[EM] Re: Efforts to Improve on CR's Strategy

[MIKE OSSIPOFF]

Bart had said:

>...  In your 10 candidate, 1 issue trial, are you able to account
>for why sincere CR, exaggerated CR, Condorcet, Borda, IRV, and Plurality
>all yield exactly the same average across 100,000 elections?  It looks
>like top-two Runoff is within 0.1% of the same score.
>

I think it's simply the case that with 1 issue, all voters' CR profiles
are precisely correlated (i.e., any two profiles differ only by a
multiplicative scale factor), so all these methods become equivalent.

I reply:

You forgot to tell us why you think that is so.

You continued:

What I call "ExaggerateCR" is not actually the optimal zero-info CR
strategy, which would be equivalent to Approval.

I reply:

And yet you have people voting that way in your simulation. Could that 
reduce the meaningfulness of the simulation's results? Yes.

You continued:

"Sincere strategy"? From my perspective all strategies are insincere.

I reply:

Obviously a matter of definition, and not meaning much unless the 
definitions are specified.

You continued:

Based on the optimum zero-info strategy, should the approval cutoff be
at the mean CR of ALL candidates, or of just the highest- and
lowest-rated candidates? (I assumed the latter for "ExaggerateAV".)

I reply:

Optimum Approval 0-info strategy, in public elections, is to vote (only) for 
the candidates whose utility for you is above the mean of all the 
candidates' utility.

You continued:

Here's a conceptual example that I think better illustrates the problem
that I observed. Suppose you vote in an election in which there are 6
candidates and you have no idea how anyone else votes. Your sincere CR
profile for candidates A ... F is
    SincereCR: A(0.7), B(0.5), C(0.3), D(0.1), E(-0.1), F(-0.3)
(This assumes signed CR's, with an approval cutoff of zero.) What I call
"ExaggerateCR" simply applies a linear transformation so that the max
and min CR's are +1 and -1:

I reply:

If you do anything other than mutliplying all of a particular voter's  
ratings by the same factor, then you'll get something that's meaningless.

And if you multiply different voter's ratings by different factors, then you 
don't have a valid CR count. Not that you're necessarily doing a CR count. 
It isn't clear exactly what you're doing.

You're using lots of new terms of your own, and it won't mean anything 
unless you define them.

Do that, and then write down exactly what you mean to say.

Mike Ossipoff

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