[EM] Markus, Gibbard-Satterthwaite

[MIKE OSSIPOFF]

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 haven´t seen the Gibbard-Satterthwaite theorem, but, as 
I´ve 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 I´m 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, there´s 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 I´ve 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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