[EM] Fair and Democratic versus Majority Rules

[Kristofer Munsterhjelm]

Abd ul-Rahman Lomax wrote:
> At 08:57 AM 11/16/2010, Kristofer Munsterhjelm wrote:
>> Condorcet doesn't give proportional representation. If you have an 
>> example like:
>>
>> 51: D1 > D2 > D3 > D4
>> 49: R1 > R2 > R3 > R4
>>
>> and pick the first four, all the Ds will win.
> 
> Just for fun, suppose this is STV, to elect 5 seats. Accurate 
> proportionality is not possible, but it can get close. I will assume 
> acccurate vote transfers. As an exercise, I will use the Hare quota, 20 
> votes, and then look at what Asset would do.
> 
> This turns, below, into a general discussion of Asset Voting, which was 
> originally proposed as a tweak on STV, in 1883, by Lewis Carroll 
> (Charles Dodgson).
> 
> The seats chosen are:
> 
> 1. D1.
> 2. R1
> 3. D2
> 4. R2
> 
> leaving
> 
> 11: D3 > D4
> 9: R3 > R4
> 
> Nobody has a quota for the fifth seat. This is why the Droop quota is 
> used in most implementations of STV. But let's go back to Dodgson's idea.

Perhaps one could augment STV by starting at Hare and going towards 
Droop until it finds a quota that all candidates meet. I'm not sure what 
criteria such a method would pass, but it would be interesting. In the 
case above, it would still give a 3:2 result, though.

> D1 now owns 11 votes that remain, and R1 owns 9. If they can agree, they 
> can elect a seat. If they cannot agree, my proposal for the rules is 
> that the seat is vacant until they do, or until a special election is 
> held. I think that leaving the seat open may be superior to a special 
> election, but if a special election is held, it should be one that would 
> find a compromise candidate. It should not be IRV! It should not be a 
> partisan election, party affiliation should not be on the ballot, my 
> opinion.

That's also a good thing to think about. If the ballots were somewhat 
more complex, you'd want to perform a single-winner election for that 
remaining seat, but with power redistributed so that those who already 
have it get less. In STV, that single-winner election is IRV. A good 
proportional method should here act more like Condorcet (or Range, or 
your favorite method) with power-equalized ballots.

I suppose Asset works by retaining the power that could not be cleanly 
assigned to candidates, and then having the candidates who could have 
won decide how to collect the numerous almost-seats into fewer 
(compromise) seats.