Monday, December 20, 2010

Social Choice theory and opinion polls

So, somewhere, not sure where I ran into this article over on Slate entitled "Polled and Confused. How should America improve its economy? Don't ask Americans for guidance." It's a summary of the various polls about the economy, and what to do about it. One excerpt reads:
She barely liked the 2009 stimulus when Congress passed it, and she certainly does not like it now. (The financial regulatory reform bill? She's made her peace with that.) Yet, in an enduring example of the polled American's propensity for containing multitudes, she likes virtually all of the elements of stimulus, such as the tax breaks, unemployment insurance, infrastructure investment, and bolstered food stamps—a case of the parts besting the sum, apparently. And she thinks the country needs more of those provisions.
That quote, and the article in general carries with it at least a whiff of the notion that the average American really doesn't have well thought out political positions. While this may be true, it doesn't really follow. Let us consider three people polled on what to have for dessert. Furthermore, suppose Alice is allergic to nuts, Bob is allergic to dairy. and Carol is allergic to Eggs. A nut custard containing nuts, eggs, and milk is suggested. If you poll for all three ingredients separately, each will get the support of 2/3 of the population, yet the egg custard will be rejected unanimously. Remember, There is no average American, and the 43% that agree on something probably aren't the same 43% that agree on something else. This is related to Arrow's impossibility theorem which basically says that there is no "right way" for a group to decide on what to do. Democracy is hard.

Thursday, December 2, 2010