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I am in the early stages of planning my senior project and was wondering if anybody had some recommendations of literature about the applications of ultrafilters in social choice theory, along with any other introductory level reading about ultrafilters. Thanks in advance!

Martin Sleziak
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Marcus Dupree
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  • Are you saying that an incredibly abstract set theoretic/topological concept has applications in the humanities?! That's actually pretty cool! – shalop Apr 14 '15 at 02:58
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    It is very cool! If you are interested, ultrafilters are used in regards to Arrow's theorem when an infinite amount of voters is allowed. – Marcus Dupree Apr 14 '15 at 04:45
  • A naive way to find some materials would be simply to search for some relevant keywords in Google or Google Books or Google Scholar. I might be mistaken, but I think that Michael Greinecker works in some related area, so let's hope he notices your question. – Martin Sleziak Apr 14 '15 at 05:48
  • @Shalop You can find a bit more about Arrow theorem, mentioned by Marcus, also here on MSE: http://math.stackexchange.com/questions/585110/arrows-impossibility-theorem-and-ultrafilters-references and http://math.stackexchange.com/questions/35450/applications-of-ultrafilters/35720#35720 – Martin Sleziak Apr 14 '15 at 05:51
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    @Marcus: They can be used even when only finitely many voters are allowed: one way to prove Arrow’s theorem is to show that a certain family of decisive sets of voters must be an ultrafilter. Thus, if the set of voters is finite, it must be a fixed ultrafilter, and you immediately get a dictator. – Brian M. Scott Apr 14 '15 at 16:53

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