[EM] [CES #4445] Re: Looking at Condorcet

[robert bristow-johnson]

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                  rbj at audioimagination.com

"Imagination is more important than knowledge."