[EM] Condorcet divisor method proportional representation

[Kristofer Munsterhjelm]

Kathy Dopp wrote:
> On Mon, Jul 4, 2011 at 11:18 AM, Kristofer Munsterhjelm
> <km_elmet at lavabit.com> wrote:
>> Kathy Dopp wrote:
>>> Thanks Kristofer.  I ignored the "all* in "all others".
>>>
>>> I must say then, I simply do not like the Droop quota as a criteria
>>> because it elects less popular candidates favored by fewer voters
>>> overall and eliminates the Condorcet winners some times. The Droop
>>> quota seems to go hand in hand with IRV and STV methods.
>> Then the question you should ask is where you want to balance
>> proportionality and majoritarianism. When dealing with multiwinner
>> elections, there are two objectives that work against each other. On the one
>> hand, you'd want proportionality, so that variation in the electorate is
>> reflected by variation in the assembly or council. That is, you'd like it to
>> have members that some people like a lot. On the other, you'd want quality
>> across the board, i.e. candidates that every voter can like to some extent.
> 
> The questions I would ask are:
> 
> 1.  how to minimize "unhappiness" of the voters.  (perhaps this is
> similar or the same as "Bayesian regret"?), and
> 2. how to ensure all voters' votes are always treated equally.
> 
> In your scenario 55% of people hate 50% of the winners and 45% hate
> (ranked last) 50% of the winners.  If the Center and Right win, only
> 45% of the voters hate 50% of the winners and everyone else is happy.
> Also, in your scenario, often the voters' votes are treated unequally
> and only some of the 2nd choices of some voters are counted - thus
> causing undesirable results  -- on the part of a majority of voters --
> on occasion.

If you want to minimize unhappiness of the voters by electing candidates 
  hated by few, you can make the same kind of argument against the 
majority  criterion for a single-winner method as you did against the 
Droop proportionality criterion. That is, imagine an election of the sort:

51: Left > Center > Right
45: Right > Center > Left
  4: Center > Right > Left.

The majority criterion forces Left to win in a single-winner election. 
However, Left is hated by 49% of the voters.

Borda, which fails the majority criterion, would elect Center as a 
compromise. Center is not hated by any of the voters, and so by your 
metric, that would be a better outcome.

Yet I suppose that since you like the Condorcet criterion, you also like 
  the majority criterion that it implies. That means that some methods 
(like Borda) can be *too* centrist by your/the Condorcet measure.

It is, of course, possible to disregard majority rule entirely and 
instead focus on satisfaction, electing the alternative that would 
benefit the people the most. That is what Range is supposed to do, and 
does under certain assumptions (linear comparable utility functions, 
honest voting). It's relatively simple to imagine elections where such a 
  method would overrule a majority, e.g.

51 voters value X at 99%, Y at 50%, Z at 0%
49 voters value Y at 99%, Z at 10%, X at 0%,

where the majority choice (X) makes the minority quite unhappy (assuming
these are honest votes, comparable, etc), but where the compromise, Y,
leaves the majority satisfied and the minority happy. By Range's logic, 
electing Y is the *right* thing to do (and it produces the least 
Bayesian regret) - but doing so does fail the majority and Condorcet 
criteria.

> I.e. I'm looking at satisfying the most number of voters and fairness,
> *and* on proportionality - but a much greater proportion of voters
> avoid dissatisfaction by avoiding the Droop quota requirement and
> looking at all voters' 2nd choices.

How much proportionality for how much satisfication? Majority rule is 
itself a sort of proportionality (single-seat proportionality, that is), 
in that a majority can control the outcome. Droop seems to be another 
sort of proportionality: per-seat majorities, if you will.