[EM] Proportional Representation from Ratings Ballots

[Brian Olson]

On Nov 5, 2009, at 12:37 PM, Raph Frank wrote:

> Party A (65 voters):
> A1: 0.7
> A2: 0.7
> B: 0
>
> Party B (35 voters)
> A1: 0
> A2: 0
> B: 1
>
> Round 1
> A1: 45.5
> A2: 45.5
> B: 35
>
> All 3 have exceeded the quota.
>
> A1 or A2 will be elected and that will cause the 2nd unelected member
> of that party to increase his vote since they exceeded the quota.
> Thus after round 2, both A1 parties will be elected.

Oh, that is a problem. It gets the right answer if I use L1 norm  
instead of L2. I think L2 norm is going to work better for single-seat  
IRNR but L1 norm better for multi-seat. L2 inflates the amount of vote  
that winds up getting applied to multiple choices.

Warren Smith pointed out some pathological cases like: what if  
everyone voted (1,0,0,0,0) or (0,1,1,1,1), but I just can't get worked  
up over how if everyone voted weirdly they might get a weird answer.

I'm working up a set of election space diagrams for STV, IRNRP and an  
artificial method that maximizes happiness where every voter gets a  
maximum of 1 unit of happiness (no point in giving any one voter too  
many of their favorite choices).

What I want out of a PR election method:
1. Evaluate the whole ballot at once (not just first place vote like  
IRV/STV). This tends to find better solutions.
2. No wasted vote. Choices that don't win (disqualified in  
intermediate rounds) don't detract from a voter's ability to elect the  
best choice they can. Voting for a very popular choice leaves you some  
vote left for less preferred choices. (STV with Meek redistribution  
does this OK)
3. Poportionality. Colloquially: An N% constituency should get about N 
% of the seats.
4. Utility. Maximize the sum happiness of the population.
5. Fairness. No one or no group should be unnecessarily shut out.
6. Strategy resistance. For any voter or bloc of voters, honest voting  
maximizes expected utility.


Brian Olson
http://bolson.org/