Alex had said:
That's not entirely true. The famous Gibbard-Satterthwaite (GS) Theorem makes reference to preferences. The theorem, crudely speaking, says that there's no ranked election method that doesn't, from time to time, give voters an incentive to vote insincerely. You could think of the method by first imagining that every voter votes sincerely. Then, based on tallies of sincere votes, ask if any of the voters would have preferred the outcome that would have obtained if he or she individually had voted differently. The theorem says that there will always be cases where at least one voter would have been happier if he or she had voted insincerely.
Markus replied:
That's not entirely true. It is something completely different whether someone (like Gibbard or Satterthwaite) refers to sincere preferences in the motivations of his criteria and then defines his criteria in terms of cast preferences or whether someone (like Mike Ossipoff) defines his criteria in terms of sincere preferences.
I reply:
I must admit that I havenīt seen the Gibbard-Satterthwaite theorem, but, as Iīve heard, Gibbard & Satterthwaite said, and showed, that every nonprobabilistic method can sometimes give voters incentive to vote contrary to their preferences.
Now, Markus, tell me if Iīm mistaken about this, but it sounds to me that they made a statement about voting systems that involves preference--what you would call sincere preference.
Therefore, thereīs good precedent for making, about voting systems, statements involving preference--which you call sincere preference.
A general statement that nonprobabilistic methods need strategy. What I mean by nonprobabilisitic method is nonrandom methods, as Iīve defined that term.
So, G & S made a general statement about the strategy need of nonprobabilistic methods.
The defensive strategy criteria could, and should, be regarded as particularizations of that general statement.
...statements about when partticular methods need strategy, and what strategy particular methods need.
Mike Ossipoff
Markus Schulze
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