[EM] PR methods and Quotas

[Andy Jennings]

On Sun, Jul 24, 2011 at 6:30 AM, Jameson Quinn wrote:

>
> 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.
>

The main idea I had was to eliminate first the ballots which don't rate any
of the remaining hopefuls above zero, then the ballots which rate one
remaining hopeful above zero, and so on.  Where there are ties, I would
probably prefer fractional de-weighting to random discards.

Suppose I'm seating candidate A and need to eliminate 10 ballots and there
are
7 voters who rated all the rest of the hopefuls at zero
5 voters who rated only one other hopeful above zero

Then I would eliminate all seven of the first class and de-weight the other
5 by 60% (multiply by 0.4).

The idea is to prevent degeneration in the final round as much as possible,
we give priority to ballots which give non-zero scores to the most
candidates.  Even to the point of incentivizing them.

This might incentivize turkey-raising, but only to the first non-zero level.
 And with Hare quota, there's a real chance that it WILL make a difference
in the final round, so instead of raising turkeys, hopefully voters will
give a non-zero score to anyone they can live with.

Of course, we'll still probably have a tie at zero in the final round, so
we'll elect the candidate with the fewest zero votes, a form of
lowest-denominator approval.


  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).
>

I don't know what to call it.  Maybe one of:

Sequential Hare Favorite
Successive Hare Favorite
Sequential Favorite Voting (SFV-Hare)

Are those acronyms taken?


- Andy
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