[EM] Re: Cardinal Pairwise: Guilty till proven innocent

[MIKE OSSIPOFF]

I'd said:

>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.

You reply:

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.

I reply:

Then the burden of proof is on you, to show that it's ok for Cardinal 
Pairwise to fail Participation, Consistency, and votes-only IIAC.

As I said, major long-tem study is needed before people can consider a  
method such as Cardinal Pariwise that, in some ways, is known to be worse 
than Plurality.

You continue:

	Of course I am willing to accept some tradeoffs in abandoning one method
for another.

I reply:

Oh, so now it's that trade-offs are acceptable, even though your method in 
some ways is known to be worse than Plurality.

You continue:

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.

I reply:

In other words, we should take your word for it? You haven't even begun your 
arguments.

I'd said that CR doesn't fail anything that Plurality doesn't fail.

You say:

	Well, what about the majority criterion?
I reply:

CR passes the Majority Criterion.

You continue:

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."

I reply:

That isn't the Majority Criterion. The Majority Criterion is a votes-only 
criterion:

If a set of voters consisting of more than half of the voters vote X over 
each of the other candidates, then X should win.

[end of Majority Criterion definition]

You've written a new criterion that could be called the "Preference Majority 
Critrerion" (PMC). It's ironic that some people on EM refuse to recognize 
any criterion that mentions preference, because they feel that tradition 
requires that criteria be votes-only--and now you want to say that the 
Majority Criterion is a preference criterion. EM: You can't have it both 
ways.

You continue:

	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

I reply:

It's a perfect one. At least as I define sincere voting:

A voter votes sincerely if s/he doesn't falsify a preference or fail to vote 
a preference that the balloting system in use would have allowed him/her to 
vote in addition to the preferences that s/he actually did vote.

[end of sincere voting definition]

Elsewhere on EM I've defined voting a preference and falsifying a 
preference.

In Plurality, by that definition, to vote sincerely in Plurality is to vote 
for your favorite.

You continue:

..., but it is commonly made

I reply:

Good.

I'd said:

>But Borda fails Majority Favorite, a simple votes-only criterion
>reasonably met by Plurality and CR.
>

You say:

	Majority favorite? Is that more or less the same thing as the "majority
criterion" as stated above?

I reply:

How could it be? I said that Majority Favorite is a votes-only criterion. 
It's also known as the Majority Criterion. What you've stated above is not 
the Majority Criterion. It's a new criterion that could be called the 
Preference Majority Criterion (PMC).

You've come up with a new critrerion, in order to find something that 
Plurality passes and CR fails.

You continue:

I don't see how CR meets it. I must be missing
something...

I reply:

Actually, it doesn't, but I didn't know that before.

By the definition of voting X over Y, a voter, in CR, votes X over Y if s/he 
gives more points to X than to Y. Say 51% of the voters, in 0-100 CR, give 
one more point to X than to Y. The other voters give 100 to Y and 0 to X.

So CR fails the Majority Criterion. Well, there's still a method that isn't 
worse than Plurality in some way: Approval. But not by your new Preference 
Majority Criterion.

But PMC's indication that Plurality is better than Approval isn't very 
convincing. Those voters who vote for X and Y even though they prefer X to Y 
are presumably doing so because they're making an informed strategic 
decision that they need to help Y beat someone worse. Approval gives them 
the freedom to vote for compromise in addition to favorite. Plurality 
doesn't. Does it make any sense to call that an advantage of Plurality over 
Approval?  PMC penalilzes Approval for giving voters more freedom than they 
have in Plurality. Maybe we should rename PMC the Freedom-Hater's Criterion 
(FHC).

Maybe I should have said that there's no criterion that Plurality passes and 
Approval fails, except maybe for new criteria that could be designed for 
just that purpose.

Anyway, if you can invent new special-purpose ad-hoc criteria, so can I. 
Here's a PMC that CR (including Approval) passes:

A method fails PMC if it's possible to contrive a configuration of 
candidates, voters, and voter preferences such that a majority prefer X to Y 
and it isn't possible to contrive a votes-configuration such that everyone 
votes sincerely (according to the abovementioned voter preferences) and X 
wins.

[end of PMC definition contrived to make Approval pass PMC]

But what if we say that your PMC is PMC,  and say that in that way CR, 
including Approval, is worse than Purality?

Well, someone could argue for rejecting a special-purpose ad-hoc new 
criterion, and go instead by the existing Majority Criterion, which Approval 
passes. So we've still got one method that isn't Plurality-inferior: 
Approval.

But people are leery about Approval because they think it gives some voters 
more power than others, or violates a very important standard called 
1-person-1-vote. It can be shown that Approval doesn't give as unequal power 
as Plurality does, and that 1p1v is a worthless rules-criterion, but whether 
that can be shown to the average voter is another matter.

What can I say, James. Learn to like Plurality :-)

Mike Ossipoff

_________________________________________________________________
Don’t just search. Find. Check out the new MSN Search! 
http://search.msn.click-url.com/go/onm00200636ave/direct/01/