[EM] Getting carried away and claiming RV is as good as Condorcet...

[Warren Smith]

Ossipoff:
Range Voting isn't a bad method, and it's very winnable, but let's not get carried
away and say that RV is as good as Condorcet.

--my earlier post which stimulated this, was merely claiming that, as a matter
of experimental fact, Range Voting produces Condorcet winners more often than
Condorcet methods do.  At first this statement seems impossible by definition,
but the reason it is true is I am speaking of a 50-50 honest+strategic voter mix,
and asking what it the probability the winner is the same as the (honest voter)
Condorcet winner.

My computer sims showed that range voting does so more often than Condorcet methods
based on rank-order ballots.  Paradoxical seeming.  But true.

Since this is an experimental fact, it is indisputable.  Computer simulations.
The page discussing this is
    http://www.rangevoting.org/StratHonMix.html
(Also, same results happen for other mixes than 50-50...)

CAVEAT:  I should note that IEVS presently is only doing rank order ballots, I.e.
equalities in rankings were forbidden in these sims.   Quite possibly the situation
would change in future IEVS versions that will permit rank-equalities and wv-condorcet methods.
I urge EMers to help me program more such stuff into IEVS.  The IEVS source code
(which continues to evolve) is available
    http://www.rangevoting.org/IEVS/IEVS.c

To riposte to the caveat, I note that there are theoretical reasons why range voting is highly
likely to generate honest-voter-Condorcet winers, when the range voters are strategic.
The theorem is presented at
    http://www.rangevoting.org/AppCW.html .
I am not sure that Ossipoff was aware of this theorem or that he was aware of my computer-sim
results.  I want to make it clear I am not just ranting the counterintuitive claim that
range voting is more likely to generate Condorcet winners than Condorcet methods.  I am proving
it via both theorem and computer simulation.
(The computer sims are independent evidence from this theorem since they were not using the
kind of strategic voters in the theorem, at all.)

In the model of strategic behavior in this theorem, range voting with strategic voters
generates Condorcet winners 100% of the time when they exist.  Condorcet methods -
even wv-condorcet methods with rank-equalities permitted - presumably do so less than 100%
of the time?  If yes, then range is definitely better than Condorcet methods for the purpose
of generating Condorcet winners;  if no, they are the same.

In my view, this theoretical plus experimental evidence is a very strong reason for
Condorcet supporters to prefer range voting.   Condorcet supporters presumably want
to elect Condorcet winners.  Therefore they should support simpler methods more
likely or as likely to do so, than Condorcet methods.  Namely, range voting.

Warren D. Smith
http://rangevoting.org