[EM] Gerrymandering and PR

Forest Simmons fsimmons at pcc.edu
Tue Mar 19 12:59:58 PST 2002

On Tue, 19 Mar 2002, [iso-8859-1] Alex Small wrote:

> Good point about geographical concerns.  In a bicameral state legislature
> it would be reasonable to elect one house by PR and the other with single-
> member districts.  We can debate which house of the legislature should be
> elected by PR, but I think the basic idea is reasonable.  Also, I think PR
> should stick to districts of 5 or 6 members, rather than operating state-
> wide, to keep the district sizes half-way reasonable.
> >Also by the way, we would get much better 'PR' using PAV applied to
> >individual candidates, not parties.
> I agree that PAV would provide excellent proportionality while keeping the
> scrutiny on individual candidates.  However, as I understand it, PAV
> requires keeping 2^n tallies when there are n candidates.

Actually the number is  C(n,m) or "n choose m" where m is the number of
seats and n is the number of candidates.

> In CA there are
> normally 7 parties on the ballot.  If we had 5-member districts that could
> lead to 35 candidates, or 2^35 = 34 billion tallies.

C(35,5) is 35*34*33*32*31/5! which comes out to 324632, less than a third
of a million.  About one megabyte would do fine.

Another thing to remember is that the summability issue is not so
important in local elections where it is reasonable to assemble all of the
ballots in one place.  Sequential PAV can be done efficiently from
(electronic copies of) the ballots, even with hundreds of candidates and
hundreds of seats to fill.


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