[EM] Proportional Representation via Approval Voting

[Bart Ingles]

LAYTON Craig wrote:
> (In relation to your first message) I'm in the minority, but I can't get
> over single winner Approval and Cardinal Rankings' failure of a basic
> majoritarian criteria, which I consider to be vital - ie, a candidate who is
> the most preferred candidate of an absolute majority of voters should always
> win if voters vote sincerely (of course, with some definitions of sincere
> voting, like Markus', then Approval does actually pass this).  The fact that
> this is highly unlikely if voters use strategy and available polling
> information isn't good enough in my opinion.  Also, the fact that approval
> is likely to elect the Condorcet candidate if there is one isn't really good
> enough, either.

To me, the social utility argument overrules the Condorcet candidate in
some situations.  In fact it's possible for a Condorcet candidate to
have essentially zero social utility.

When collecting full ranking information, you are placed in a position
of having to use it consistently, even when a large part of that
information is meaningless (either that or be willing to justify your
method's apparent failure in that regard).  This need for
self-consistency places too much weight (IMO) on conforming to the
Condorcet criterion, or to Saari's symmetry requirement, or Arrow's
criteria, etc.

With a non-ranked system, it is much easier for the method itself to be
internally consistent, while still remaining flexible enough to
accommodate non-equidistant utilities, etc.  It is not as important to
maximize Condorcet efficiency, for example, since you have no actual
ranked votes on which to determine the Condorcet winner.  A moderately
high but consistent Condorcet efficiency (based on unvoted sincere
preferences) is probably more desirable than a perfect one, since this
leaves room for eliminating extremely unpopular Condorcet winners.


At least regarding Arrow's original theorem, the approval voting method
itself doesn't violate any of the four conditions.  We know that
Approval complies with non-dictatorship, non-imposition, and
monotonicity in any case.

As far as independence of irrelevant alternatives, if you start from
voters' unvoted sincere preference orders, then of course no method
which meets the first three criteria can comply.  But with actual voted
ballots, Approval *does* comply.  So any IIA non-compliance is
accomplished by the voters prior to marking their ballots, and not by
the actual approval voting method.

On top of that, the voters have more than ranked preferences to work
with -- they have full access to their own sincere utilities.  And any
decision by the voter to allow his/her vote to be swayed by the addition
or deletion of an irrelevant candidate is likely to be based in large
part on this additional information -- a voter would likely only change
votes for ambivalent choices, and not for candidates whom they strongly
support or oppose.

In other words approval's apparent failure regarding IIA is a result of
the voters using information beyond rankings to adjust their approval
ballots, and not a result of the voting mechanism itself.


As far as always electing the most preferred candidate of an absolute
majority, you have to be able to guarantee sincere ranking in order to
guarantee that outcome.  If you can't guarantee sincere ranking, then a
ranked method can only claim a majority based on the actual ballots --
which you can do just as well with Approval.

Bart