[EM] Proportional representation through Bucklin-STV/Asset

[Abd ul-Rahman Lomax]

I'm copying this from a post of mine sent yesterday, on the list at 
Sat, 27 Mar 2010 14:55:49 -0400.
I'd like to get specific comment on this method. I use the Hare 
quota, generally, with Asset methods, because it provides natural 
consequences for inability to compromise. The loss of a seat is not 
particularly harmful if this is a large-member election. If it is an 
election of a limited number of members from each district (which 
means loss of proportional representatin), then I presume a Droop 
quota would be used, because gaining a full slate would be important. 
On the other hand, one could use the Hare quota for district 
elections, then allow the Asset electors with votes remaining from a 
district election to amalgamate across the entire legislative 
jurisdiction, thus providing small-minority representation 
state-wide. I like that, isn't it interesting? District elections, 
but no loss of minority representation!

Asset really is a very powerful tool, unexplored for way too long.

I have edited this to correct a few errors. I have removed the "pure 
Asset" section that did not use Bucklin process.

Suggested Asset/STV method. Ranked ballot. (Given the Asset 
provision, three ranks might be just fine.)

1. Q = V / N. (This can be done with the Droop quota to make it more 
deterministic. I oppose it for reasons I won't detail here.)

2. Any candidate with Q votes gains a seat. Those ballots are then 
deweighted, if there were M votes for the candidate, to now represent 
collectively M-Q votes. Think of each ballot as now being marked with 
the fraction (M-Q)/M.

3. On each ballot where the first position candidate gains a seat, 
the candidate in first position is marked as inactive (because 
elected) and the second rank vote, if any, becomes active, being 
added to the existing totals, according to the fractional value, for 
the candidate. If multiple candidates are elected from a ballot, the 
fractions are multiplied appropriately, so that a voter, if the 
ballot is fully used up, has contributed no exactly one full vote to 
all elections summed.

4. This iterates until all ballots have been read. No eliminations 
have taken place. Lower ranked votes where the candidate in first 
position has not been elected have not yet been read below first position.

5. Because there have been no eliminations, all elections so far can 
be seen as rigorously correct and fair.(skipped original sections)

10. The ballots are now treated as Bucklin ballots. The second rank 
is counted. ("Second rank" means "second active rank.") Seats are 
assigned whenever a candidate, in a round of counting, gains a quota 
of votes, and those ballots are devalued accordingly. In this case, 
an elected candidate might be in a lower position on the ballot. The 
candidate is marked as elected, but the higher position candidate 
remains active, and may attain election through votes from other 
ballots, to the extent that any voting strength is left. As a winner 
is found, any ballots counted for that candidate are devalued as before.

11. When all ballots have been counted to the last rank, and no more 
candidates have attained the quota, the election then collapses to 
Asset for any ballots remaining with unused voting power. The vote is 
assigned to the candidate in first position. (There is another choice 
here, where a voter has added additional ranked candidates, and the 
first position has been elected, but my opinion is that it dilutes 
the power of the Asset method, which is to make the *most trusted 
candidate* the effective proxy for the voter.)

12. The Asset electors, who are public voters, complete the election 
by negotiation of amalgamation of the remaining votes to the quota. 
As the quota is the Hare quota, any unassigned votes will result in a 
seat vacancy. I'd make this remediable at any time, no deadline. 
Except, of course, the next election, where the voters whose votes 
weren't used just might decide to vote for someone different.... depending.)

I believe this is monotonic. It is also an STV method, but does not 
use eliminations except of elected candidates. Asset in general 
doesn't actually eliminate any ballots or candidates at all, using 
the Hare quota. I do not know how Carroll would have specifically 
applied his asset concept to STV counting methods. I just made up the 
above. I actually prefer, personally, Asset with a non-ranked ballot. 
It is also STV, in fact, but with flexible vote transfer as 
determined by the effective proxy for the voter.

The voter can safely vote for one candidate, or can vote for more 
than one. Neither strategy is clearly superior, and it probably 
depends on the degree of knowledge of the voter. I think I'd tend to 
vote for one, always, unless I really had trouble choosing, in which 
case, I'd hope that equal ranking is allowed! Equal ranking works 
fine with this method, because it collapses to equal ranking in the 
Bucklin process anyway. In the event of equal ranking in first 
position, the Asset votes would be divided equally.

I think this is precinct summable. But the data is greater, because 
the devaluations are ballot-specific. On the other hand, the number 
of ranks is limited, as I proposed it. This would work with *one* 
rank! (Very simple to canvass, definitely no problem with precinct 
summability, because all votes are treated equally, there is no 
consideration of rank at all.) If course, it is then pure Asset, and 
if equal ranking is allowed, it's Proportional Asset Approval Voting. 
Two might be enough ranks, particularly if equal ranking is allowed.

I'm not familiar with Proportional Approval Voting, but I'd guess it 
is like this, one rank, but no Asset, so it's deterministic and would 
use a Droop quota.