[Election-Methods] [EM] RE : Re: RE : Is "sincere" voting in Range suboptimal?

[Abd ul-Rahman Lomax]

At 12:44 PM 7/23/2007, Kevin Venzke wrote:

>--- Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> > We now know that in the two-voter case, the optimal vote is sincere.
> >
> > This alone would be sufficient to refute the insufficiently qualified
> > claims made that started this discussion. However, on the face of it,
> > it is possible that in the large-election case, the advantage of
> > voting sincerely vanishes. I am in process of examining that possibility.
>
>Have you changed your opinion?

Is the Pope Catholic? My knowledge deepens, my 
opinions vanish like the fog in the sunshine.

>  When I produced simulation results to
>show that in the zero-info case one improves one's expectation under
>Range by voting at the extremes, you essentially ridiculed me for bothering
>to show something so obvious.

I'd be interested to see how I made such an 
error. Perhaps I'd been influenced by the barrage 
of experts claiming this.... and I'd like to see those simulations again.

Note that what I've done now is *not* a 
simulation. It is an exhaustive listing of the 
election possibilities, looking first at the 
two-voter situation, then generalizing this to 
many-voter elections by noting that only in 
certain elections does the vote of our voter make any difference.

"Making a difference" means that there is a 
possible vote cast by the voter which would 
change the outcome. Aside from initial vote 
patterns -- before our voter cast the vote -- 
where such a change can occur, the voter's vote 
is moot, it doesn't matter how the voter votes as 
far as determining the winner is concerned, so 
the voter might as well vote sincerely, it may 
improve how well he or she sleeps at night....

And it is a remarkable result that the sincere 
vote is optimal. If I've erred, my suspicion 
would be that somehow I misindentified some case 
and the truth is that the sincere vote and the 
Approval style vote have the same utility. What I 
suspected, embarking on this, was that in the 
equal preference situation I studied, the 
Approval Vote and the sincere vote might have the 
same expected utility; I was surprised to get the 
result I did. I was *expecting* to see that 
result with imbalanced utilities, not with the balanced case.

By the way, if by "voting at the extremes", 
Venzke means casting extreme votes for the 
favorite and most disliked, I was right to 
ridicule him. So to speak, I don't think it is a 
good thing to ridicule people for taking steps to 
prove what seems obvious, somebody should do it, 
or else we keep on thinking that the Majority 
Criterion is an absolute necessity for a good election method. It's so obvious!

Until one realizes that preference can be 
infinitesimal or maximal, and the MC doesn't care....