[EM] Re: What IRV optimizes

[John B. Hodges]

>Date: Fri, 8 Aug 2003 12:28:48 -0700 (PDT)
>Subject: Re: [EM] What IRV optimizes
>From: "Alex Small" <asmall at physics.ucsb.edu>
>To: <election-methods-electorama.com at electorama.com>
>
>John B. Hodges said:
>>  IRV is the one-seat case of the Single Transferable Vote. The point  of
>>  STV is to maximize "ballot effectiveness", i.e. to minimize
>>  "wasted votes". Votes are wasted in two ways: Undervotes, where you
>>  vote for someone who fails to win a seat, and Overvotes, where you  vote
>>  for someone who gets more votes than they need to win a seat.
>
>Yes, but STV accomplishes that not only by transfering votes, but also by
>electing multiple candidates to ensure that as many people as possible get
>a representative.  I don't see how the variational principle you cite
>applies in the single-winner case.

We can talk about "total" ballot effectiveness for the method (what 
percentage of ballots elect a candidate), and the distribution of the 
ballot effectiveness through the electorate (what percentage of 
voters cast effective ballots). If ballots are ranked and fractional, 
these two figures need not be equal.

In the single-winner case, IRV (and other majoritarian methods) give 
a total ballot effectiveness of 50%, no more or less; total ballot 
effectiveness under Plurality would be the vote percentage received 
by the second-place candidate, which would always be less than that. 
More generally in the N-seat case, total ballot effectiveness is 
equal to the sum of the winning thresholds, expressed as percentages.

The distribution IMHO is even more important; proportional 
representation tries to maximize the percentage of the electorate 
that have effective ballots. This is in contrast to "winner take all" 
methods. The effectiveness of individual ballots will almost always 
be either zero or a fraction, since very few candidates win seats by 
exactly one vote.

Someone once described Approval as "Plurality done right"; It's a 
interesting point that in the single-seat case, Approval could give 
"ballot effectiveness" figures far above 50%. MCA would set a 50% 
floor, but the second-place candidate could rack up more than that.

Another thought I had regarding STV. STV deals with undervotes by 
transferring them from last-place candidates to others with more 
chance of winning. It measures "last place" by the votes the 
candidate has accumulated so far, up to that point in the process. It 
might be (has been) argued that this is not the best possible 
measure. For example, a better measure might be the candidate with 
the lowest Borda Count. I recall hearing of "Borda Elimination", I'm 
sure it has its own flaws.
-- 
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John B. Hodges, jbhodges@  @usit.net
Do Justice, Love Mercy, and Be Irreverent.