[EM] approval vs. IRV: value of FBC and WDSC compliance

[James Green-Armytage]

Mike Ossipoff wrote previously:
>Judge them by criteria. Approval meets FBC & WDSC. IRV meets Mutual
>Majority (MMC). But, as I discuss below, every MMC example is an IRV
>failure example in wihch IRV fails FBC & WDSC. One must choose which is
>more important. 

	Since before the dawn of time, Mike Ossipoff has been arguing that
approval is superior to IRV because approval satisfies these criteria: FBC
and WDSC. I agree that it does satisfy the criteria, but I don't think
that this fact is impressive enough to settle the issue.
	First let me quote the definitions of the terms, from electionmethods.org

Favorite betrayal criterion / FBC: "For any voter who has a unique
favorite, there should be no possible set of votes cast by the other
voters such that the voter can optimize the outcome (from his own
perspective) only by voting someone over his favorite."

Weak defensive strategy criterion / WDSC: "If a majority prefers one
particular candidate to another, then they should have a way of voting
that will ensure that the other cannot win, without any member of that
majority reversing a preference for one candidate over another."

	The key to both of these criteria is incentive to *reverse* the order of
your preferences. A broader criterion which envelops these would be the
strategic reversal criterion (SRC), which I'm making up now if it doesn't
exist already:
	"For any set of voters that share a sincere preference ranking of the
candidates, there should be no possible set of votes cast by the other
voters such that this set would achieve a more-preferable result by
ranking / rating a candidate who they prefer less above a candidate who
they prefer more."
	Condorcet, IRV, and a great deal of other ranked ballot methods fail this
criterion. Actually, so many good methods fail it that it is rather
useless as a criterion in itself... what is more useful is to talk about
the *degree* of strategic reversal incentive (SRI) in a given method. But,
wait, approval passes SRC. Wow!!! That seems really cool, until you stop
to put it into perspective.

	The strategic reversal criterion should not be considered without
considering its twin, the strategic compression criterion (SCC). The
strategic compression criterion could be worded as follows:
	"For any set of voters that share a sincere preference ranking of the
candidates, there should be no possible set of votes cast by the other
voters such that this set would achieve a more-preferable result by
ranking / rating a candidate who they prefer less equal to a candidate who
they prefer more."
	This is identical to the SRC definition except that I have substituted
the words "above a candidate they prefer more" with "equal to a candidate
they prefer more." Once again, so many methods fail SRC that it isn't
really very useful in itself. What is useful is trying to understand the
*degree* of compression incentive in a method (SCI).

	What I'm trying to say is that there are two types of strategic
manipulation, one is REVERSAL and one is COMPRESSION, or insincere
equal-ranking. If a method passes SRC, you shouldn't get too excited about
its strategic properties until you see how it does with SCC. 
	Cardinal ratings is the best example of this. It passes SRC with flying
colors. But how does it do with regard to SCI? It does horribly with SCI.
While other methods that allow equal ranking (such as Condorcet and equal
rankings IRV) will in some cases give incentive for strategic compression,
cardinal ratings will *almost always* give incentives for compression.
And, typically, CR will give you incentive to compress *more* of your
preferences than Condorcet will. Thus, you can meaningfully say that the
compression incentive is much much more frequent and severe in cardinal
ratings than it is in those other methods.
	My main point is this:

	BOTH ORDER-REVERSAL AND COMPRESSION ARE DISTORTIONS OF VOTER PREFERENCE!

	That is, incentives for order-reversal can be a real problem. They are a
problem for IRV, for Condorcet, and so on. There's no getting around that
fact. They distort voter preferences and can lead to different outcomes
from the sincere preferences, while at the same time making it impossible
to know what the sincere preferences were.
	However, incentives for compression are ALSO A VERY REAL PROBLEM, for the
same reasons. There is a lot of really important information that you will
lose when voters engage in compression strategy.
	All else being equal, is reversal more severe than compression? Yes, it
is. If one method gives compression incentives about as often as another
method gives reversal incentives, I'd probably take the first method, all
else being equal.
	However, what if it's a choice between one method that only has a
moderate amount of reversal incentive versus a method that has a very
severe amount of compression incentive? That is, the second method compels
compression more often than the first method compels reversal, or the
second method typically compels many more preferences to be compressed
than the first method compels preferences to be reversed.
	Which brings us to approval voting. Not only does it always give
incentive to compress their preferences, it always *FORCES* voters to
compress their preferences! So you are not only encouraging distortion of
preference, you are mandating it.

Mike Ossipoff wrote:
>And before someone argues that WDSC & FBC aren't to be found in journal 
>articles, I suggest that criteria be judged on their own merits. 
>Millions 
>of voters are cowed by the lesser-of-2-evils problem, so that they bury 
>their favorite because of it. It matters what a majority has to do in
>order 
>to make a greater-evil lose. It matters to those millions who are going
>to 
>bury their favorite in November for that purpose.

	I agree with you here. The lesser of two evil problem is a serious one
indeed. A method that has incentive for strategic reversal is problematic,
and IRV has reversal incentive in a pretty bad way. In particular, it
often compels voters to reverse as part of a "compromising" strategy. I
don't mean to belittle or ignore this point. My point is that, while
reversal is a serious problem, compression is a serious problem as well.
And it is possible for one method's compression incentive (or mandate) to
be more problematic than another method's reversal incentive.

sincerely,
James

P.S. I don't really want approval *or* straight IRV in public elections,
although I will admit that they are both substantially better than
plurality. But at this point I think that I would prefer
equal-rankings-allowed IRV (with whole votes) over approval.