Tuesday, January 27, 2009

Is green the new black?

Compared with other vices, envy gets a bad press. For years, the phrase "politics of envy" has been a trusty weapon of political discourse, wheeled out again and again whenever someone rails against excessive boardroom pay rises, or suggests raising the top level of income tax. Recently, things have changed - articles like this one are becoming fashionable, as we find out about the pay received by top bankers whose organizations are now being bailed out by the taxpayer.

It is a fair counter-argument that the excessive bonuses are a small percentage of the overall losses that banks are passing on to the public, and that to curb them would not cut the taxpayer's bill very much. But, there is a growing understanding that curbing other people's excessive bonuses simply feels good for its own sake -- it requires no financial justification. We don't penalise the bankers in order to save money -- we do so because it makes us happy.

In psychology and economics, envy requires one to be prepared to pay a small amount of money in order to see someone else lose a larger amount of money. The above attitude appears to qualify therefore, since if you get your kicks out of seeing some overpaid banker have to give up his 100 foot yacht, then there exists some sufficiently small amount of money that you would be prepared to pay for the spectacle.

Maybe this will provide a boost for envy-related research? There's an interesting line of research that has attracted some computer scientists, on the problem of envy-free cake cutting. The general topic is: how do you generalize the I-cut-you-choose idea, when there are more than 2 people who want to share a divisible good (such as a cake)? I just read a very nice paper: Thou Shalt Covet Thy Neighbor's Cake, by Ariel Procaccia. It shows that envy-freeness is harder to achieve than proportionality, in the sense that it requires more cuts, as a function of number of players. (Envy-freeness means that everyone can guarantee that they value their own share at least as much as anyone else's; proportionality means that everyone can guarantee a "fair share", but with the risk they end up thinking certain other players did better. So, proportionality is a weaker requirement.) The paper uses the Robertson-Webb model of cake-cutting procedure in which a centralized algorithm is allowed to submit certain queries to the players about what value they would assign to various parts of the cake. For me, a very interesting aspect of this model is the parallels with the query protocols that have been studied in computational learning theory.

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