[EM] approval doesn't meaningfully meet majority or mutual majority

[James Green-Armytage]

James replying to Mike...
>
>
>I claim that my PMC gives answers more in accord with the intent of the 
>majority criterion than does FHC or the original votes-only MC.

	I disagree with that claim. Here is your PMC...

>Preference Majority Criterion (PMC):
>A method fails PMC if it's possible to contrive a configuration of 
>candidates, voters, and voter-preferences such that a set of voters 
>consisting of more than half of the voters prefer X to each of the other 
>candidates, and it isn't possible to contrive a votes-configuration such 
>that everyone votes sincerely and X wins.
or:
>If a set of voters consisting of more than half of the voters prefer X to 
>each one of the other candidates, then they should have a sincere way to 
>elect X.

	This is not a meaningful way to do preference criteria for approval
voting, at least not for criteria like majority, mutual majority,
Condorcet, etc. Consider that if you write preference criteria for
approval this way, approval once again passes almost anything, as with the
votes-only criteria. 
	For example, I'm pretty sure that approval passes "preference" Condorcet
criterion, if you word it this way. ("A method fails PCC if it's possible
to contrive a configuration of candidates, voters, and voter-preferences
such that one candidate X is a CW with regard to voter-preferences, and it
isn't possible to contrive a votes-configuration such that everyone votes
sincerely and X wins." or: "If X is a CW with regard to voter preferences,
then voters should have a sincere way to elect X.") For example, say that
everyone (except those who consider X their least favorite) approves of X,
and does not approve of any candidate whom they like less than X. X will
surely win.
	Do you really think that it is meaningful to say that approval passes the
Condorcet criterion? I'm convinced that it is not meaningful. Similarly, I
assert that there it is not meaningful to say that approval passes the
majority or mutual majority criteria. 
	These sort of criteria (i.e. majority, mutual majority, Condorcet, Smith)
aren't about whether the "correct" candidates *can* always win given
*some* sincere vote-configuration of any preference ordering; they're
about whether the "correct" candidates *will necessarily win* given *any*
sincere vote-configuration of any preference ordering.
	Approval is simply not designed to meet any majority criteria. In
reality, it may often choose from the mutual majority set, the Smith set,
etc., but that depends on the the voters' coordination and information.
	On the other hand, I think that it is meaningful to say that approval
meets criteria like participation, consistency, monotonicity, etc. As for
IIA, it depends on whether you assume that voters base their approvals on
the relative merit of the candidates in the race, or whether they consider
each candidate in isolation. If you assume the latter, approval passes. 
	To sum up, I think that approval generally does not meet majority
rule-related criteria, but usually does meet "continuity" criteria.
>
>As I said, Plurality isn't better because a majority-favorite candidate
>wins 
>if we suppose that everyone votes sincerely. That's because Plurality
>makes 
>people not vote sincerely. It makes them bury their favorite. Approval 
>doesn't. Plurality's better showing in FHC is completely unrealistic. FHC 
>isn't measuring anything genuine when it gives Plurality a better answer 
>than Approval.

	I'm not interested in comparing approval to plurality. Approval is
better. I am interested in comparing approval to IRV and ER-IRV. And in
that comparison, it is meaningful to say that IRV passes the majority,
mutual majority, and Condorcet loser criteria, while approval fails. That
doesn't necessarily mean in itself that IRV is better than approval, but
it is a meaningful and valid point of comparison.
>
Mike:
>>Maybe we should rename PMC the Freedom-Hater's Criterion (FHC).
James:
>	What a strange idea, especially when so many ranked ballot methods pass
>it, methods that give voters freedom to express many levels of
>preferences, rather than only two.
Mike:
>No, we were comparing Plurality to a method that adds some voter-freedom
>to 
>that of Plurality.
>
	Well, I was using that particular majority criterion definition to
compare approval to plurality, but the same criterion can be used to
compare approval to any other method, e.g. IRV, ER-IRV, WV, Borda, etc. So
the criterion itself is not limited to, and hence not solely defined by,
the approval-plurality comparison.
	I hope that on some level you appreciate the extreme absurdity of your
dubbing my majority criterion definition the "freedom hater's criterion".
First of all, the name "freedom hater's criterion" is like a parody of
ridiculously biased terminology. Secondly, ER-IRV and WV offer the voters
more freedom than approval, and still pass the criterion, so there's no
necessary connection between satisfaction of the criterion and limitation
on voter expression. Furthermore, we agree that CR fails the majority
criterion, and so if approval passes any cooked-up version of the majority
criterion, it must be as a result of reducing the voters' freedom by
giving them only two scoring options (0 and 1) rather than 101 (0-100) or
whatever CR scale you use.
>
>But CR isn't subject to the 1p1v illusion. By proposing CR instead of 
>Approval, we completely avoid that public misperception. 

	To me, it seems that it would be harder to convince people that CR
satisfies 1p1v than it would be for approval. But that's just my opinion.

Sincerely,
James
http://fc.antioch.edu/~james_green-armytage/voting.htm