More voting theory (this time mathematical)

posted Nov 03, 2002

Nearly all political elections in the United States are plurality votes, in which each voter selects a single candidate, and the candidate with the most votes wins. Yet voting theorists argue that plurality voting is one of the worst of all possible choices.... Unlike these procedures [described in the elided section], the plurality system looks only at a voter's top choice. By ignoring how voters might rank the other candidates, it opens the floodgates to unsettling, paradoxical results.

Slashdot had a story about this article. There is something in this article worth highlighting, though, which is the section called "No One's Perfect", which references something called Arrow's Theorum, which shows that no voting system can be perfect.

Slashdot user Theodore Logan found a link to the actual mathematical proof of the Arrow Theorum.

In short, the author set out to create a perfectly fair voting system and instead discovered it's impossible to create one. Specifically, he proved that it is impossible to create a system with certain properties, all of which are reasonable and necessary, but some of which are difficult to explain in English. It may still be profitable to discuss whether one system is better then another for a given purpose, but there can be no One Perfect System.

You can take this one step further: The best way to truly define a "fair" election is to produce a process that results in a fair result. Any rigorous definition of "fair" that matches our fuzzy notions of "fair" should in fact be able to produce such a process. (Logically speaking, the existance of a rigorous definition of fair bi-directionally implies the existance of a fair voting scheme. I haven't proven this, because it would basically be self-proving based on how carefully you define the terms, which often happens when treating fuzzy human terms with logic tools.) Thus, this theorum can be interpreted to mean that there is no such thing as "fair"... "fair" is a polite social fiction when it comes to voting systems.

It can still be profitable to discuss whether a particular voting system is better for some purpose or another, but since there is no final definition of fair, there will inevitably be politics involved unless the debate can truly be held to the standards of mathematical rigor. (Unlikely, but as Arrow's Theorum shows, not actually impossible.) Thus, while the article is interesting, I find myself suspicious of the other people they quote lamenting our current system... what are their agendas? Does Terry Bouricius like "instant-runoff" voting because he really likes it, or because France uses it and he expects that if we used it here, the political environment would look more French? I don't know.

Perhaps we should hold a vote on which voting system we should use. (Actually, as darkly humorous as that may be, any proposal at reform would itself need to be voted on, though not necessarily by the same system that is being reformed, so it's not as silly as it may sound at first.)

The real lesson to draw from recent election anomalies, voting theorists say, is that citizens should think carefully not just about how well the election machinery counts up the votes but also about how they want the votes to count.

Which is probably the best thing you can carry away from this article to act on. This is why I added if you feel you can possibly afford it in any given race in my call for voting for third-parties in my last post; you need to consider the results. For instance, I intend to vote Republican in my state's governor race, because I really don't want to see the Democrat win. That's the only race I intend to vote Republican or Democrat, but it may be a close one and the vote may really matter. In other races, it's either a foregone conclusion and I might as well bolster a third-party, or I don't really care which Republocrat wins.


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