[EM] Finding the center-most voters. A toy/experiment

[Kevin Venzke]

Here's something I put together a while ago but didn't share. Maybe it's of
interest.
votingmethods.net/legis

The premise:

Suppose we have a relatively small number of voters and they know each other's
positions in 1D issue space. We will award some sort of legislative privilege or
power to a subset of these voters. We ask each voter to cast an approval vote to
each of their own top X favorite voters (no more and no less than X), and then the
top Y vote-getters receive the privilege. The values of X and Y are configurable.
Assume all the voters are sincere, and no one boycotts the procedure. What
combinations of values are most successful at identifying the center-most subset of
voters?

The results are a subset of trials (in which every voter is given a random position
from 0.0 to 1.0 in issue space) showing all the voters lined up in spectrum order.
Winners are marked with black squares, and winners constituting a left/right
imbalance are colored red.

You can get some interesting variety. For example:

21 voters, 16 must be approved by each (76.2%), 11 winners (52.4%):
This comes out flawless, with no left/right imbalance at all.

41 voters, 31 must be approved by each (75.6%), 21 winners (51.2%):
Similarly looks flawless. So maybe these percentages are good.

Another that works flawlessly is:
51 voters, 28 to approve (54.9%), 5 winners (9.8%).

But consider:
101 voters, 48 to approve (47.5%), 10 winners (9.9%)
This basically never elects the median voter, although the winners are relatively
close to the median.

101 voters, 35 (34.7%) to approve, 23 winners (22.8%):
This mostly elects a block of voters in the middle of each of the left and right
halves, staying rather far from anyone at the median.

The underlying notion is that if every voter would approve the 50% (plus one)
voters closest to themselves, then the median voter himself should end up with 100%
approval. So perhaps we can identify a selection of voters near the median.

Of course, strategic voting or uneven distributions of voters in the issue space
could ruin this effort.

Kevin
votingmethods.net