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Social Choice and Beyond
Sunday, October 25, 2009
Why I Deserve the Nobel Prize
Mood:  a-ok
Topic: Social Choice

It may seem somewhat arrogant and egotistical to write a blog about why I deserve the Nobel Prize. However, I will make my case as follows. In the nineteenth century the English utilitarians, Jeremy Bentham and John Stuart Mill, posited that society should be organized according to utility theory, the essence of which was the greatest possible good for the greatest possible number. It was assumed that everyone could measure his or her own personal utility for various options, and those individual utilities could be amalgamated to come up with an overall social utility. This work has been carried on to the present day by those trying to find an alternative to GDP, namely the Greatest Happiness Principal or Sarkozy's recent commission to come up with a better way to measure societal well-being than current methods.

In the 1950s Kenneth Arrow attempted to carry the English utilitarian political and economic theory to the next stage by mathematizing utility theory. He changed the name to social choice theory. Social choice theory encompassed both voting theory and economic theory. However, Arrow only succeeded in proving, supposedly, that social choice was impossible. In other words no one could come up with a social theory based on the greatest possible good for the greatest possible number. This gave capitalists a huge sigh of relief because it was considered to be a theoretical endorsement of capitalism. Also it reinforced the idea that direct democracy was impossible giving encouragement to the idea that representative democracy was the best you could do. For this Arrow received the Nobel prize for essentially proving that socialism or economic democracy and direct political democracy were both impossible. Arrow's Impossibility Theorem became famous. Conservatives were overjoyed.

But some pointed out that Arrow's Impossibility Theorem meant that solutions were impossible only in certain cases. In many other cases it was actually possible to find a solution. Therefore, Arrow's Impossibility Theorem only meant that a soloution was not possible in every case. Others pointed out that the Borda voting method came up with a solution in every case, and also that Arrow's analysis only applied to rank order preferences. Preferences that were indicated by real numbers on the real number axis (a measure of utilities over various options) also were exempt from Arrow's Impossibility Theorem. So then additional work was necessary in order to discredit the possibility that direct democracy and economic democracy were less than desirable. That work culminated with Gibbard and Satterthwaite who proved that any social system that was not impossible according to Arrow's Theorem was subject to being manipulated or gamed. Some individuals could strategize their inputs to the system in order to gain an unfair advantage over other participants. This again delegitimized the notion that direct democracy or economic democracy constituted viable alternatives to capitalism and representative democracy.

Recent work by Warren Smith has shown a method for optimal strategizing or gaming the system whether or not you have knowledge of how others will vote. His work is for voting systems based on a voting method called range voting which is essentially a formalization of the English utilitarians' idea of personal utility. I came up with the idea of range voting independently of Warren but I will give him the credit for it. Warren and I have both pointed out that range voting escapes Arrow's Impossibility Theorem, and I have pointed out that, by an extension, it escapes Gibbard and Satterthaite's proof that every social choice system is manipulable. This is easy to see if we take Warren's proof for the optimal way for an individual to strategize and just let the system itself apply that to every individual. Since it is up to the system to amalgamate all individual inputs, part of that process would be to make every input an optimally strategized input thus denying any unfair advantage to any individual and maximizing the potential of every individual input whether that input be a political vote or an economic alternative. I call this method Range-Approval Hybrid voting and it can be applied to economic systems as well.

Therefore, both Arrow's Impossibility Theorem and the Gibbard-Satterthwaite Manipulability Theorem have been overcome, and each participating individual can be assured that he or she can express his or her true utilities whether political or economic and no other individual can game the system in such a way as to gain an unfair advantage. Any individual who tries to game the system will either come out worse off or at least will not come out better off. Then the resultant social choice or utility will represent the best possible solution for a system that is unmanipulable and can't be gamed. There is a price to pay, however, in that a better solution might be found if it were assumed that everyone were completely honest in their expression of personal utility, but that price is relatively small in order to guarantee a stable system.

So the age old quest for a social system based on individual and social uitility has been found despite the fact that Arrow proved such a quest impossible and Gibbard and Satterthwaite proved that any system that escaped Arrow's Impossibility Theorem could be gamed. This opens up new vistas (previously thought to be closed) for forms of societal organization based on cooperation and promises to reduce conflicts and limited choices available under present poltical and economic systems. If Arrow received the Nobel Prize for proving that human progress was impossible in this realm, I deserve one for proving that that avenue of human progress is indeed still open.

Here are the links to Range Voting and Social Choice and Beyond for additional background.

Posted by jclawrence at 6:52 AM PDT

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