[EM] Postscript: Multiseat Bucklin?

[John B. Hodges]

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."
-- 
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John B. Hodges, jbhodges@  @usit.net
Do Justice, Love Mercy, and Be Irreverent.