[EM] PR methods and Quotas

[Jameson Quinn]

2011/7/24 Andy Jennings <elections at jenningsstory.com>

> 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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