<br><br><div class="gmail_quote">2011/7/24 Andy Jennings <span dir="ltr"><<a href="mailto:elections@jenningsstory.com">elections@jenningsstory.com</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
Like Jameson and Toby, I have spent some time thinking about how to make a median-based PR system.<div><div><br></div><div>The system I came up with is similar to Jameson's, but simpler, and uses the Hare quota!</div>
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<br></div><div>Say there are 100 voters and you're going to elect ten representatives. Each representative should represent 10 people, so why not choose the first one by choosing the candidate who makes 10 people the happiest? (The one whose tenth highest grade is the highest.) Then, take the 10 voters who helped elect this candidate and eliminate their ballots. (There might be more than ten and you'd have to choose ten or use fractional voters. I have ideas for that, but lets gloss over that issue for now.) You can even tell those 10 voters who "their" representative is.</div>
</div></blockquote><div><br></div><div>Glossing-over noted. I'd like to hear your ideas, but I agree that they should not be part of the basic definition of the system. </div><div><br></div><div>Also, this "hard elimination" is where your method differs from AT-TV. Your method certainly has a stronger free-riding incentive than AT-TV. It is radically simpler, though, so perhaps AT-TV is adding too much complication in an attempt to minimize the (fundamentally inevitable) free-rider incentive.</div>
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</div><div><br></div><div>Electing the next seat should be the same way. Choose someone who is the best representative for 10 people. Repeat.</div><div><br></div><div>The only problem is when you get down to the last representative. If you follow this pattern, the last candidate is the one whose LOWEST grade among the remaining ballots is the highest, which is rather unorthodox. You could change the rules and just use the median on the last seat, but using the highest minimum grade does have a certain attraction to it. You're going to force those last ten voters to have some representative. It makes some sense to choose the one who maximizes the happiness of the least happy voter. (Though ties at a grade of 0 may be common.)</div>
</blockquote><div><br></div><div>If you use the Droop quota instead of the Hare, ties at 0 will be less likely. In general, I think that with the Hare quota, ties at 0 wouldn't just be common, they'd be universal; and they'd still be common with the Droop quota. In either case, the obvious solution (and the one which AT-TV uses) is to elect the candidate with the fewest 0 votes.</div>
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<div><br></div><div>But this system doesn't reduce to median voting.</div></blockquote><div><br></div><div>Right, it doesn't. But it does if you use the Droop quota.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div> Which got me thinking... Is there anything that special about the 50th percentile in the single-winner case anyways? I can imagine lots of single-winner situations where it's more egalitarian to choose a lower percentile. In a small and friendly group, even choosing the winner with the highest minimum grade is a good social choice method. It's like giving each person veto power and still hoping you can find something everyone can live with. This is the method we tend to use (informally) when I'm in a group choosing where to go to lunch together.</div>
</blockquote><div><br></div><div>The Droop quota reduces to the median. The Hare quota reduces to the highest minimum grade. You could also use any number in between. (I note that "modified Saint-Lague" is, I think, actually used in some places, and amounts to a similar compromise idea.)</div>
<div><br></div><div>The higher the quota (up to Hare), the smaller a group of strategic voters can be and still determine the result (if everyone else is honest). I'd argue that this makes pure Hare a poor solution. I am open to compromises. 2/(2N+1), the quota half way between Droop and Hare (I bet it already has a name, but I don't know it), reduces to the ~33rd percentile in the single-winner case. From what I've seen of supermajority requirements in contentious high-stakes contexts (California tax hikes, US senate filibusters), 2/3 is the highest reasonable supermajority requirement, and may already be too high. But, as you say, a higher requirement may make sense for smaller, friendlier decision-making.</div>
<div><br></div><div>In sum: I like your method. It is certainly similar to, but simpler than, AT-TV. I prefer it with the Droop quota. What do you call it? (It would be good if you had terms for both the Droop and Hare versions).</div>
<div><br></div><div>JQ</div></div>