multiseat pairwise?

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multiseat pairwise?

Craig Carey-2
To:            Kevin Hornbuckle <[hidden email]>
Date:          Tue, 19 Mar 1996

Kevin (who I think is not an election-methods subscriber) asked:
>If you use pairwise in a multiseat election, can it be said to yield
>proportional representation?

I haven't thought about it before; my first thoughts are "no."  
It would seem to be like the system which asks each voter to vote N
distinct choices in an N seat election: the same majority which
elects the top choice can elect the rest, totally shutting out a

Example:  2 seats up for grabs
  Summary of the ranked ballots:
  26%  Dole, Alexander, Clinton
  25%  Alexander, Dole, Clinton
  49%  Clinton

 The pairings:
   Dole over Alexander    by 1% (26-25+0)
   Dole over Clinton      by 2% (26+25-49)
   Alexander over Clinton by 2% (26+25-49)
 The results:
   Dole undefeated, wins seat #1.
   Alexander beat Clinton, and Alexander's worst loss (1%) is smaller
   than Clinton's worst loss (2%).  Alexander wins seat #2.

Is this proportional?  I don't think so.  The 49% who liked only
Clinton have no way to get him 1 of the 2 seats.  

So 51% can take all.  Unless the method is somehow modified to
subtract out the ballots which have already served to elect
candidates (Dole) before recalculating the remaining seats
(Alexander vs Clinton), it won't be proportional. I don't know
if there's a reasonable way to do this.

Here's an attempt:
After each seat is awarded, subtract S = Total_votes/N (where N is
the total number of seats) from the seat winner's ballots before
recalculating.  The ballots which are subtracted are the ones which
listed the winner as ranked first.  If there aren't enough ranked-first
ballots, also subtract ranked-second, etc.  If there are more than
enough ranked-first ballots (i.e., > S), then subtract appropriate
fractions of each.

Reworking the example using this new "multiseat pairwise":
 Dole wins seat #1.
 Since N=2, 50% of the ballots must be eliminated:
   First subtract all 26% {Dole Alexander Clinton} ballots, since
     these are the ones which ranked Dole 1st.  
   Then subtract 24% from the ballots which ranked Dole 2nd.
 The recalculated pairings:
    1%  Alexander, Clinton  (original25 - 24)
   49%  Clinton
 The rest, giving Clinton seat #2, is left as an exercise.  :-)

It's an interesting question; I'm cc:ing it to election-methods-list.

This looks a bit more complicated than STV.  Is anything gained by
using it instead of STV?  And does this method have an established


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multiseat pairwise?

Craig Carey-2
I'm going to check it out. Improving on STV in that way is an interesting
idea. I'll check out the consequences of that proposal.

One application of Pairwise to STV is Pairwise-Elimination, where
when it's necessary to eliminate someone, Pairwise is repeatedlyk
used to find the collective 1st choice, the collective 2nd choice,
etc., and eventually the collective last choice. Alternatively,
the alternative with the lowest Condorcet score could simply be
eliminated, without the iteration. I'm not sure which of those
2 ways of using Condorcet--iterative or non-iterative--would be
the better of the 2.

And then there's the "Hallett Elimination" that I spoke of earlier.

Niklaus Tideman has proposed a Pairwise STV that doesn't use any
elimination. It's extremely calculation-intensive, and may not
be computable for big public elections with ordinary-speed
computers. I have a copy of it somewhere. I can send it if you
like. Etiher I'll find the e-mail copy, or, if I don't still
have it, I'll copy the essentials into e-mail from my paper copy.

Also, I can tell where I got my paper (Xerox) copy:

The Journal of Economic Perspectives, 1995, Winter Quarter. There's
discussion of single-winner methods in there. Nothing useful except
a definition Simpson-Kramer. In general, you won't find anything at
all useful in Journal articles on single-winner methods, and I
advise against wasting your time with them. But the issue also has
articles on STV, including Tideman's proposal. Tideman suggests
several possible computational shortcuts that could make his
method computable in big public elections with ordinary-speed

Let me know if you want a copy of Tideman's article, if I can find
the e-mail copy, or at least an e-mail transcription of the essentials,
including the definition of his method, & the most important comments
he makes about it.