Chris Benham asked me that question, and I pointed asked him what strategy guarantees he wants for people uninterested in strategy. Of course there are other kinds of guarantees too, and Approval does offer those, even to people uninterested in strategy.
Say that, instead of voting strategically, people just vote for the candidates who are acceptable, or deserving. Then Approval guarantees that the winner will be the candidate who is acceptable or deserving to the most people. What other kind of guarantee do you want for someone uninterested in strategy, presumably because s/he is uninterested in maximizing hir expectation. For hir, that overall social optimization is enough.
But Approval offers social opimization guarantees to voters uninterested in strategy (and to voters who are interested in strategy) even if the other voters are strategizing to maximize expectation:
Then, if it's 0-info, Approval guarantees that the winner will be the candidate who is above the mean for the most voters. If it isn't 0-info, then Approval guarantees (with some reasonable approximations) that the winner will be the candidate whom the most voters consider so good that they'd rather have hir in office than hold the election. These social optimizations are demonstrated at our website, http://www.electionmethods.org at the Approval Strategy pages.
The first of those 2 guarantees is actually a special case of the 2nd one.
Approval also does much better by social utility than IRV does.
These considerations, along with FBC, are the reasons why some say that Approval is better than the best rank methods. That of course is an individual judgement, and I agree with the importance and desirability of those considerations, though I personally prefer SFC, GSFC, & SDSC, available with the best Condorcet versions, or at least SFC, available with PC. Or SFC & SDSC., available with PC with AERLO.
As for Approval vs ERIRV(fractional), I don't have a very strong opinion on that issue, because, as I said, SFC is the criterion that I like the most, and it isn't met by ERIRV.
Unlike unmitigated IRV, ERIRV's MMC & ICC compliance are usable in comparisons with Approval. And ERIRV avoids the co-operation/defection dilemma that James described. I don't think that dilemma is as important as he does, but it's still somewhat important. And, with AERLO, ERIRV meets SDSC.
I'm not saying that's conclusive proof that ERIRV is better than Approval. There's no definite answer to that, of course. They're both good. It depends on what you want. It's a question of FBC & the social oiptimizations vs the ERIRV advantages stated above. I like the criteria that ERIRV brings, though it isn't nearly as good as PC, it seems to me. I tend to prefer ERIRV's advantages to those of Approval, but that's just a personal subjective opiniion.
Mike Ossipoff
Mike Ossipoff
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