[EM] Proportional multi-winner ranked voting methods - guidelines?

robert bristow-johnson rbj at audioimagination.com
Thu Feb 23 20:45:40 PST 2017

---------------------------- Original Message ----------------------------

Subject: Re: [EM] Proportional multi-winner ranked voting methods - guidelines?

From: "Toby Pereira" <tdp201b at yahoo.co.uk>

Date: Thu, February 23, 2017 5:09 pm

To: "rbj at audioimagination.com" <rbj at audioimagination.com>

"election-methods at lists.electorama.com" <election-methods at lists.electorama.com>


> I suppose it depends what you want from a multi-winner election. A faction of 51% could command all the seats if you did it that way.

yes, i know that.  but, OTHER THAN GEOGRAPHIC division of the constituency into  groups (we might call those divisions "districts" or "wards"), i can't see how a government can legitimately divide the constituency into groups based on race or ethnicity or
gender-preference identity, just to get proportional representation.  we can't have folks in Greenwich Village registering as gay or straight so that the gays get their allotted proportion and the straights getting their proportion.
the alternative is that we elect someone to office even
though *more* of us voters explicitly mark our ballots that we prefer someone else.  that's the whole point behind Condorcet compliance.

---------------------------- Original Message ----------------------------

Subject: Re: [EM] Proportional multi-winner ranked voting methods - guidelines?

From: "Kristofer Munsterhjelm" <km_elmet at t-online.de>

Date: Thu, February 23, 2017 5:20 pm

To: rbj at audioimagination.com

"election-methods at lists.electorama.com" <election-methods at lists.electorama.com>


> On 02/23/2017 09:59 PM, robert bristow-johnson wrote:

>> i wasn't aware that any STV would be Condorcet compliant (except for

>> bottom-two runoff STV).


>> my only thought about a multi-winner method that *is* Condorcet

>> compliant is to simply run the rank-choice election according to some

>> Condorcet method (say Schulze or RP or MinMax or BTR-STV), pick the

>> Condorcet winner and assign that candidate to the first available seat,

>> decrement the number of available seats by one, remove this winner from

>> the candidate pool, and then see who the next Condorcet winner is from

>> the remaining candidates. rinse and repeat until all available seats

>> are assigned.


>> what would be wrong with that approach to multi-winner elections?


> That method fails the Droop proportionality criterion and amplifies

> majorities into unanimities.


> E.g.


> 51: A>B>C>D

> 49: E>F>G>H


> Four to elect gives a council of {A, B, C, D}. If one wants a

> proportional outcome (which is what all the quota business in STV is

> intended to accomplish), then a majoritarian multiwinner Condorcet

> election doesn't help much. If you want a majoritarian method, then it's

> okay, but the subject says "Proportional" :-)
yes, i know.  i just think, in reality (despite what i know about the Chittenden Senate District in the state of Vermont) that with D and E on the edge (and maybe even C and F), that there would be probablistic influences on the
vote that might elect people from the slightly smaller group.
the Chittenden Senate District of the state senate of Vermont is, AFAIK the largest (most seats) legislative district in the United States.  the district elects six candidates (the six biggest vote-getters in a mark-up-to-six
race) and, in the past, many people voted with bullet voting.  this was because there was *one* Republican (she is the daughter of a former governor who happen to die while in office that that was the beginning of Howard Dean's gubernatorial term) that was well-liked and perceived to be
guaranteed election.  then the six Democrats (or Dem/Progs) on the ticket were literally running against each other in a sorta musical chairs because one of them wasn't gonna get elected.  but Ms. Snelling was appointed to some administrative position and is not on the ticket anymore and
the Dems (or Dem/Progs) have locked out the GOP from that senate district and the GOP really want to slice up that district (after the next census) and i don't blame them.  proportionately, they should get at least one seat and there is likely a portion of Chittenden County that would elect a
GOP state senator.  now the Dems don't bullet vote because their incentive is different.  rather than try to elect the particular candidate they really want, they'll just vote for the whole slate of six candidates because there is no longer this remaining GOP shoe-in candidate that we used
to have.
even though many of us are a bunch of hippies and Vermont is the bluest (or second bluest) state in the U.S., we have our goofy electoral dynamics in the state (which includes having the most successful third party in U.S., in terms of getting people elected) and this mondo 6-senator
district is a little goofy.  i call it a "cluster fuck".

> A more proportional Condorcet method could be accomplished this way -- I

> think that would be the most simple somewhat proportional Condorcet

> method. For n seats:


> * Repeat lots of times:

> - Randomly divide the voters into n groups

> - Order the groups in random order.

> - Determine the first group's winner according to the Condorcet method.

> - Give the first seat to this winner and eliminate him from every

> ballot (of every group).

> - Determine the second group's winner, elect, and eliminate.

> - Do so until you have n candidate assignments.

> * Choose the assembly that you saw most often.


> In the 51/49 example above, it's basically a coin toss as to whether any

> given group will elect one of {A,B,C,D} or one of {E,F,G,H}, and so you

> get a 50-50 split.
this is cool.  but the problem is in the lack of determinism (this "randomly" do anything will cause objection with some).
is there a totally deterministic way to come up with these ensemble averages to get a good estimate of the proportional
representation?  like the outcome should be that A, B, E, and F are winners if there are four seats in this multi-winner election. (and the simpler, the better.  the only way i can think of is to geographically subdivide the district into smaller and smaller into atomic communities or

r b-j                  rbj at audioimagination.com
"Imagination is more important than knowledge."
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