[EM] Cardinal Pairwise: Guilty till proven innocent

[James Green-Armytage]

James replying to Mike...

James:
>They [voting systems] must be
>assumed to be assumed to be worse than the status quo until it can be very
>conclusively demonstrated that they are better.
Mike:
>
>But wait....Does Cardinal Pairwise pass Participation and Consistency? 

	No.

>Did 
>you know that Plurality passes those criteria?

	Yes.
>
>James, you can't expect us to take Cardinal Pairwise seriously till you
>show 
>that it's potentially serious violations of Participation and Consistency 
>aren't going to be serious problems. How you're going to prove that, I
>have 
>no idea. But you must prove it before Cardinal Pairwise can even be 
>considered.

	Of course one can't mathematically "prove" that some axioms are more
important than others. When I said "conclusively demonstrate", I didn't
mean it in a mathematically tautological way. All I meant was that the
burden of doubt should be cast on any new voting method, and that voting
methods designers should actively hunt for the flaws in theoretical
systems rather than assuming those flaws to be nonexistent until they
occur in practice. 
	Of course I am willing to accept some tradeoffs in abandoning one method
for another. If we lose participation and consistency by switching from
plurality to IRV or Condorcet, that is acceptable as long as a very
convincing argument can be made that the new benefits are clearly better
than the new liabilities. This argument isn't a mathematical proof, but
rather a holistic argument, e.g. one that explores the likely social and
political ramifications of the new method.
>
>Until you can prove that, there is a method that is _already_ known to be 
>better than Pluralitly in every way: Cardinal Ratings. Of course Approval
>is 
>one version of CR. CR passes Participation and Consistency, and
>additionally 
>passes FBC and WDSC, two criteria that Plurality fails.
>I don't know if you can find a criterion that Plurality passes and CR
>fails. 
>How silly a criterion will you have to come up with, in order to find one 
>that Plurality passes and CR fails?

	Well, what about the majority criterion? That is, this majority
criterion: "If more than half of the voters prefer candidate X to all
other candidates in the election, and vote sincerely, X should win." That
is, a special case of the mutual majority criterion where the majority set
has one member.
	Assume that a sincere vote in plurality means voting for your first
choice of the candidates who are running. This assumption may not be a
perfect one, but it is commonly made, and without it, it is very difficult
to evaluate plurality with respect to any criteria whatsoever.
	Given these definitions, plurality meets the majority criterion. As far
as I can tell, cardinal ratings and approval fail this criterion. Here is
an example.

55: A>B>C (100, 90, 0)
25: B>A>C (100, 10, 0)	
20: C>B>A (100, 30, 0)
Rating sums...
A: 5750
B: 8050
C: 2000

55: A>B>>C
25: B>>A>C
20: C>>B>A
Approval scores...
A: 55
B: 80
C: 20

>But Borda fails Majority Favorite, a simple votes-only criterion
>reasonably 
>met by Plurality and CR.
>
	Majority favorite? Is that more or less the same thing as the "majority
criterion" as stated above? I don't see how CR meets it. I must be missing
something...

James