I think I've figured this out.<div><br></div><div>Use a quota of 2/11 for normal slots. The quota for quoted slots will be somewhere between 3/22 and 2/11; thus the remainder will be between 1/11 and 2/11.<br><div><br>
</div><div>When you hit a quoted slot, first see who would win the remaining slots under normal STV — call that set Ⓐ. Then see who would win it, starting with current ballot weights, if the ballots only included the correct gender — call that candidate X. X wins. Ⓑ is the set of candidates in Ⓐ who would have been elected before X. All ballots that helped X win are deweighted, using the following test to see what quota to use: If a ballot voted some member of Ⓑ over X, then that ballot is deweighted using a quota of 3/22; otherwise, it is deweighted with the normal quota of 2/11. For the next (non-quoted) slot, any candidates which had been eliminated to elect X are restored (if they truly deserve elimination, they will soon be re-eliminated), but all deweightings are of course preserved.</div>
<div><br></div><div>You could probably construct a scenario in which a strategic vote could get a more-favorable deweighting by raising a less-preferred candidate Y over a quoted candidate X without making Y win. However, for that to work, Y would have to be at least a potential non-quoted winner (ie, be in Ⓑ), so such strategies must be inherently risky¹ to be effective, and therefore I don't think people would waste time with them.</div>
<div><br></div><div>Jameson</div><div><br></div><div>¹If Y comes up in a non-quoted slot, which are 3/5 of the slots, they will simply win. In that case, a strategic ballot will be unfavorably deweighted, and the preferred candidate X has almost no chance of winning. So unless you have impossibly good info on which candidates will be elected in which slots, the chances of this strategy backfiring are at least 60%.</div>
<div><br><div class="gmail_quote">2013/2/8 Raph Frank <span dir="ltr"><<a href="mailto:raphfrk@gmail.com" target="_blank">raphfrk@gmail.com</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div class="im">On Thu, Feb 7, 2013 at 8:24 PM, Peter Zbornik <<a href="mailto:pzbornik@gmail.com">pzbornik@gmail.com</a>> wrote:<br>
> Here is an example to illustrate the problem:<br>
> Coalition 1: 32: w1>w4>w3>m3<br>
> Coalition 2: 33: w1>w3>w4>m4<br>
> Coalition 3: 35: w2>w5>m1>m2<br>
<br>
</div><div class="im">> Thus, the right distribution, intuitively is:<br>
> 4th seat - m3<br>
> 5th seat - w5<br>
<br>
</div>Is this a constraint issue? You could just say that the balance<br>
between genders at each level is required.<br>
<div class="im"><br>
W - W - W - M - M<br>
<br>
</div>would not be allowed, since the top-2 in the list are women.<br>
Effectively, for any N, the difference in the number of men and women<br>
in the top-N cannot be more than one.<br>
<br>
One nice feature of PR-STV is that its proportionality property is<br>
maintained if you change only the elimination rule.<br>
<br>
You could run the normal rules and just say that you cannot eliminate<br>
a candidate if the number of candidates elected for that gender is<br>
less than the number of candidates for the other gender.<br>
<br>
However, this doesn't guarantee balance.<br>
<br>
100) W1 > W2 > W3 > W4 > W5 > M1 ....<br>
<br>
would cause the women to reach the quota one after another and thus<br>
would be elected, no matter what the elimination rule. This might be<br>
acceptable, if the objective is to encourage, but not force an even<br>
balance between the genders.<br>
<br>
You could have a ballot updating rule. For example, if you moved M1<br>
to after W1 on all ballots, it would allow M1 to be elected in round<br>
2. I am not sure how to make that low complexity though.<br>
<br>
Fundamentally, strategy is going to kick in. If a ballot is used to<br>
elect a candidate, it needs to be de-weighted.<br>
<br>
Another option would be run 3 tallies of the ballots. Use PR-STV to<br>
elect 2 women and then elect 2 men and and finally add the condorcet<br>
winner. This is less proportional though.<br>
<div class="HOEnZb"><div class="h5">----<br>
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</div></div></blockquote></div><br></div></div>