[EM] Will to Compromise

[Jobst Heitzig]

Dear Greg,

you wrote:
> Nondeterminism is a delightful way of skirting the
> Gibbard-Satterthwaite theorem. All parties can be coaxed into exposing
> their true opinions by resorting or the threat of resorting to chance.

Actually, if I remember correctly, that theorem just said that Random Ballot was the only completely strategy-free method (given some minor axioms such as neutrality and anonymity), so it's not really "skirting" it but just taking it seriously. 

However, it seems some minor possibilities for strategizing are acceptable when they allow us to make the method more efficient. FAWRB tries to be a compromise in this respect.
 
> I don't dispute that. The nondeterminsitc methods I have seen appear
> to be designed to tease out a compromise because a majority cannot
> throw its weight around.

Right, that's the main point.

> The abilities of nondeterministic methods to generate compromises is
> formidable, but since we speak of utility, I would like to point
> something out.
> 
> 1) Using Bayesian utility, randomness is worse than FPTP.

Two answers: i) Please cite evidence for this claim, ii) Bayesian utility is not a good measure for social utility in my opinion. We had lengthy discussions on this already a number of times on this list, so I won't repeat them. Instead, I will produce evidence from simulations this weekend which shows that no matter what measure of social utility is used, Random Ballot does not perform much worse than optimal.
 
> 2) False compromises are damaging

What do you mean by "false"? If a proposed compromise fails to be desirable by most voters over the Random Ballot lottery, it will not get much winning probability. If it is, on the other hand, it is not a "false" but a good compromise. The simulations I will report about this weekend show that usually we can good compromises to exist which have quite large social utility.

> The reduced power of a majority means that at any choice with a
> greater-than-random-ballot average utility is a "good compromise"
> Notice how lousy the Bayesian utility of random ballot is and you
> begin to see my point.

See above. In simulations with well-known preference models, Random Ballot results are not lousy at all.

> Also note that the method for determining the compromise is
> majoritarian (to the extent that approval is) so the intermediate
> compromise procedure is a red herring that produces some nasty
> side-effects. The compromise is determined to be the most-supported
> at-least-above-average candidate. How does this avoid the original
> criticism of majoritarian methods?

You are right in that the majority still has some special influence on the *nomination* of the compromise. But the important difference to majoritarian methods is that they can't make any option get more winning probability than their share without the minority cooperating in this. So, yes, they can present the minority with a compromise they value only slightly better than Random Ballot. This is not perfect yet, but it guarantees the minority to get a better-than-average result where a majoritarian method doesn't guarantee a minority anything!

Yours, Jobst