[EM] Monotonicity, but Participation too

[MIKE OSSIPOFF]

One thing that I forgot to add: When a method reacts to your
change of vote in a way that's opposite to how you changed your
vote, that makes it obvious that you're using a method that
sometimes malfunctions, which brings the validity of that
methods results into question. The method isn't always
acting in a way that makes sense.

So it's understandable that that counts against SD.  But
what if, in an election using any of the _best_ rank methods
we've been discussing, you vote a ballot that ranks Gore over
Bush, but the fact that you showed up & voted causes Bush to
win, when Gore would have otherwise won?

That's the Participation Criterion. SD doesn't have a monopoly
on embarrassments. Admittedly, your ballot has more on it than
Gore>Bush, whereas that ballot change in a nonmonotonic example
does nothing but downrank the person that it elects. So
Monotonicity is a worse, and more difficult, criterion to violate
than Participation is.

Still, it's irrational for the method to react to your ballot
in a way that's opposite to your expressed wishes. That shows that
we have to accept a little occasional irrationality, in return
for some very desirable other criterion compliances. It's worth
it of course.

SD's violation of Monotonicity, vs the best methods' violation
of Participation--it's a matter of degree. Is there an obvious
ledge at which to draw the line?

None of this should encourage in IRV advocate to discount
IRV's failure of Monotonicity & Participation: As I said,
IRR's Monotonicity violations are much easier to make, with
fewer candidates, and more obvious, and sometimes much more
outrageously extreme. As for Participation, yes the best methods
fail it too. But before you use that as a defense against
my criticism that IRV fails it, ask yourself what IRV offers
to make up for its Participation failure. With the BC complying
methods, you get some valuable compliance with lots of other
criteria of great practical importance. With IRV you get nothing
but meritlessness, no matter which criterion you judge IRV by.

Mike Ossipoff

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