[EM] Re: "More general 5-candidate IRV failure example"

[Markus Schulze]

Dear Mike Ossipoff,

you wrote (26 Aug 2003):
> Please read the posting that you're replying to. I didn't say
> in that posting that Nurmi said that the compromising voters
> were "criminal", "cheating", "shameful" or "dishonest". Neither
> did I say that you said that compromising voters were "criminal",
> "cheating", "shameful" or "dishonest".

You did. You wrote (23 Aug 2003):
> To Markus's authors, and therefore to Markus, the important thing
> about strategy is that someone is cheating the voting system by
> voting insincerely. So if you have to give up your hopes of voting
> for Nader, in order to elect a Democrat to keep a Republican from
> winnilng, then shame on you :-) You're cheating the voting system
> by votinlg insincerely, and you must be prevented from getting
> away with your dishonesty. But is that really the problem, or is
> that just what the problem is from the viewpoint of Nurmi, and,
> therefore, of Markus? No, I'd say, and most would agree, that the
> real problem there is that you're stratgegically forced to bury
> your favorite. You're the victim, not the criminal. That's the
> difference between Markus and his Nurmi, and the rest of us.

******

You wrote (26 Aug 2003):
> You said that when I define defensive strategy in terms of the CW,
> then it's a presumption of mine that non-Condorcet methods are
> lousy methods. Then, by "Condorcet methods", you must mean
> Condorcet Criterion methods, a class of methods that includes much
> more than just Condorcet's method. But, then again, I wouldn't
> want to try to guess what you mean, and I sure don't want to keep
> debating it. If I misguessed what you meant, let's not have that
> be an issue. One wording of Condorcet's Criterion is that if
> there's a CW, and people vote sincerely, the CW should win. So
> when you said that my definition mentioning the protection of
> a CW's win means that non-Condorcet methods are lousy, it's
> reasonable to guess that, by "Condorcet methods", you mean
> methods that meet the Condorcet Criterion.

We both know that Condorcet has proposed 3 different methods.
Therefore, there is no unique "Condorcet's method."

Proposal 1:
> To compare just 20 candidates two by two, we must examine
> the votes on 190 propositions, and for 40 candidates, on 780
> propositons. Besides, this will often give us an unsatisfactory
> result; it may be that no candidate is considered by the
> plurality to be better than all the others, and then we would
> have to prefer the candidate who is just considered better
> than a larger number; and when several were considered better
> than the same number of candidates, we would have to choose
> the candidate who was either considered better by the greatest
> plurality, or worst by the smallest plurality.

Proposal 2:
> From the considerations we have just made we get the general
> rule that whenever we have to choose we have to take successively
> those propositions that have a plurality - beginning with those
> that have the largest - and to pronounce the result as soon as
> these first propositions create one.

Proposal 3:
> Create an opinion of those n*(n-1)/2 propositions that win
> most of the votes. If this opinion is one of the n! possible
> then consider as elected that subject to which this opinion
> agrees with its preference. If this opinion is one of the
> (2^(n*(n-1)/2))-(n!) impossible opinions then eliminate of this
> impossible opinion successively those propositions that have
> a smaller plurality and accept the resulting opinion of the
> remaining propositions.

Markus Schulze