[EM] Borda strategy

[Richard Moore]

Mike,

By strategy matrix, I mean the matrix that would be multiplied by
the voter utilities to get what you call the strategic values. Asking
what the matrix looks like is not the same as asking what the
strategy should be. Even though you don't need a strategy (other
than sincere ranking) for Condorcet, that matrix exists (for
practical purposes, I believe it's the identity matrix). So it was a
bit of a rhetorical question where Condorcet is concerned.

For Borda, and for that matter, for cumulative voting, I think there
are some interesting things to be learned from looking at the strategy
matrix. Not things to be learned about strategy, but things to be
learned about the methods themselves. This may even point to ways
to improve those methods. Probably, others have already picked up
on this, and I'm just being redundant.

I suspect there is a mathematical way to calculate an IRV strategy
matrix, at least in principal. It would probably fill several pages,
though. I also suspect that, for some regions of probability, the
values in that matrix will have some ugly characteristics. Actually,
I don't suspect it, I know it, but a mathematical proof of IRV's
badness wouldn't be a bad thing to be able to point to. Would
such a proof be possible? I don't know.

 -- Richard

MIKE OSSIPOFF wrote:

> >2. What does a strategy matrix look like for Condorcet? For Borda?
> >For IRV? What conclusions can we draw from those?
>
> Borda strategy is to rank the candidates in order of their
> strategic value. I told how strategic value is calculated in a
> previous posting, but I'll re-post it upon request.
>
> The important thing about Condorcet is that voters don't need
> strategy.
>
> In 0-info elections, Blake pointed out that in a 3
> candidate election, it's sometimes advantageous to insincerely
> uprank your 2nd choice by voting him equal to your 1st choice.
> Actually that's so if his utility for you is more than 2/3 of
> the way from your last choice to your 1st choice.
>
> I don't consider that important because our elections are not 0-info,
> and because you'd only benefit from it in natural circular ties.
>
> In non-0-info elections, someone could try offensive order-reversal,
> and in fact the only people with reason to use strategy are the
> person wanting to try offensive order-reversal and the person
> defending against it. It's very unlikely that offensive order reversal would
> be tried by enough people to change the election result.
> That means that in Condorcet you can ignore strategy. SFC & GSFC
> are about that.
>
> IRV strategy? Cox has described Runoff strategy, and IRV strategy
> would be a vastly more complicated extension of that. So it isn't
> just that IRV strategy is more drastic, as compared to Approval--
> it's also incomparaby more complicated. I haven't heard of anyone
> writing a formula for it.
>
> You might say that if the IRVies succeed in enacting IRV, it
> will be necessary for someone to calculate its strategy. Not as
> far as I'm concerned--I just won't vote in IRV elections.
>
> Mike Ossipoff
>
> >
> >  -- Richard
> >
> >
>
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