[EM] ERIRV(fractional) doesn't fail WDSC in Markus' example.

[MIKE OSSIPOFF]

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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