[EM] Borda strategy

[Richard Moore]

MIKE OSSIPOFF wrote:

> >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).

> You're fairly sure that Condorcet uses Weber's strategic values?

On the contrary. I'm fairly sure a Condorcet strategy would use the
identity matrix, though it could be possible that it might deviate
(slightly) from the identity matrix. So except for those deviations,
if they exist, I don't think the Condorcet matrix is very interesting.

> And I wasn't aware that we'd discussed any other strategic values.

Not until now.

> (Actually Weber had a different name for those. "Strategic value" is
> a term that I got from Merrill--it seems to be more descriptive).

And I like the term myself. I've been using awkward phrases like
"vote utility" so I think I'll adopt "strategic value" from here on.
Thanks for the suggestion.

> In the event that people actually used strategy in non-0-info
> Condorcet, it would only make sense as a game-theory sort of situation.
> I'm not so sure that you'd have a reason to calculate Weber's strategic
> values.

Of course not. The strategy matrix is different. The strategic values will
equal the voter's utilities if the strategy matrix is the identity matrix.

> In IRV it wouldn't be enough to calculate Weber's strategic values,
> which is what you say your strategy matrix is about.

I do? I remember saying the strategy matrix for approval is related to
Weber's strategic values. But I think you may be overgeneralizing if
you interpret that to mean that an IRV strategy matrix would produce
anything at all like Weber's results.

> In Runoff, where it's vote-for-1, there's something roughly analogous
> to strategic values, involving several summations and having many kind of
> probabilities as input. But I'm not sure what "strategic value" could
> mean in a rank method.

In a rank method, you'd calculate the strategic values of a vote for each
candidate. You then rank the candidates on your ballot according to
those calculated values.

Not a very interesting calculation if you use the identity matrix. In fact,
with zero info, you use the identity matrix for IRV and Condorcet alike.
The strategy matrix only becomes interesting for non-zero info strategies.

 -- Richard