Richard Moore <[EMAIL PROTECTED]> wrote:
> deltaEU = X*( 100*deltaPa + 50*deltaPb )
> ...
> Consider that if
> 100*deltaPa + 50*deltaPb is positive, you will get a
> positive strategic benefit ...
> maximized if X is set to the full-scale positive
> rating. On the other hand, if the value in parentheses is
> negative, ...you would want to minimize the negative impact by
> voting B at the lowest end of the scale.
So we'd have to know deltaPa and deltaPb to know how to vote
strategically, or at least know whether the magnitude of dPb is >
twice dPa. I presume that if dPb = -2dPa, we vote sincerely.
Strategic voting (at least, among non-statisticians) is based on a
perceived runoff: a sense that the race is really between (or among)
a subset of the candidates. When voters have that perception, they
will normalize their votes for those who are. Granted. I don't think
that necessitates degenerating completely to Approval. Those who
aren't considered in the race would still be voted sincerely (to
scale).
Your example seems to ignore deltaPc, which has positive utility to
the voter. Is that because the support for C is zero? I'm not sure
that multiplication can properly be applied to utility. Is a utility
of 1 really infinitely more -- um, utilitous than a utility of zero?
Of course, I'm one of those non-statisticians I spoke of.
The other thing your example ignores is group dynamics: when a lot of
people are in the same situation, they will have similar decisions to
make, and a lot of them will choose similarly. Hence, the linearity
in X is questionable, because the population might effectively be
made small by a lot of people acting as one. (cf Goedel, Escher, Bach)
