I'd said:
ERIRV(whole) meets WDSC. Surprisingly, ERIRV(fractional) seems to also.
Markus replied:
ERIRV(fractional) doesn't meet WDSC. Example:
20 A=B=C>E>... 20 A=B=D>E>... 20 A=C=D>E>...
7 B>E>... 7 C>E>... 7 D>E>...
38 E>...
A majority of the voters strictly prefers candidate A to candidate E and ranks candidate A tied for top. Nevertheless, candidate E is the winner.
I reply:
WDSC doen't say that if a majorilty prefer X to Y, then Y mustn't win if that majority rank X tied for top.
Here's what WDSC says:
If a majority of the voters prefer X to Y, then they must have a way of voting that will ensure that Y won't win, without any member of that majority reversing a sincere preference.
Because you say that a majority prefer A to E, we can assume that you're saying that your rankings represent sincere preferences. Then, as you said, a majority prefer A to E.
Do they have a way of voting that ensures that E won't win, without any of them reversing a sincere preference? Sure. They can all insincerely vote A alone in 1st place.
When they do that, A has an immediate majority and wins.
The A=B voters who insincerely vote A over B, and the A=C voters who insincerely vote A over C, are falsifying a preference, but they aren't reversing a preference. WDSC only requires that they be able to keep E from winning without reversing a preference.
Of course, in that example, even unmitigated IRV doesn't fail WDSC. But I've posted examples in which unmitigated IRV fails WDSC.
For instance, my standard 3-candidate example:
Sincere preferences:
40: ABC 25: BAC 35: CBA
A majority prefer B to A.
But A wins unless at least some of the C voters insincerely vote B in 1st place, over C.
In ERIRV(fractional), if the C voters voted C=B>A, then we have these initial vote totals:
A: 40 B: 25 + 35/2 = 42.5 C: 17.5
C is eliminated and transfers its 17.5 votes to B, who then has 60 votes, the votes of all the B>A voters.
Bucklin & Participation:
But your Bucklin Partilcipation failure example is valid. It had seemed to me that Bucklin couldn't fail Participation because no X>Y voter ever gives a vote to Y without first giving one to X. But, as you pointed out, a set of X>Y voters who don't vote X 1st can, by adding to the total number of voters, prevent X from having an initial majority.
But, though Bucklin doesn't meet Participation, it's still the most easily-counted method that meets SDSC. WDSC & SDSC are a good accomplishment for such an easily-counted method.
I want to clarify that I still say that Approval is a strong 2nd to Condorcet, because I'm referring to actual proposals. Bucklin isn't proposed as a public method. Among methods proposed for public use, Approval is the 2nd best, after Condorcet.
As I said, if rank balloting is used, and since computer counting is available for public elections, there'd be no point in using any less than Condorcet. Condorcet meets SFC & GSFC, two criteria that Bucklin doesn't meet. SFC & GSFC are Condorcet's most impressive advantages.
Mike Ossipoff
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