[EM] Bad Condorcet winners?

[MIKE OSSIPOFF]

>A Bad Condorcet winner is a low utility Condorcet winner.  For those who 
>see
>the primary purpose of election methods to elect the highest utility
>candidate, and see voters as rational utility maximisers, this is a
>crucially important flaw.
>

This would require that there's a candidate who'd beat each of the
others in separate 2-way elections, and he's so unliked that he
minimizes social utility. How likely does that sound to you?

The scenario I've heard is that there's a voter-median candidate who
is unknown, and people vote this unknown over the rival party.
Give voters credit for knowing the difference between "unknown" and
"better". Voters are adults, and they must judge who seems better,
and we should accept their choice. Besides, the voter median point
will be a popular crowded place, and it's unlikely that an unknown
will be the only candidate there.

Or in some versions of the scenario, the voter median candidate is someone 
with much non-positional disutility (crooked, scandals, etc.)
so that each side rates him barely over the opposite side.

Again, though, that universally-undesirable candidate won't be the
only one at the voter median. There will be popular candidates, honest
candidates, ethical candidates, well known candidates, candidates with
combinations of those attributes.

Anyway, I don't think it's fair to assume that Middle is the only
one who is crooked, scandal-ridden, etc.

Another thing, Condorcet is tops for electing CWs. CWs are typically
social utility maximizers. You've misunderstood how SU is important.

Average SU is what gives a measure of your expectation for some distant
election by an as-yet unchosen method. The better the average SU of
the method that we choose, the better your expectation for that future
election. Condorcet has better average SU than almost any other method.
Perhaps Borda beats Condorcet--if everyone voted sincerely in Borda.
But pairwise-count methods in general do far better than any other
methods, by average SU. IRV is way down there in that regard, due to
its "squeeze" problem, which tends to often defeat voter median
candidates.

So Condorcet could elect a scandal-unpopular CW, and so you want to
use IRV which tends to jump to extremes, resulting in a far poorer
average SU?

And now that you mention universally disliked candidates winning,
IRV, but not Approval, fails UUCC, the Universally Unpreferred Candidate
Criterion. UUCC is about the possibility that when everyone prefers
X to Xc, and Xc wins, and then someone changes their ballot to no longer
vote Xc over X, that causes the election of someone whom they
like less than Xc. Plurality fails that criterion. IRV fails it.
Approval passes. For a precise wording, check the archives for 2000.

I don't get into Condorcet vs Approval arguments, because they're
both excellent methods, by the standards important to most people.
Approval of course does far better than IRV in terms of average SU.


Mike Ossipoff




_________________________________________________________________
Get your FREE download of MSN Explorer at http://explorer.msn.com