[EM] Reverse Symmetry Criterion

[MIKE OSSIPOFF]

>As someone pointed out recently, most methods based on preference ballots
>fail the Reverse Symmetry Criterion. But how many of them still fail it
>when there is a Condorcet Winner? And how many of then still fail it when
>there is no possible assignment of ratings (consistent with the
>preferences) that would give the least and greatest candidate (hence all
>the candidates) the same average rating?
>
>It seems to me that these modified (weaker) Reverse Symmetry Criteria
>would be more useful in distinguishing good methods from bad (more useful
>than the version that most methods based on preference ballots fail
>anyway).

Markus has shown that BeatpathWinner meets the stronger Reverse
Symmetry Criterion. Cloneproof SSD does too, since it's equivalent
to BeatpathWinner. SSD meets that criterion in public elections,
because under those conditions it chooses the same as Cloneproof SSD.

So the strong version of the criterion is making a useful distinction.
It isn't unmeetable. There are a number of good methods that meet it--
methods that are the best by other standards & criteria too.

But you make a good point when you show that IRV fails even the
weak versions of that criterion.

Mike Ossipoff


>
>If your favorite method fails the ordinary Reverse Symmetry Criterion,
>then you can say, "Big deal, so does just about every other method."  But
>if your method fails these weaker versions, then you will have to make up
>a lot of ridiculous excuses or find a better method to support.
>
>So here they are:
>
>First version:
>
>If a preference list based method picks the same winner forward and
>backwards when there is a unique Condorcet winner, then it fails this
>modified reverse symmetry criterion.
>
>Second version:
>
>If a method based on preference ballots picks the same winner with
>preferences reversed when there doesn't exist any possible assignment of
>ratings (consistent with the preferences) that would give all of the
>candidates the same average rating, then the method fails this test.
>
>We have just seen that IRV fails both of these modified criteria.
>
>Forest
>

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