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roystgnr comments on Godel's Completeness and Incompleteness Theorems - Less Wrong
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I'm fascinated by but completely failing to grasp your first comment. Specifically:
Suppose we:
Which of Arrow's criteria is violated when considering this to be a result of the votes in FS but not violated when considering this to be a result of the votes in IS?
Good question! It's dictatorship. In such a situation, any non-principal ultrafilter picks out one of the congruence classes and only listens to that one.
More generally, given any partition of an infinite set of voters into a finite disjoint union of sets, a non-principal ultrafilter picks out one member of the partition and only listens to that one. In other words, a non-principal ultrafilter disenfranchises arbitrarily large portions of the population. This is another reason it's not very useful for actually conducting elections!