March 11th, 2008 by Rightsideup

I came across a reference recently to something called Arrow’s Impossibility Theorem and followed a link to the Wikipedia article on this topic. The theorem is named for Kenneth Arrow, who posited that it is impossible for a society of any size to make collective choices (e.g. through voting) that will reflect the underlying choices of the individuals who make up the society. There is a complex mathematical proof accompanying the theorem, which is given in some detail in the Wikipedia entry, but it’s actually also pretty intuitive.

Since there are often two serious choices in an election – Democrats versus Republicans, usually, in the US – and since the two parties often offer policies which are in effect opposites (raise taxes vs. lower taxes, permit vs. ban abortion, etc.) the election of candidate from either party alienates those who voted for the other. That’s the extreme, but the Impossibility Theorem also suggests that even if you simply have three options and individuals are able to rank them by preference, it still isn’t possible to have a solution which is optimal for society as a whole, since even if Option A comes out top, there will be members of society for whom Option A was the third (i.e. last) choice.

What does all this mean in practical terms? Well, it means that, no matter how well we exercise our civic duty, we will frequently find ourselves on the losing side and therefore feel frustrated that we have expressed our preferences but not apparently influenced the result. This is the problem behind at least some voter apathy (ironically, a sense that there is little difference between candidates is another), but it is also a factor behind dictatorships and even violent movements within democracies. Groups which constitute a minority in electoral terms but nonetheless have significant membership become frustrated when they are consistently thwarted in their aims by the electoral process, which gives power to the majority. After a time they become disillusioned with the process and seek to enforce their will through alternative means, whether seizing power by force, engaging in terrorist acts designed either to enforce their will or exact vengeance for non-compliance, or through some other method.

This is the charge democracy is most vulnerable to: that although it produces results which are acceptable to a majority, that can leave over 49% of society feeling disenfranchised. However, as Winston Churchill said, “democracy is the worst form of government, except for all the others.” As flawed as democracy can be, it is still the best method for ensuring that a majority, and not a vocal or violent minority, dictates societal outcomes. This November, no doubt, there will be many who feel frustrated once again at the political process, but in all likelihood none of these people will feel strongly enough to effect a change in the underlying system of representative democracy, the great national experiment which can indeed “long endure” despite its flaws. And in the context of the violence which is typical during and after elections in some of the other nations of the world, that is a miracle in itself.