[EM] Tideman and GMC
nkklrp at hotmail.com
Sat May 13 14:38:00 PDT 2000
>You wrote (11 May 2000):
> > The older "Tideman fails GMC" example posted by Mike O was even
> > more extreme, showing the Schulze method preferred a candidate
> > even though no voter preferred it to the Tideman winner which
> > beat it pairwise.
>I couldn't find in the archives Mike's example where the Schulze
>method chooses a Pareto inferior candidate. Could you please
>repost this example?
Steve didn't say that Beatpath Winner chose a Pareto inferior
candidate or violated Pareto. He merely said that it chose
a candidate whom no voter preferred to the Tideman winner, and
which was pairwise-beaten by the Tideman winner.
That doesn't require a Pareto violation. For instance, say
that a few voters rank the Tideman winner over Beatpath Winner's
winner, and that the rest of the voters are indifferent between
those two. The situation that Steve described exists, without
a violation of Pareto.
Actually, though Pareto is usually described in terms of
everyone preferring one candidate to another, I believe that
what's really meant by the Pareto criterion is that a candidate
shouldn't win if another candidate is _voted_ over him by
all the voters. If that criterion were really about sincere
preferences, then lots more methods would fail the criterion.
UUCC, however, is about sincere preferences.
I don't have a copy of the "Tideman fails GMC" example, and
I haven't looked it up in the archives yet.
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