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Talk:Prefer Accept Reject voting: Difference between revisions
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imported>Homunq (Created page with "Here's an email regarding PAR: I said earlier that I couldn't think of a realistic scenario where PAR fails to choose the CW. I've now thought of one: 22: A>B 4: A>C 25: B>A...") |
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I said earlier that I couldn't think of a realistic scenario where PAR fails to choose the CW. I've now thought of one:
* 22: A>B
* 4: A>C
* 25: B>A
* 49: C>AB (or C>anything including at least 3% which accept C, and at least as many C>A as C>B)
This can be thought of as a variety of center squeeze, with A as the center. (Sorry, I know that the convention is to use B as the center, but I don't want to rewrite this whole email.)
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* 22: A>B
* 4: A>C
* 5: BA
* 20: B>A
* 49: C>AB (or C>anything including at least 3% which accept B, and at least as many C>A as C>B)
In this case, C wins, but the 5 BA voters could elect A by voting A>B.
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So in general, PAR violates FBC in a center-squeeze scenario in situations where the Condorcet loser is not majority-rejected. In a situation where the honest preferences are roughly as in the second scenario above, there are several ways that the CW could still win:
The A voters largely reject B (defensive truncation)▼
# The
▲# The
# A few B voters say ?>AB (defensive, um, I don't know what that is called. "Denormalization"? "Weakening"? Technically, this could be seen as restoring FBC compliance, but that's a stretch. I'd call that "semi-FBC" at best.)
# Combination of 1 and 4 above
# Combination of 3 and 5 above (although since either one requires relatively few voters, it's unlikely that both would be needed.)
In general, I still think that PAR does exceptionally well with naive ballots, because I think that cases where the problem arises, but none of the above solutions happens naturally, would be rare. But hmmm... failing FBC... I recognize that that looks bad.
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