[EM] proportional constraints - help needed

[Raph Frank]

On Thu, Feb 7, 2013 at 8:24 PM, Peter Zbornik <pzbornik at gmail.com> wrote:
> Here is an example to illustrate the problem:
> Coalition 1: 32: w1>w4>w3>m3
> Coalition 2: 33: w1>w3>w4>m4
> Coalition 3: 35: w2>w5>m1>m2

> Thus, the right distribution, intuitively is:
> 4th seat - m3
> 5th seat - w5

Is this a constraint issue?  You could just say that the balance
between genders at each level is required.

W - W - W - M - M

would not be allowed, since the top-2 in the list are women.
Effectively, for any N, the difference in the number of men and women
in the top-N cannot be more than one.

One nice feature of PR-STV is that its proportionality property is
maintained if you change only the elimination rule.

You could run the normal rules and just say that you cannot eliminate
a candidate if the number of candidates elected for that gender is
less than the number of candidates for the other gender.

However, this doesn't guarantee balance.

100) W1 > W2 > W3 > W4 > W5 > M1 ....

would cause the women to reach the quota one after another and thus
would be elected, no matter what the elimination rule.  This might be
acceptable, if the objective is to encourage, but not force an even
balance between the genders.

You could have a ballot updating rule.  For example, if you moved M1
to after W1 on all ballots, it would allow M1 to be elected in round
2.  I am not sure how to make that low complexity though.

Fundamentally, strategy is going to kick in.  If a ballot is used to
elect a candidate, it needs to be de-weighted.

Another option would be run 3 tallies of the ballots.  Use PR-STV to
elect 2 women and then elect 2 men and and finally add the condorcet
winner.  This is less proportional though.