2011/7/24 Andy Jennings <[email protected]> > Like Jameson and Toby, I have spent some time thinking about how to make a > median-based PR system. > > The system I came up with is similar to Jameson's, but simpler, and uses > the Hare quota! > > 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. >
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. 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. > > Electing the next seat should be the same way. Choose someone who is the > best representative for 10 people. Repeat. > > 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.) > 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. > > But this system doesn't reduce to median voting. > Right, it doesn't. But it does if you use the Droop quota. > 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. > 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.) 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. 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). JQ
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