[EM] A few more words about Reversal-Symmetry

[Michael Ossipoff]

Suppose you and I are candidates in a rank-balloting election.

One ballot ranks me in 1st place, and you 2nd to last.

Another ballot ranks me last, and you in 2nd place.

Those two ballots seem to cancel eachother out. If the count-rule is
Borda, or a pure pairwise-count method, one that looks only at
pairwise order comparisons, then those two ballots will indeed cancel
eachother out.

But is that somehow necessary? Or is there some reason why a voting
system must be a positional voting system, or a pure pairwise-count
method?

1st place rank-position means more than just order or distance above
another candidate. Favoriteness, top-rating, has significance beyond
that.

For one thing, in particular, a count of ballots ranking someone in
1st place is a measure of a faction-size. Such a measure is helpful as
part of one way of automatically avoiding the chicken dilemma, as ICT
does.

The Plurality voting system might seem to give top-count,
favoriteness, a bad name. But actually favoriteness isn't without
meaning, relevance and value. ICT doesn't share any of Plurality's
problems.

1st choice rank-position therefore has meaning, relevance and
significance greater than mere order or distance above another
candidate.

There's no reason why a voting system must be a positional voting
system or a pure pairwise-count method (unless you're an advocate of a
pure pairwise-count method).

Sure, positional methods have a number of desirable
criterion-compliances. Approval and Score do, in particular.

As I said, Approval and Score comply with Reversal-Symmetry, if that
criterion is generalized to apply to all methods, instead of just to
rank methods.

Of course the advocacy of Reversal-Symmetry by traditional unimproved
Condorcet advocates might have something to do with the fact that some
TUC methods pass that criterion.

Mike Ossipoff