Sunday, January 22, 2012

Adaptive Online Adversaries

This year there are presidential elections in both France and the US. The leading party of the opposition is the Republican party in the US and the Socialist party in France.

This year for the first time in France the Socialist candidate was chosen by election, in a quick two-round affair: a one-day vote to wean all but two of the candidates, and a one-day runoff vote one week later.

The Republican primaries in the US are a prolonged game of suspenseful fractional elections, state by state, little by little.
Since the voters of the beginning period are not a random sample of the whole set, their votes are not necessarily representative of the final outcome. Information about voters' intentions is revealed gradually, and late voters can adapt their choice given knowledge of previous voters' choices. They have more information than in France, but that information is not uniformly distributed among voters: early voters have no information. It's like an online algorithm in which votes arrive online and the adversary's choices for the ith vote can depend on votes 1 through i-1. That makes for exciting news!


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  2. I think you're thinking of this backwards: the issue is not that the early voters have no information; the issue is, if everyone were to vote at the same time, then the early voters would have absolutely no say - because they are part of the less populated, mostly non-representative states. The system was designed to give those people (for instance the poor Iowan corn farmers) a say, they would otherwise not have since the bulk of the electorates is concentrated on the outer states. So in turn their vote is generally not descriptive but prescriptive.

    There are many disadvantages to this system, of course. For instance: these early voters have a completely oversized sway over the election's outcome and get too much attention (or as Gail Collins humorously put it, "[... early] voters are so entitled that they find it hard to support anybody who hasn’t been to the house for dinner, or possibly a sleepover"); and on the other hand, these lagging nominations have the potential to hurt parties a lot. That said, seeing how it's the Republicans this time around, and they have practically bottomless sources of cash, I feel like getting some of that spent will bode better for the general election.


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