[EM] Reverse Symmetry Criterion

[Martin Harper]

Forest Simmons wrote:

> I like your idea.  But I still think there is no stigma attached to
> failing the reverse symmetry criterion when there is no (unique) Condorcet
> winner, so I would suggest that you throw those out of the count.
>
> Forest

Hmm - I'm not entirely convinced. It's certainly more reasonable to fail RSC when
there's no condorcet winner - but I'd rather state this the other way: it's hugely
bad to fail RSC when there's a condorcet winner, and methods which do so should be
avoided like the plague. However, all other things being equal, I'd say that a
method which passes RSC is better than one that passes RSC only when there's a
condorcet winner.

Here's a stupid example:

11 A>B>C>D>E>F
10 B>C>A>E>F>D
9 C>A>B>F>D>E

Now there's neither a Condorcet Winner, nor a Condorcet Loser, but I reckon any
method which elects the same person as both the best and worst candidate has to
have made a mistake somewhere...

On a side note, it's possible that a set of votes has a CW, but no CL (or vica
versa). Would you judge such situations as having no stigma either? Or to have less
stigma than the case where there is both a unique CW and CL?