[EM] approval vs. IRV: majority loser criterion

[James Green-Armytage]

	Here is a definition of the majority loser criterion that is designed so
that limited-rank-ballot methods such as plurality and approval can't
weasel their way out of it:

"If a candidate is the sincere last choice of a majority of voters, and
that majority votes sincerely, then that candidate shouldn't win."

	As far as I can tell right now, Condorcet (winning votes or margins, even
without a Schwartz or Smith requirement) passes this criterion, and IRV
passes this criterion. Approval fails it. Let me give an example of this.

Sincere preferences, plus approval cutoffs
20: L>>A>B>C>D>E>F>G>H
15: A>>B>C>D>E>F>G>H>L
13: B>>A>C>D>E>F>G>H>L
12: C>>A>B>D>E>F>G>H>L
11: D>>A>B>C>E>F>G>H>L
9: E>>A>B>C>D>F>G>H>L
8: F>>A>B>C>D>E>G>H>L
7: G>>A>B>C>D>E>F>H>L
5: H>>A>B>C>D>E>F>G>L

approval scores:
A: 15
B: 13
C: 12
D: 11
E: 9
F: 8
G: 7
H: 5
L: 20

	So, 80% of the voters strictly prefer every other candidate to candidate
L. And yet L wins using approval, because everyone only approves of their
favorite. Yikes! It's crazy! Why doesn't A win, since she wins pairwise
comparisons with every candidate by at least an 80-20 margin? Or at least
B, who wins all of his pairwise comparisons with everyone except A?
Approval is just that crazy, folks.
	Yes, although A wins in the example above, you can make IRV failure
examples that look sort of similar to this one, but at least they're not
majority loser examples, because IRV passes that criterion.
	Is this example plausible? Hell no. Is it contrived? Hell yes. Still,
it's embarrassing for approval, because of what a huge majority it is that
opposes candidate L.
	It's not so hard to contrive examples that seem a bit more 'natural', in
which approval still fails majority loser. For example:

sincere preferences, plus approval cutoffs:
20: A>B>>L
10: A>>B>L
15: B>A>>L
7: B>>A>L
48: L>>A>B

approval scores:
A: 45
B: 42
L: 48

	This is a more plausible example, which can be imagined as the result of
a defection/cooperation dilemma between the A and B voters. Most of them
chose to cooperate, but there were enough of them who chose to defect to
hand the election over to L, who in this example is our majority loser. (A
52/100 majority sincerely rank L in last place.)
	Since we already know that approval fails mutual majority, is it
redundant for me to point out that it fails majority loser as well? Maybe
a little, but I think not entirely. I think that majority loser might be a
bit easier to satisfy. For example, two round runoff doesn't always pass
mutual majority, but--at least in its top-two form--it passes majority
loser.
	I realize that plurality fails majority loser, at least by this
definition. So, while it seems hard to convince people to adopt approval
voting for public elections when they learn that it can elect majority
loser, it would admittedly not be a good argument for keeping plurality
instead.
	However, it could be seen as dubious to switch from runoff to approval,
since approval can elect a majority loser but runoff cannot.

sincerely,
James