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Saturday, October 04, 2003
Cap'n Den Beste has written a number of times on the "tragedy of the commons". Now a reader writes to him discussing the problem and doesn't buy the example of sheep on the commons. A better "real life" example illustrating the problem of the tragedy of the commons in today's world where all of the sheep are in Australia and New Zealand:

Ten houses are on the shores of a lake. Each house has a cesspool that drains into the lake and the lake is therefore polluted enough to prevent swimming and fishing. With the lake polluted, each house is worth $100,000. With the lake cleaned up, each house would be worth $125,000. To clean up the lake, at least six householders have to spend $5,000 each on plumbing.

Without the intervention of some outside force (ie: government), no one will install the plumbing required to clean up the lake. At best, each householder makes a rational decision to wait for five others to install the plumbing first. That way, when the sixth householder spends his $5K, he is assured of a $25K return. Householders one through five spend their $5K with no assured return. Of course, each of the ten householders also wants to be one of the four holdouts who spend nothing and get the $25K return anyway.

The generalization is: the sum of a series of rational decisions can be an irrational outcome. This can happen literally anywhere. It even occurs in government.

Assume a legislature is divided politically into three groups of equal size (Groups 1, 2 and 3), and that, on a particular issue, there are three available choices (Choices A, B and C). Assume further that each political group orders its preferences among the available choices as follows:

Group 1 prefers A over B and B over C
Group 2 prefers C over A and A over B
Group 3 prefers B over C and C over A

If all three alternatives are presented for a vote at one time, there is no majority and no plurality for any one alternative.

If the three alternatives are presented for a vote one pair at time, the outcome is determined by the order of presentation.

In a contest between alternatives A and B, Groups 1 and 2 vote for A, so A survives to face alternative C.

In a subsequent contest between alternatives A and C, Groups 2 and 3 vote for C, so C wins and is presumably enacted into law.

But change the order of the presentation and you get the following:

In a contest between alternatives B and C, Groups 1 and 3 vote for B, so B survives to face alternative A.

In a subsequent contest between alternatives B and A , Groups 1 and 2 vote for A, so A wins and is enacted into law.

The change in the order of the presentation of the alternatives changed the outcome. The order of presentation has nothing to do with anyone's preferences, much less the merits of the issue. Having the outcome determined by a factor like order of presentation is irrational, but each group ordered its priorities rationally and voted rationally on those preferences.

For those of you with a mathematical bent, the problem can be described as an impossible equation:

A > B > C > A

In the (increasingly) dim recesses of my memory, I recall that someone once researched the issue and found that the problem had occurred on at least a few identifiable occasions on the record in Congress over the last two hundred years. And, of course, there are vastly greater possibilities of it having happened off the record as well, for example within administrative agencies.

For those of you foolish enough to want to know more, pick up a book on game theory. As I recall, the one I used in college (way too old) was by William (?) Riker and was, oddly enough, entitled "Game Theory". But since I can't find either Riker or the book in the Library of Congress catalogue, I must be either searching or remembering incorrectly.

The above examples illustrate Arrow's Theorem. The subject also encompases other problems and quirks concerning how choices are made in the public policy arena. While driving through the midwest in the late 40s, someone (Arrow?) noticed that, in each town large enough to have both a Sears and a JC Penney, the stores were located on opposite corners in the center of town, from which he theorized that each organization was locating itself at a geographical point which minimized the distance between itself and its potential customers, thus maximizing the number of potential customers, who were assumed to treat the two stores identically and buy from the closer one. Arrow or whoever applied that observation to political parties. The opinions held by the population on a given issue will be distributed along a bell curve. Each political party will adopt a position it hopes is closer to the center if that curve so as to maximize the parties appeal to voters.

And we can't forget the ever popular the Prisoner's Dilemma. Two people accused of jointly participating in the same crime are arrested and interrogated separately. Each is offered the following choice: If the prisoner confesses and agrees to testify against his partner, he will receive a sentence of 3 years, while his non-confessing partner gets 15 years based on that testimony. Each accused criminal knows that if neither confesses, neither will be convicted, and that if they both confess, they will both get 10 years. Unless there is some reason for the prisoners to trust each other, the likely outcome is that they both confess and the aggregate sentence is maximized. This is the reason that organized crime presents such a problem for law enforcement.

By the way, you can thank a certain Iowa housewife for this post. Memorial link indeed. The reports of my demise have been greatly exaggerated.
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