did not. In reality, there are any number of ways to refuse to contribute without this being known. They can hide their money, cook the books, lie, or steal back what they contributed, just to name some examples. The $300 in cultural and legal sanctions will not do any good if we do not know who to punish.

We can find an answer to this problem by looking at the nature of these payoffs. I have been measuring the payoffs in terms of dollars. However, dollars (for the most part) have value because of what you can do with them. People use dollars to fulfill their desires, given their beliefs. This could well include desires to help others – so we do not need to assume that everybody is totally selfish. A person who wants to give to charity cannot give what he does not have.

So, let us assume that I have the power to give you a desire to contribute to public goods that is stronger than any other desire that you could fulfill for $300. In other words, when choosing between contributing to a public good, and choosing to have $300, you could go either way. However, the $250 benefit that you would receive from not contributing to the public good in this example just isn’t enough money. Here, contributing and having $1500 is worth $1800 to you, while refusing to contribute and having $750 is only worth $1750.

Please note that, on this model, acting to serve the public good is not an act of self-sacrifice. To the person who desires to eat chocolate ice-cream, the act of eating chocolate ice-cream is not an act of self-sacrifice. Similarly, to the person who desires to contribute to the public good, contributing to the public good is not an act of self-sacrifice. To such a person, contributing to the public good becomes his ice-cream. In fact, it could become better than ice-cream.

Using Moral Sentiments

There is, then, a reason for each person to give others either a desire to contribute or an aversion to refraining from contributing (selfishness). The question remains whether there is a way to accomplish this end.

The methods of ‘rewards’ and ‘sanctions’ certainly does exist. So, we each have reason to support an institution of rewards (praise, honors, prizes) to those who contribute and sanctions (condemnation, ostracism, boycotts) against those who refrain from contributing.

We know that interaction with the environment alters brain structure. We see this in terms of beliefs, where different interactions with the environment cause different agents to acquire different beliefs. We also see this in desires – particularly in the way different societies have different desires, but people within a given society come to have common desires. This pretty much proves the proposition that social forces can influence desires.

To whatever degree social forces can influence desires, people generally have reason to promote those desires that fulfill other desires, and inhibit those desires that thwart other desires. In this posting, I have shown how people generally have reason to use social forces to promote a desire to contribute to the public good, and to promote an aversion to refraining from contributing to the public good.

We have reason to praise and honor those who contribute to the public good as a way of promoting this desire not only in those we praise and honor, but those who are a witness to praise and honor. We even have reason to provide people with hypothetical examples of those who would deserve praise and honor as a way of encouraging others to become that type of person.

All of this applies as well to those we condemn and punish.

1 comment:

Xerographica said...

I look at the problem a bit differently. If we wouldn't purchase all the same private goods...then why should we have to purchase all the same public goods?

My solution is to allow tax payers to vote with their taxes.

My solution accepts taxes as necessary to combat the free-rider problem. But once people are directly involved in deciding which public goods they "purchase" then perhaps there is somewhat less incentive for people to over-deduct or under-report their income.