Kevin, You wrote:
"Suppose we're using a WV method:
40 A>B>C 35 B>C>A 25 C>A>B
There's an A>B>C>A cycle. B>C is the strongest win (75 votes), followed by A>B (65 votes) and C>A (60 votes). So C>A is discarded and A wins.
But suppose the B>C voters see this coming and perhaps don't feel as strongly between B and C. They might instead vote B=C>A. When that happens, there is still a cycle, but now B>C is the weakest win with only 40 votes. Now C wins.
(Incidentally, this also works in the CDTT method I suggest. The CDTT
is {a,b,c} at first; when the B>C voters rank B=C, the CDTT becomes
just {c}.)I don't consider that the B>C voters get this advantage for free. In order for it to work, they have to give up the opportunity to distinguish between B and C."
Those last two sentences are just putting a bizarre spin on rewarding indecisiveness. Suppose those B=C voters
(in the modified example) really are too stupid and lazy to decide which they prefer out of B and C, they just hate A.
Then they *are* "getting an advantage for free"!
Based on the sincere rankings, what possible case is there that electing C is "better" than electing A? In this classic
3-candidate cycle scenario, if the method meets Majority then there are always voters with an incentive to Compromise.
Based on these particular sincere rankings, I can't see that we really have any guide as to which is the "best" winner other than the
Borda scores, and C is the big Borda loser (having the fewest first-preferences and the most last-preferences)!
Russ and others might be interested to know that there is a method that meets Woodall's Symmetric Completion and Plurality criteria,
doesn't have any 0-info. strategy incentives (meets NZIS), meets all the Condorcet criteria, (mutual)Majority, 3-small Mono-raise
(monotonicity with no more than three candidates) ,Clone Independence and "naturally" meets Minimal Defense.
SCRIRVE!
Ranked ballots, truncation allowed. Then the ballots are "symmetrically completed" and reversed. Based on the resulting profile, repeatedly
eliminated the IRV "winner" (until one candidate remains).
This is the definition that fits the acronym, but the "symmetrically complete" stage can be omitted, and then working on the reverse profile,
"fractional" equal-ranking IRV is used to repeatedly exclude candidates.
When there are three candidates in a cycle, then SCRIRVE is equivalent to "elect the candidate with the fewest last-place rankings (fractional)".
It handles this example very well. Assuming that we are allowing non-last equal-rankings, it elects B both times.
Chris Benham
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