[EM] Proportionality in perspective

[Bart Ingles]

One reason I have never been overly impressed with the argument that one
multi-winner method is better than another merely because it is more
accurately proportional, is that this seems to imply that other criteria
(locality of representation, monotonicity, some form of utility, etc.)
are unimportant.  In particular I dislike the CVD's term
"semi-proportional" as a pejorative applied to methods such as
cumulative voting (the other CV), in favor of more complex methods.

But while the supposedly more accurate methods seem to have the
"proportional" side of "proportional representation" down pat, I have to
wonder about the "representation" part.

For example, suppose you have a multi-seat election in which two of the
factions (of roughly equal size) are capable of electing one candidate
each.  Below are the two factions' preference orders for candidates A,
B, C, and D, with utilities or ratings given in parentheses:

                 Candidate(rating)

   Faction 1:   A(10)  B=C(9)   D(0)

   Faction 2:   D(10)  C=B(9)   A(0)

   Faction 3 through n:   ...


The question is, which pair of candidates best represents the two
factions.  Is it [A and D], or  [B and C]?  If you were a member of
faction 1, which candidates would you rather see elected? 

Bart