[EM] Postscript: Multiseat Bucklin?

[Alex Small]

Here's an example where I think it does a bad job:

2 parties, party A getting 40% of the vote and party B getting 60%.  There
are 5 seats up for grabs.  Clearly, A should 2 seats and B should get 3
seats.  Each party runs 5 candidates, and the voters within each party are
largely indifferent, so each candidate within each party has the same
number of first place votes, the same number of second place votes, etc.

First round:  All candidates in party A have 8%, and all candidates in
party B have 12%.  Nobody meets or exceeds the Droop threshold of
16.6667%.

Second Round:  Add in second-place votes.  All candidates in party A have
16%, all candidates in party B have 24%.  All 5 candidates in party B
exceed the Droop quota (and the Hare quota, for that matter) and all 5
candidates in party A fall short of the Droop quota.

All 5 seats go to party B.

Not very proportional.  And this is a pretty simple and plausible 2-party
scenario.


John B. Hodges said:
> Dammit, I found an oversight in the algorithm. Corrected algorithm
> follows.
>
> Naiive proposal for an N-seat version of Bucklins' procedure: All
> voters submit ballots ranking their most-preferred candidates, as  many
> or as few as they wish. (I suppose ties could be allowed, each  tie
> counting as a fractional vote for each of the tied candidates.)  The
> "winning threshold" I propose to be the Droop quota, i.e. (total  # of
> ballots / # of seats plus one.)
> (1) Count voter's ballots. Each ballot counts as a vote for the
> highest-ranked candidate still in the race, i.e. not yet awarded a
> seat. Add these counts to each candidate's previous total.
> (2) Has any candidate reached the winning threshold?
> 	If not, count voters' next-ranked choices and add these
> counts to the candidates' totals. (If a ballot has nobody ranked
> next, it counts as an abstention. If there are no ballots with anyone
> ranked next, go back to (1).) Go back to (2).
> 	If so, go to (3).
> (3) Are there now more "winners" than seats? I.e. do we now have more
> candidates with vote totals above the winning threshold than there  are
> seats remaining to be filled?
> 	If so, award the seats to the candidates with the largest
> totals. (If two such candidates are tied, break the tie by a Borda
> Count. If they are tied by Borda Count, flip a coin.) You are
> finished.
> 	If not, award seats to those candidates who have exceeded the
> threshold. Go to (4).
> (4) Have all seats been filled?
> 	If not, recalculate the winning threshold for the remaining
> seats. Go back to (1).
> 	If so, you are finished.
>
> "I really hate this damned machine, I wish that they would sell it.  It
> never does quite what I want, but only what I tell it."
> --
> ----------------------------------
> John B. Hodges, jbhodges@  @usit.net
> Do Justice, Love Mercy, and Be Irreverent.
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