[EM] Range Voting "unbeatable"?

[Jameson Quinn]

2009/8/31 Warren Smith <warren.wds at gmail.com>

> >What you could do is take a "poll" and have 10 random voters.  You
> then work out optimal assuming that they are the electorate.
>
> --there is no such thing as "optimal strategy" in games with >=3
> players.


This is true.


> Game theory breaks down.


I disagree. The big result is the "Nash equilibrium", which requires perfect
information, and is only unique under certain limited circumstances. In
other words, in most cases, there are several possible equilibria. For
instance, if all voters strategize based on expecting each other to focus
only on two arbitrary "frontrunners", that can be a self-fulfilling
prophecy; but other equilibria could also be possible under some systems,
such as: a mixture of honesty, offensive strategy, and defensive strategy;
or perfect honesty if polling evidence suggests that strategy won't work for
anybody and gang-up-against-the-one-frontrunner strategy otherwise.


>  So, in general, this cannot be
> done.  The only way to do it is to add to game theory some other
> ingredient, such as some model of how the other voters act
> (which will thenbe, in fact, false, since it isn't the way YOU are
> acting!).


As I understand it, the point of Nash equilibrium, the reason it's called
"equilibrium", is that in such cases the model for how other voters act can
include the fact that they're expecting you to act under the same model. So
it is self-consistent. In general, though, it is not unique; which of the
various (or infinite) possible equilibria the system settles into can depend
on many factors.


>
>
> --------
>
> Also, to reply to (yet another) confused claim by Jameson Quinn, he
> follwoing K.Venzke had the wrong notion that
> (i) range voting was "absolutely unbeatable" with honest voters using
> Bayesian Regret as yardstick
> (ii) which is false, and a counterexample is the BRBH voting system in my
> paper
> (iii) so then JQ replied this was only under some unrealistic model
> (called RNEM in this case)...
> (iv)  which completely missed the point that of course, under pretty
> much any other model, some other voting system would have beaten range
> voting's Bayesian Regret.   The point of RNEM model was not its
> realism (which was poor to middling), but rather that it was
> sufficiently simple that you could work a lot of things (such as the
> BRBH voting system, and its Regret) out as explicit formulas.


"pretty much any model" is true, as is "pretty much any probabilistic
(linear) combination of models" (which would be another valid way to compare
systems - "I want the system that does best on average across this range of
voter behaviour"). So you're basically right here. My point is that that
doesn't give you the right to say that I'm categorically wrong, because it
is certainly possible to create a model, or a range of models, in which
Range voting is the best system, and even easier to create a (range of)
model(s) in which it's better than any given system such as BRBH.

If it would help, I can stop it with the quibbling about minor points. I
want to be discussing practical questions here. I started off the parent of
this thread with a provocative big-picture statement, trying to provoke
debate about that larger point. I feel that getting caught up in whether
Range has the best possible BR with honest voters, or merely the best out of
any conceivable system that anybody would ever honestly advocate as a good
idea in practice, is distracting us, and insofar as that distraction is my
fault, I'd be happy to back down - that is, to cede any further debate on
this point.

I'll certainly try to avoid lightly using words like "absolutely" or
"utterly" around here in the future, to try to avoid overheated debates. And
in response, I'd ask others to do the same. I still want you point out where
I'm wrong, but can you please not call me names? I may deserve it, but I
doubt it advances the debate.

Warren, let me say that I owe you a significant intellectual debt, and also
an apology (sorry) for incorrectly assuming I could guess your position on
Range and BR. You owe me nothing but civility. Peace?

Thanks,
Jameson
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