[EM] multiwinner election space plots

[Abd ul-Rahman Lomax]

At 06:46 AM 8/13/2009, Brian Olson wrote:
>I had been
>kinda resigned to STV being the state of the art in multiwinner
>methods, but we seriously ought to be able to do better.

Well, there is reweighted Range Voting, as to a theoretical system. 
As to one in actual practice, STV is pretty good. Those 
discontinuities are largely down in the noise, the more winners there 
are, the less important they are, they mostly affect the last 
determined winners.

But that assumes full ranking, and Lewis Carroll (Charles Dodgson), 
writing in 1884, realized that most common voters would really only 
know who their favorite was. So he hit upon what a number of writers 
on this list called Candidate Proxy and Warren Smith called Asset 
Voting. So Dodgson proposed that exhausted votes may be exercised by 
the favorite on the list. (I'm not sure of exact mechanism, I've 
never seen a copy of the original paper, only commentary on it.) It's 
actually better than a mere election method, because we can think of 
the secret ballot, if secret ballot is used, as creating a college of 
public electors, known individuals controlling blocks of votes, and 
that can be a standing college, used for many different purposes, 
including replacement of vacated seats midterm. The College either 
meets after the balloting, or electors may recast votes as needed by 
registering them. It can be used to create a floating-district but 
still geographically based Assembly, if electors choose to cast their 
votes in precinct blocks, while another seat may represent scattered 
votes over the whole jurisdiction.

It can also serve as a standing advisory network, where electors may 
be approached by voters and pass on filtered requests, instead of the 
voters trying to deal directly with a holder of a seat.

We mostly think only of elections as a static, one-ballot process, 
this list has given almost no consideration to multiballot methods. 
Plurality is damn good if a majority is required, probably better 
than IRV, and spectacular -- definitely better -- if write-ins are 
allowed in the runoff. Recent election in Long Beach CA where the 
incumbent mayor was not allowed by term limit rules to be on the 
ballot. She ran and got a plurality in the primary, then a plurality 
in the runoff, (because there was only one name on the runoff, due to 
the rules, and there was a minor additional runoff candidate. It gets 
even more efficient if the ballot method is Bucklin in both the 
primary and runoff, because spoiler effect in a runoff can be avoided 
(which then allows those runoff votest to be write-ins without 
spoiler harm). If we require that a "preference" must be significant 
to be worth considering, Bucklin satisfies *in purpose* Condorcet, 
and even plurality satisfies Condorcet if the process requires a 
majority to complete (and there is a Condorcet winner and the number 
of ballots to reach a majority is not limited, and each ballot is a 
new one, no eliminations. I.e., standard Robert's Rules of Order 
elections satisfy the Condorcet criterion! -- in the end, that is, 
because a majority winner on a plurality ballot satisfies Condorcet.).

Asset is very, very good, because it can create a truly 
representative assembly without political parties. It's personal 
representation, chosen freely, very few wasted votes, the only votes 
wasted are those who are not recast by an intransigent candidate 
holding them. (I'd probably use the Hare quota and leave that last 
seat vacant, or give a few candidates observer status in the 
assembly, or something like that, and there are other solutions. It's 
really a minor problem compared to the vast gap in representation 
that currently exists. )