[EM] The "Single Contest" method

[Jameson Quinn]

>
>
> >This would probably not test as well - it's hard
> >to get simulated voters to use absolute ratings in a meaningful
> >way -
>
> I am really curious why you say this. When my voters can rate the
> middle candidate either 33% or 67%, or 100% or 0%, they will just make
> this decision based on what works the best. In 3-slot Range they very
> nearly turn it into Approval. In MCA it depends on the scenario. In
> 3-slot CWP they feel free to give more middle ratings.
>
> By "meaningful" you don't mean "sincere" or something do you?
>

Well... sorta. More like "anchored by sincerity". The point is that with
real voters, if strategic pressure isn't too strong, the median will stay at
some predictable place, which then can be used for others' strategy. With
simulated voters, the smallest strategic pressure, or even a random walk,
will eventually push the median to max or min rating, and then the method
loses its power of discrimination.

So I'm not hoping that everyone will be "sincere", I'm just positing that
"sincere" should have some meaning which voters can fall back on if there
isn't any particular strategic reason not to. This is similar to Balinski
and Laraki's insistence on "common terminology of judgment", which they
spend several chapters of their book discussing.


>
> >but it would be more voter-friendly, both because empirical
> >results show that rated ballots are easier, and because it
> >removes the hard-to-explain and inevitably-strategic requirement
> >of setting an approval threshold. And I believe that this method
> >of automatically setting the threshold would naturally find a
> >threshold that was about right - around the median of the winning
> >pair, because the median naturally has the most approval-decisive
> >information per ballot. I'd call this method Automatic Single
> >Contest (ASC), because Single Contest Automatic Threshold has a
> >bad acronym.
>
> I'm interested to understand what you're proposing. You say to "auto-
> set the global absolute approval cutoff to whatever number maximizes
> the number of approval-decisive votes in the contest."


Let me be define the terms. If the pair with the greatest approval coverage
is A and B, then "approval-decisive votes for A" D(A,X) at threshold X means
the absolute number of ballots with A above X and B below X. The "mutual
approval" M(X) is the number of ballots which approve both A and B; and the
"mutual disapproval" U(X) is the ballots which disapprove both. Possible
cutoff metrics to maximize:

D(A,X) + D(B,X) : (what I suggested) On second thought, this could elect the
guy who most thoroughly beats Hitler.
D(A,X) * D(B,X) : Avoids the problem above, but too much of a focus on
"contested" results, whether or not these are majority results
min(D(A,X), D(B,X)) : like the previous, but worse
-max(M(X), U(X)): this looks good to me. Unlike the metric I first
suggested, this does target some form of "median" for the cutoff.
-(M(X) * U(X)): Similar to the previous

So, I guess I'm saying, instead of maximizing the approval-decisive votes,
minimize the max of (the mutual approvals or the mutual disapprovals). Or
perhaps their product.

JQ
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