Thursday, April 8, 2010

Thoughtful Thursday, Can Voting Optimize? Can the Voters Learn

"Learning, voting and the information trap" Aleksander Berentsen, Esther Bruegger and Simon Loertscher! (I saw this in Public Choice 2005, but it seems to be at The authors published a journal article of the same title in Public Economics Volume 92 5 to 6, June 2008 pages 998 to 1010, which I will track down for a future Thoughtful Thursday.)

Can voting optimize? In engineering, optimization is finding the values of the parameters of an object or process so as to minimize weight, cost, environmental damage, etc. There are often constraints. Thus, what thickness of material, size of pipe, temperature in furnace gives us the best output from our chemical process. Constraints would be from the fact that at certain tempertures, materials would break down as well as the stoichiometry or arithmetic of the chemical process itself. In social science, it might be what is the tax rate that makes people on average happiest. That is basically the question that Berentsen, Bruegger and Loertscher asked. The voters don't know how effective tax money is in accomplishing a "public good," let's say education. So they increase or decrease taxes, see how much education they got for their taxes and vote again.

Will the voters find an optimal or at least Pareto optimal tax rate? (If the tax rate falls unequally upon individuals, more taxes for the wealthiest, the wealthier might prefer less goods and less taxes while those paying less taxes would prefer the opposite.) How some tax rates, very high ones, might lead to a situation that everyone considers bad--and a very low tax rate with no education at all everyone also considers bad. These are not Pareto optimal!

But there is a problem, the voters don't know exactly how much good they will get for their tax money. In other words, does more money equal better educated children, and by how much? Can the voting system find this out? The answer from their mathematical proofs based upon probability theory is that it would not. They don't. It is likely that society will end up believing the wrong thing about the relation between education and the amount of money put into it. It is likely that they would not achieve a Pareto optimal result for the amount of tax. The more mistaken society starts out, the more likely they would never get to the right place. They also looked at random noise or shocks. That is, other factors affect the quality of the students coming out of the school that have nothing to do with the amount of money in taxes--that upon which the people are voting. Some of these might vary as shocks--more like a sudden rise in oil prices affecting the economy.

There is a well known model of candidate voting, where each party chooses a position on the issue, in this case how much to tax. The authors use this rather than a participatory democracy rule. Obviously, I hope to simulate some of the tax policies I discussed in earlier postings to see if we get similar results--I expect that we will.

Although the authors did not look at it, this is a good model of the recent arguments over taxes. To what extent do high taxes discourage work and investment. As a people, we try high tax rates and see what happens with the economy and vice versa. Will we ever learn the true relationship between taxes and the economy? Assume one has a progressive tax. Can the voters find the optimal amount of progression. If it is too progressive, confiscatory, it might destroy incentives for people to work hard and achieve. And we would have less revenue -- Laffer's Curve. That is, as tax rate goes from zero to one hundred, there is a peak. The government of course gets no revenue at zero percent for obvious arithmetic reasons. They get no tax revenue at one hundred percent because they have no incentive to work or they find a ways to avoid the tax. If it is not progressive enough, insufficient revenue might be achieved to get public goods. I proposed voting on taxes and budget in the form of genetic algorithms--can the voters find the optimal function and find the true function determining work as a function of progressivity.

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