[EM] Alright, next try. Range voting fix, version 2.

[rob brown]

Again, very interesting.

Forgive me if this is again reinventing, but I can certainly think of ways
that might eliminate cycling.

The problem seems to be that there are still "cusp points" that need to be
smoothed out.  Averaging the totals helped, but it wasn't enough.  When one
candidate's total passes another's, regardless of averaging, suddenly lots
of voters' strategies change because there is a different front runner (or
different runner up).  Which then might cause the numbers to go back on the
other direction, and so on.

Instead, we would need to make it smooth, so that with each incremental
change in the totals, a proportionally small number of ballots would tend to
change.

So we no longer think of the simple boolean of whether or not a candidate is
a front runner or not, but instead consider "how close" they are to being a
front runner, or "how solidly" they are a front runner.  Then we put this
into a formula that also uses the ratings on each ballot (the "how much do
they prefer" one candidate to the next) to determine whether each candidate
gets a yes or no on each ballot.

I have to think about this more.  Before I try to work out a fuzzy logic
formula maybe you (or someone) has already tried this and run into something
I haven't thought of.  (I'm not ruling out the possibility that there could
still be a cycle, but it seems all the less likely if we eliminate cusps)

BTW I should point out again that I'm not really proposing any of this as a
practical solution.  I see it more as a big thought experiment that is
helping me completely wrap my head around the relationship of condorcet,
approval and range.

-r
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