On 2/7/12 2:07 PM, Kevin Venzke wrote:
Hi Robert,
I think that the basic claim of "Condorcet doesn't necessarily pick
the option whom the elecotorate prefers" (in terms of
total utility) won't be too controversial. Any kind of model usually
assumes internal utilities (such as based on distances in
issue space) because we need these to figure out how voters
prioritize. One could try to assume that some set of
internal utilities might have some absolute, aggregable value. In that
case it is really easy to produce a scenario where the
majority favorite isn't the utility winner.
in the two-candidate case, you would have to assume unequal treatment
for voters. if all voters' votes have equal weight, you must accept
that the majority candidate is also the choice maximum general utility
to the society that the voters come from.
All you need is one case and you get Clay's "not necessarily."
sure, but attaching "not necessarily" to "proven mathematical fact" is a
pretty meaningless semantic. the proven mathematical fact says
essentially nothing. like a tautology.
but when Clay says that Score or Approval is better at picking the
Condorcet winner than is a Condorcet-compliant method, *that* is no
tautology is obviously controversial, since it says that there is a
number closer to 3 than the number 3 itself.
You ask how we can decide, then, not to elect voted majority
favorites. Assuming voters are strategic I don't know of a good answer
to this.
You suggest a model where there are only two candidates and the
voter-for-candidate utilities are all either 0 or 1.
if it isn't 0 (for when you don't get who you voted for) and 1 (for when
your candidate is elected), then some voter is diluting their utilities
and i think it's pretty useless and in bad taste to ask voters to do
that explicitly with a Score ballot.
If that's an accurate model then Clay's claim doesn't work. But with
virtually any other model it will be true sometimes
that the voted majority favorite isn't the utility maximizer.
well, once we get three or more candidates, it's a question as to whom
either the "majority favorite" is or who is the "utility maximizer."
Condorcet doesn't go there. Condorcet makes no other assumptions other
than the "simple majority" and "one person, one vote" (which are what we
already base two-choice elections on) when any two candidates are paired
up. and then Condorcet imposes logical consistency: If Candidate A is
the best choice for office, then Candidate A must be a better choice
than Candidate B. And Candidate A must be a better choice than
Candidate C. etc.
--
r b-j [email protected]
"Imagination is more important than knowledge."
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