# [EM] Proportional representation through Bucklin-STV/Asset

Abd ul-Rahman Lomax abd at lomaxdesign.com
Sun Mar 28 20:02:24 PDT 2010

```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
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.

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