Methods of elimination in quota preferential STV

[LAYTON Craig]

While it is unarguably crucial to discuss the ideal single winner method
(both simply in terms of the logic of majoritarian decision making on
specific issues and in cases eg presidential elections, where only one
winner is possible), are you all sure that you should be advocating any of
these systems for the election of a legislature?

Perhaps in terms of political expediency, yes (but some aren't so concerned
with political expediency).

It doesn't seem that the accuracy of single winner systems have any
relevance at all in a multi-member decision making body.  The overall result
is always fairly random, and depends more on electoral boundaries than
anything else.  All reasonably good multi member systems (like Bart's below,
or David's, or Demorep's variable voting power, or standard quota
preferential STV) will always produce a more accurate result than single
winner, no matter how carefully derived the single winner system.

CVD gets alot of flack, but they do advocate PR wherever possible (and only
IRV where it seems that PR is too much of an uphill battle).

There is, I know, long standing prejudice against multi winner systems, and
there's always Federalism to contend with.  But, even in relation to the
latter, it's important to note that even wildly differing electorate sizes
will still produce better results than single winner systems (ie, make each
state an electorate with either 5, 7 or 9 members, depending on the state's
size.  The fact that some states are ten times larger than others won't
affect the result as much as single winner electorates, and will keep the
smaller states happy).  Of course, it has to be unicameral, which is another
change that is perhaps too radical to suggest.  Nevertheless, if you're
after the best system.....

-----Original Message-----
From: Bart Ingles [mailto:bartman at netgate.net]
Sent: Thursday, 5 October 2000 15:20
To: election-methods-list at eskimo.com
Subject: Re: Methods of elimination in quota preferential STV


I haven't had time to think about multi-winner methods much, but I have
been leaning toward a modified cumulative voting method with
elimination.  I'm pretty sure the following method has been shown to
violate monotonicity & participation (see below), but I suspect the
violations may be less severe than STV's. 

Voters simply vote for multiple candidates, as they would with approval
voting, except that each choice gets an equal fraction of the vote (e.g.
if you vote for five candidates, each gets 1/5 of your vote).  You then
eliminate the weakest candidate and recount, so that the remaining
candidates get a larger share (if one candidate was eliminated from your
ballot, the remaining candidates now each get 1/4 of a vote).  Continue
eliminating candidates in the same fashion until the required number
remain.

No quotas are necessary since each voter always has the same cumulative
vote.  The fact that voters must weigh compromise choices rather than
simply rank them should yield higher overall utilities, and the method
is certainly simpler than STV.

I have the following references regarding the method (I haven't seen
them):

Bolger, E. M. (1983), "Proportional representation" in: S. J. Brams, W.
F. Lucas and P. D. Straffin, Jr., eds., Modules in Applied Mathematics,
Vol. 2 (Springer-Verlag, New York) 19-31.

Bolger, E. M. (1985), "Monotonicity and other paradoxes in some
proportional representation schemes," SIAM Journal on Algebraic and
Discrete Methods 6: 283-291.

-Bart