[EM] 2nd Query for Approval advocates

[John B. Hodges]

Yesterday I asked about "Generalized Bucklin"/MCA: Voters submit 
ranked ballots, which may include ties, and need not list all 
candidates. First-choice votes are tallied; if any candidates get 
votes from  a majority (more than 50%) of the voters, the one with 
the largest majority wins. If none get a majority, second-choice 
votes are tallied and added to the first-choice totals; again we look 
for the largest actual majority. If there is none, third-choice votes 
are tallied, and so forth. I asked how this compared to plain-vanilla 
Approval, and Adam Tarr said
>I think that three-slot MCA is almost indisputably better than regular
>approval.  The only argument for regular approval over MCA is simplicity of
>implementation and explanation, although those are strong pragmatic arguments.

He also said that GB/MCA looked cloneproof. I think the 
cloneproofness depends on allowing voters to rank two or more as 
tied; one of the clones will win, who cares which one. If voters were 
required to strictly rank the candidates, clones would split the 
vote. If the counting reaches far down the ranks, it may not matter 
much; keep this in mind.

IRV and STV-PR are the same system, invented by Hare. IRV is the 
one-seat case of STV. A lot of the support for IRV comes from a 
desire ultimately to get to proportional representation, and STV is 
the most-preferred system of PR (of the systems that are widely 
known, at least). It is much easier to explain STV-PR to someone who 
is already familiar with IRV. Simplicity, and a record of experience 
in actual use, are great virtues if you hope to persuade the general 
public to adopt a new system. The fact that STV has been in actual 
use for decades, in real elections in real countries, is a major plus 
for persuading people to consider it seriously.

I recall reading somewhere that all methods that eliminate some 
candidates before selecting a winner violate monotonicity. Advocates 
of Condorcet-method-X and of Approval constantly harp on IRV's lack 
of monotonicity. Bucklin would be monotonic, whether voters were 
allowed to rank several candidates as tied, or not.

In a single-seat election, the 50% requirement for a winner could be 
considered a Droop quota: total votes divided by (number of seats 
plus one). I was wondering if GB/MCA could be applied to multiseat 
elections. I suspect not, unless perhaps if strict ranking were 
required. If you had an N-seat election,allowing voters to count 
multiple candidates as tied, tallied first-choice votes, and gave a 
seat to all who got a Droop quota (or the largest count above a Droop 
quota), the clones would swamp the process. If you did not allow 
voters to rank several as tied, it might work.

So, my 2nd query to Approval advocates: Can we make strictly-ranked 
Bucklin perform as a method of PR for multiseat elections? This 
approach would replace "One person, one transferable vote" with "One 
person, one vote per round." Voters submit ranked ballots, no ties 
allowed. BUT, by compensation, repeat votes for the same candidate 
ARE allowed. Ballots are counted toward the total of the 
highest-ranked candidate still in the race, i.e. not already awarded 
a seat. First-round votes are tallied; all candidates who get more 
than a Droop quota are awarded a seat. If there are seats remaining, 
THE DROOP QUOTA IS RECALCULATED, second-round votes are tallied and 
added to candidate totals. If there are still open seats, the Droop 
quota is recalculated, third-round votes are tallied, and so forth. 
If there are at any stage more candidates exceeding quota than there 
are open seats, the seats go to the candidates with the highest 
totals.

I'm just "thinking out loud" here...

Has anybody already analysed this idea? If not, it might be worth the 
time. If it works well, it would give a simple and straightforward 
multiseat PR version of Approval, that would not require the use of 
supercomputers. Replace STV with Bucklin for both single-seat and 
multiseat cases, and you would blow the IRV advocates out of the 
water.
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John B. Hodges, jbhodges@  @usit.net
Do Justice, Love Mercy, and Be Irreverent.