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

[Abd ul-Rahman Lomax]

At 02:37 PM 2/8/2007, Warren Smith wrote:
>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.

Warren has a tendency to hyperbole, but his point should not be 
missed. Unless and until it is confirmed, his work must be taken with 
some salt, but it nevertheless does show what he claims. It appears 
that some are criticizing it without being familiar with it, perhaps 
on the basis that they find the results unpalatable. But the *huge* 
problem with a great deal of EM evaluation is that it is so often 
based on election criteria, presumed to be desirable, rather than on 
some kind of measurement of success in *results*.

Warren's work is not based on any specific assumption of how voters 
vote. Rather, it applies various stated assumptions, showing the 
effect of sincere voting, strategic voting, and mixes, to a large 
number of sample elections.

As he noted, the result that Range is more successful at picking the 
sincere Condorcet winner than Condorcet methods is, to say the least, 
counterintuitive. The problem, of course, is strategic voting, where 
voters do not express their sincere preferences, fearing that if they 
do, the result will be less satisfactory than if they shift them.

One of the characteristics of Range is that there is never an 
incentive to reverse preferences. Strategic or insincere voting in 
Range is limited to equating candidates at the extremes when, in 
fact, you do have a preference between them. Warren calls this 
partially sincere. I've called it "magnification;' the gain on an 
amplifier has been increased until the output pegs the meter. The 
contrast on an image has been increased until some detail is lost in 
total black or white. It isn't insincere in the same way as 
preference reversal is.

Warren likes Range with unlimited resolution because it becomes 
possible to express fine differences in preference while retaining 
effectively full voting power. (It is true that if you downrate B 
from A by a thousandth of a point, you could cause B to lose to C. 
But the possibility becomes vanishingly small. One way to look at a 
range vote of 0.999 -- compared to 1.0 -- is that it is 
one-thousandth of a vote different.

Warren's results though, were with limited Range resolution. I think 
he has done work with Approval, with Range 10 and with Range 100.

But the Condorcet Criterion itself is severely limited. Once one 
realizes how it is quite easy for the best candidate (from a social 
utility point of view, which is really the only criterion that has 
been suggested that actually measures election performance) to not be 
a Condorcet winner, the Condorcet Criterion can be seen as less than ideal.

Generally, the neglect of preference strength is the elephant in the 
living room of ranked methods. It is trivial to give simple examples 
that show, beyond doubt, how Condorcet can choose the wrong winner. 
What is really odd to me is that it seems to have taken so long to 
recognize this. Does anyone know when this began to show up in the literature?

Once a method allows preference strength to enter into consideration 
in determining the winner, the method *must* fail Condorcet. (With 
the limited exception that if preference strength is only used to 
choose between members of a Condorcet cycle, there need be no 
Condorcet violation.) Likewise the Majority Criterion, as generally 
stated, will not be satisfied in all elections.

However, quite arguably (I'd say *clearly*), Range fails Condorcet in 
order to choose a better winner. This is absolutely clear if all 
voters vote sincerely and accurately. It is muddier in the presence 
of strategic voting (the definition of which becomes somewhat 
problematic with Range), but Warren's results show what some of us 
anticipated: strategic voting doesn't do nearly as much harm as some 
Range critics have claimed it would.