On 01/08/2013 04:30 AM, Jameson Quinn wrote:
2013/1/7 Greg Nisbet <[email protected] <mailto:[email protected]>> Hey, I'd like to get a sense of what sorts of multiwinner methods are currently known that are reasonably good and don't require districts, parties, or candidates that are capable of making decisions (I'm looking at you, asset voting). Like Abd, I wonder at the basis for your criteria. I think that for reform in most English-speaking countries, districts are usually an advantage, parties arguably so, and intelligent candidates always.
Perhaps he's looking for some kind of multiwinner method for the pizza election. E.g. "n people go out for pizza and decide to split the costs of four pizzas. Which pizzas should they get?" Then you can't use asset, and districts and parties are out.
However, for a pizza election, usually n is small (definitely less than a hundred), so discussion/negotiation works much better than election.
Perhaps the method is to be used for a computer program that has to choose between different predictors of some event (e.g. a robot modeling reality). Then, again, asset is out (the predictors don't campaign) and districts and parties are not applicable. But in this case, there are lots of methods that work based on feedback so as to increase the weight of the successful predictors and attenuate those that are not. The weighted majority algorithm is one such, and probably the simplest. If testing the alternative predictors is too hard, one instead could use some form of multi-armed bandit testing, e.g. UCB1.
It would be amusing to consider a society that would do its political elections like this. These would initially elect randomly, then voters would be asked how well the candidate did, and then that would be fed back into the process. It would be elections based on what actually happened rather than what the candidates promise. However, the candidates would have incentives to game the system, and the dynamic nature of the thing (performance changing with time) would violate some assumptions in the multi-armed bandit framework, requiring restless bandit algorithms, which are, to my knowledge, PSPACE-hard.
In any event: Greg, I think we need more information about what the multiwinner method is to be used for. Why aren't districts, parties, and candidates that are capable of making decisions permitted?
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