[EM] Fwd: Preliminary Range PAV results

[Kristofer Munsterhjelm]

Just a quick reply:

Jameson Quinn wrote:

> Kristofer - have you been able to get results for this formula? 

I *think* this is the same as my "Quadratic Range STV" method, but I'm 
not sure. I have been busy with work and so haven't been able to check 
if it is indeed the same.

The quadratic Range STV method is based on this:

- In STV, we want a candidate supported by a Droop quota to be elected 
and then the voters' power to be equal to the surplus (amount greater 
than the quota).

- For the sake of fairness, we also want ballots that rate the candidate 
highly to be deweighted more than those that don't.

- However, unlike ordinary STV, we can't just adjust the weight by the 
rating. The reason is because a rated vote is weighted twice: once for 
the ballot's actual weight and once for the rating of the candidate by 
that ballot.

We thus get:
    Say ratings are 0..1, r(X) is the sum rating for candidate, s(X) is 
the sum squared, and X won. Denote a's rating of X v_a_X, and a's weight 
w_a. The Droop quota is D.

    Then define p_X to solve sum n = 1...numballots (w_n * v_n_X^2 * 
p_X) = D. This is just D/s(X).

    Then for each ballot q, its new weight is equal to max(0, w_q - (w_q 
* v_q_X * p_X)), in essence removing a Droop quota from those who 
contributed to X's victory.

Since I'm writing this quickly, there may be some errors, but you see 
the logic.

Note that other deweighting functions are possible, but I haven't 
experimented with those. To show what I mean, just consider a function 
that sorts rated ballots from rating the winner highest to lowest and 
travels down, zeroing out weights until a Droop quota has been removed. 
That won't be very fair, but it will work.

> If you send me the source code, I can try myself.

Alright, just don't claw your eyes out over my coding practices :p
I'll clean it up just a little and then send it to you along with some 
information about how to go about changing it.