Dick Burkhart dickburkhart at comcast.net
Fri Feb 7 19:13:26 PST 2014

```This is article concerns a rather narrow and somewhat artificial concept of
proportional representation. We usually think of proportional representation
as saying that the number of representatives for a group of voters should be
proportional to the size of the group. But here it is assumed that every
voter is assigned to one and only one representative and the goal is to
minimize, in some numerical sense, the mismatches voters’ desired
representative and their assigned one (which is their desired one if that
person is elected but is otherwise a second or lower place choice, assuming
a preferential ballot).

The “group” enters only indirectly, as the group of voters whose top
preference is a particular candidate, so the number of groups = the number
of candidates.  In real life, of course, voters will often for a party or
other interest group, which in many cases will promote a slate of candidates

results, such as NP-hardness, rather than practical algorithms for more
realistic concepts of proportional representation. Nevertheless I coded up
and tested out a penalty function to measure misrepresentation in a way that
seemed reasonable to me. Namely if ‘np’ positions are to be filled, then
there is no penalty if a voter’s top ‘np’ choices are exactly those elected,
with a penalty of (np – i) / np if only i < np of the voter’s top ‘np’
choices are elected. I also looked at two positive measures of
representation – the proportion of voters whose top choice gets elected and
the proportion of voters with at least one of their top ‘np’ choices getting
elected.

I was not surprised that in a number of cases (using actual votes from
Scotland and Ireland) the best set of elected according to my clustering
algorithm did not match the best sets according to the above 3 measures,
which also differed among themselves. In fact the measure of
misrepresentation that I used was least able to distinguish among different
but reasonably good sets of elected, with the “at least one elected” measure
being the best of the 3. My clustering algorithm first does a careful
pattern recognition to identify groups (or clusters) of voters who rank (or
rate) the candidates in similar ways, and only then matches candidates to
these groups according to group size. So the simplistic top choice candidate
grouping of this paper is in fact often not as proportional as it could be
in the real world of politics.

Dick Burkhart

4802 S Othello St,  Seattle, WA  98118

206-721-5672 (home)  206-851-0027 (cell)

dickburkhart at comcast.net

From: election-methods-bounces at lists.electorama.com
[mailto:election-methods-bounces at lists.electorama.com] On Behalf Of James
Gilmour
Sent: February 06, 2014 3:23 AM
Stv-Voting; election-methods at lists.electorama.com
Cc: Þorkell Helgason; Þorkell Helgason

This paper MAY be of interest.

the screen.

James Gilmour

Sent: 06 February 2014 01:21

YwMzU4MDI0MjU3MQ&s=AB2Xq4jOQm-fC-GD0JU7kCHZ1G8O0jh5PK7q8-E>

"proportional representation"

As-it-happens update ⋅ February 6, 2014

[1402.0580] On the Computation of Fully Proportional Representation -
arXiv.org

arxiv.org

We investigate two systems of fully proportional representation suggested
by Chamberlin Courant and Monroe. Both systems assign a representative ...

-------------- next part --------------
A non-text attachment was scrubbed...
Name: winmail.dat
Type: application/ms-tnef
Size: 8354 bytes
Desc: not available
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20140207/21a0445b/attachment-0004.bin>
```