[EM] What is the most useful definition of "monotonicity"?

[Rob Lanphier]

Hi Steve,

Great hearing from you!  Weirdly, I didn't receive your email from the
mailing list, but I saw your note in the archive.[a]  Since you were
frequently a lonely voice of sanity in the early days of the EM list,
I was baffled as to how your email might have been spam filtered.
Anyway, I've reconstructed your message the best I could from the
archive so that I can reply to it.  More inline below....

[a]: http://lists.electorama.com/pipermail/election-methods-electorama.com/2020-November/002598.html

On 11/16/2020 11:02 PST, Steve Eppley wrote:
> Even the "most useful" monotonicity criterion isn't very important.
> Monotonicity strikes me as something to write about when one has a "publish
> or perish" job in academia.

Do you think it's really that unimportant?  It seems that the folks
that like to make a big deal about the alleged superiority of
"cardinal voting systems" like to talk about this one, and not talk
about any of the Condorcet criteria (Condorcet winner, Condorcet
loser, or any of the other criteria named after the 18th century dead
guy).  "Condorcet Winner" is not that hard to explain, and I think
it's (by far and away) the most important criterion that failed in
Burlington in the 2009 mayoral race[b].

[b]: https://en.wikipedia.org/wiki/2009_Burlington_mayoral_election

To be clear, I fully agree with the remainder of your message about
minority coalitions to form a majority..  We may want to start a
separate thread about that.

But I'd like to keep discussing the monotonicity, since I keep hearing
about it in places I don't expect it. For example, it often comes up
in presentations made by folks at the Center for Election Science, and
prominently their website [c][d).

[c]: https://electionscience.org/learn/library/
[d]: https://electionscience.org/library/monotonicity/

I fancy myself an election methods expert, and I want to be able to go
toe-to-toe with any "publish or perish" tenure-track professor who
tries to gish gallop the readers of an online forum (like this one, or
like electowiki, or Wikipedia) by deliberately introducing ambiguous
criteria to introduce confusion.  There are a lot of people editing
Wikipedia, and some of them have an undisclosed conflict-of-interest
when they do it.

I'll say more in my response to Kevin Venzke (who has also been a
consistent voice of sanity).  In short, I really appreciate that other
criteria are probably more important (in addition to guarding against
other ways of gaming the system).  But I want to make sure there's a
truly excellent article about the "Monotonicity criterion" (either on
Wikipedia or electowiki, and preferably on both) which is approachable
by the layperson.  I want an article that the reader to learn more
(with an appropriate number of hyperlinks and footnotes), and that
doesn't implicitly tell the reader "you don't need to know that. Only
NERDS care about that".  As of right now, I fear that such an article
doesn't exist.

Rob