[EM] Weighted voting systems for proportional representation

[mrouse1 at mrouse.com]

I emailed Forest about using weighted voting systems (ones where
candidates, rather than parties, have different voting power in the
legislature), and he suggested posting it to the group for discussion.


The following method could be used with Approval, Range, and Borda ballots.

1.  Determine the size of legislature you want.

2.  Have each candidate list all of the other candidates in order of
preference.

3.  Looking at every possible slate of candidates in turn, add an amount
equal to the highest scoring candidate on each ballot to that slate’s
score.

For Approval voting, this means that a ballot with 1 or more approved
candidates on the slate would add 1 to the slate. On a range ballot, if a
ballot had A=100, B=67, C=50, and D=0, any slate with A (AB, AC, AD) would
have 100 added, any slate without A but with B (BC, BD) would have 67
added, and so on. Borda would be handled the same way as range.

4.  Looking at each ballot, the person on the winning slate with the
highest ballot score gets 1 vote added to his voting weight. If there is a
tie, the vote is divided equally among all tied candidates, *unless* the
tie is for last place. For example, if a ballot showed three Approved
candidates from the winning slate, each would each get 1/3 of a vote.
(This should help quiet the “one person, one vote” crowd.)

5.  If a ballot ranks all candidates on the winning slate in last place,
the vote is assigned in the order given by the highest scoring candidate
on the ballot. For example, if a ballot showed a bullet vote for A, and
candidate A ranked other candidates B>C=D>E=0, and CE was the winning
slate, C would get the vote. If CD was the winning slate instead, C would
get half a vote, and D would get half a vote.

6.  Any unassigned votes (for example, a blank but valid ballot, or None
of the Above vote) are split evenly between all candidates on the winning
slate.


As an example with Approval voting, using the election given on the page
here:

http://wiki.electorama.com/wiki/Proportional_approval_voting


The ballots are:

5: AB

17: AC

8: D


There are 6 possible slates: AB, AC, AD, BC, BD, and CD.


With PAV, A and C are elected. Voters for D are ignored.


With the WVPR method (or whatever it should be called), you have the
following scores for each slate:

AB = 5+17 = 22

AC = 5+17 = 22

AD = 5+17+8 = 30

BC = 5+17 = 22

BD = 5+8 = 13

CD = 17+8 = 25


AD is the winning slate. Now let's look at each candidate’s proxy power:

A = 5+17 = 22

D = 8


Of course, you wouldn't want to have a legislature of 2 candidates, since
one would always win. You would want to make sure no candidate had more
that 50% of the vote, which means 3 candidates at least, and preferably a
great many more for a truly deliberative body.

With such a system, it would be possible to have proportionality while
using Approval, Range, or even Borda ballots. (Theoretically, you could
have proportionality even with Plurality ballots, as long as candidates
had a full preference order to take care of votes that would otherwise be
wasted.)

Michael Rouse