[EM] Proportional multi-winner ranked voting methods - EPR

[Kristofer Munsterhjelm]

On 11/26/2017 10:39 AM, Juho Laatu wrote:
> On 25 Nov 2017, at 02:49, steve bosworth <stevebosworth at hotmail.com
> <mailto:stevebosworth at hotmail.com>> wrote:
>> entirely removes gerrymandering
>
> Also this one is a useful property of a proportional method.

It would be interesting to figure out the worst case gerrymandering that 
can be done by a Droop-proportional method with s seats. I suspect that 
the proportion of votes that can be misrepresented will be proportional 
to the Droop quota due to the DPC. It can't be exactly the Droop quota 
because single-winner methods have a quota of a majority, but more than 
a majority can be disarmed by gerrymandering, but I would imagine that 
it falls off in a similar fashion.

(Clearly if there are s = number of voters, it's impossible to do any 
gerrymandering at all.)

>> I mention RCV (i.e. IRV) because FairVote is currently campaigning for
>> Santa Cruz to adopt RCV for electing its Council.
>
> IRV is a single winner method for single seat districts. If you do it
> that way, you will not have good proportionality. STV would be a much
> better approach (also ranked and in many ways similar to IRV).
>
>> 100 CITIZENS:
>>
>> 40 prefer A over B over C
>>
>> 40 prefer C over B
>>
>> 20 prefer B over C
>
> Condorcet criterion could be a natural requirement for single seat
> districts. It says that B should be elected since it would pairwise beat
> all other candidates.
>
> But if we have multi-seat districts, Condorcet criterion could be
> forgotten. If we have two seats in this district, it would seem natural
> to elect A and C.

For LCR scenarios like the above, I usually think that "equal number 
left and right" is the right outcome for an even number, and "equal 
number left and right, plus one center" is the right outcome for an odd 
number -- up until the point where there are enough representatives that 
the relative size of the factions come into play.

>> at least 1/7 of all citizens who have voted
>
> You could use also a somewhat lower threshold (e.g. Droop quota).
>
>> 1)     if a voter has given more than one candidate the same relevant
>> evaluation, her evaluation will be added only to the candidate whose
>> total of evaluations would consequently be greater at that stage of
>> the count than any of the other candidates she has given the same ‘grade’,
>
> Does "at that stage of the count" mean that the order of the counted
> votes may have an impact on the outcome of the election? (depending on
> if X or Y happens to have more votes "at that stage of the count") Such
> randomness may be acceptable (if it keeps the method simple) but not a
> very good feature.
>
>> To avoid the possibility of any one Councilmember being in a position
>> to dictate to the Council, any Member who might have received more
>> than 20% of all the ‘weighted votes’ in the Council, must publicly and
>> non-returnably transfer her ‘extra’ votes to the ‘weighted votes’’ of
>> one or more of her trusted fellow Members.
>
> Would this candidate tell who will get his extra votes before or after
> the election? If before, then we might have some problems with cyclic
> transfers. If after, then we might have a problem with this candidate
> selling those votes to one of the other candidates. (There could be some
> smaller vote selling problems also in the case that candidates declare
> their preferences already before the election, but that is not as
> serious since voters can see (assuming that this information is public)
> where the votes will go.)
>
>> Again, each Councilmember would have a ‘weighted vote’ in the Council
>> exactly equal to the number of evaluations from citizens added to her
>> total.
>
> If we first elect one candidate with 1/7 of the votes rating him
> Excellent, his weight will be 1/7 of the total weight. All other
> candidates got zero Excellents. Next we count the Very Good ratings. One
> candidate gets them 2/7 of the total votes. Does this mean that the
> weight (voting power) of the second elected candidate will be higher
> than the weight of the first elected candidate? Note that it is possible
> that the first elected candidate had also lots of Very Good ratings. The
> question is if the weight of the first already elected candidate should
> be topped (maybe up to 20%) if he has lots of Very Good ratings.
>

A problem here is that MJ is (properly speaking) an ordinal method, so 
it can easily tell you whether candidate X is better than Y (in a 
transitive manner), but not quite as easily how much better X is than Y.

Suppose all the voters vote party line. Then an MJ election for a yes/no 
proposal would have that voter vote yes if the candidate he graded 
highest among those not abstaining voted yes; otherwise that voter would 
vote no.

Translating this into a weight should be relatively easy if there's 
never any abstentions, or if we suppose that voters who graded an 
abstaining representative highest would in turn abstain. Just have a 
second stage where each voter is matched with the elected candidate he 
graded highest, and each representative has a weight proportional to the 
number of voters matched with him.

This would produce somewhat different results than the above. Suppose 
that first A is elected by Excellents, then B by Very Good, then C by 
Good. Suppose that some of the B voters also gave C an Excellent grade, 
but not enough to elect C at Excellent or Very Good. Then some of the 
voters who helped elect B would be assigned to C.

If the voters would (in the model) vote according to the highest graded 
non-abstaining representative, and ignore abstaining representatives 
altogether, the above reasoning wouldn't work. It would be more of a 
pairwise matter, but since there are multiple candidates, the curse of 
dimensionality would be a big problem.

>> 4. In addition to the above advantages, since ‘grading’ candidates
>> is easier than ‘ranking’ them, this makes it more like that each voter
>> will see EPR as more user-friendly than the ‘ranking’ methods.
>
> Not necessarily since it is quite easy to use "graded" ballots and
> derive rankings from them, if the method is ok with having equal
> rankings. That would make voting equally easy in both approaches.
>
> My overall impression is that this method is on a reasonably good track
> if we start from the assumption that the society accepts the basic idea
> of having representatives with different weights.
>
> If the candidate opinion based vote transfers get too complex, you might
> consider also the more traditional approach of letting fellow party
> members to inherit all the extra votes. This might fall slightly short
> of your target of directing each vote to some clearly named single
> representative, but you might gain simplicity and understandability and
> you might get rid of the vote selling related questions.

I suspect that if there are organized parties, there would be an 
SNTV-ish equilibrium where the parties clone their candidates so that 
each gets just enough weight to be elected (plus some margin because of 
risk aversion). The benefit of doing so is to push competitors off the 
assembly altogether. In this equilibrium, everybody's weight would be 
rather similar and the method would be like unweighted PR.