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Voting paradoxes explained

posted by Jason Kottke   Nov 07, 2016

With almost every election comes a push from some to change the way Americans elect their representatives in government. The problem is, there’s no perfect method of voting. The Exploratorium has produced a video that looks at how different voting methods fail in different ways, including through the spoiler effect, cyclic preferences, and the failure of monoticity. In short, every potential way of voting allows for some irrational outcome to arise out of the choices of individuals. So says Kenneth Arrow, who came up with Arrow’s impossibility theorem, explained in more layman’s terms here on Marginal Revolution.

Paradoxes such as the above have been known for centuries. What Arrow showed is that no decision mechanism can eliminate all of these types of paradoxes. (n.b. Arrow’s theorem actually applies to any mechanism for aggregating any rankings not just voting and not just preferences.) We can tamp down some paradoxes but only at the expense of creating others (or eliminating democracy altogether.)

More generally, what Arrow showed is that group choice (aggregation) is not like individual choice.

Also, think for a minute about how Arrow’s impossibility theorem might affect what Facebook, Twitter, Pinterest, Digg, and hundreds of other media companies and apps are trying to do in aggregating the world’s news and information by social media “voting”.