What are the known proportional methods that satisfy Independence of Irrelevant Ballots?
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The ones I know of are PAV, SPAV, eliminative PAV, and something called COWPEA.
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@isocratia Yeah, COWPEA along with COWPEA Lottery. It seems a difficult criterion to pass, but also seems a logical one.
And as well as those PAV variants, there's also optimised PAV Lottery, which has the advantage over PAV of also passing Universally Liked Candidate. In this method you work out the ideal seat distribution under PAV, assuming a large number of seats and unlimited clone candidates allowed. You then sequentially elect candidates probabilistically based on the proportion of seats they would win in the ideal election. But you have to recalculate the probabilities every time a candidate is elected (and therefore removed from the pool). It's a little bit like COWPEA Lottery, except that COWPEA Lottery can be run without a computation meltdown.
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@toby-pereira
The concept of using phantom clones in a PAV-like method, and using a procedure to replace them with real candidates, has got my wheels turning. I'm coming up with new ideas now but I want to make sure these ideas aren't half-baked. -
Also for party list, the divisor methods like Sainte-Laguë and D'Hondt pass IIB. But not Hamilton (largest remainder).
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Electing the "most stable" candidate set as in this thread should pass IIB as well.