[EM] General PR question (from Andy Jennings in 2011)

[Kathy Dopp]

 Just a few words of arithmetic:

---
> From: Toby Pereira <tdp201b at yahoo.co.uk>

>
> 10 voters: A, B
> 10 voters: A, C
>
> I would argue that the most proportional result is BC even though everyone has voted for A. (Monroe would be indifferent between the three possible results, however.) Sequential electing is likely to lead to less failures of monotonicity, and perhaps less prone to strategic voting as a result.
---

Monotonicity simply means that increasing the vote share, increases
the probability of winning the election.  The above example does not
provide an instance of nonmonotonicity.

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>>With an approval ballot, if someone has voted for a particular elected candidate, then their representation from that candidate is 1/n where n people in total have voted for the candidate, and 0 if they haven't voted for them. A voter's total level of representation is the sum of their representation from each candidate. For v voters and c elected candidates in total, the mean representation for each voter is c/v (assuming that each elected candidate has at least one vote). Full proportionality is achieved if every voter has representation of c/v.
---

 The total representation for any voter is the number of candidates
the *voter* votes for who are elected to office.  The mean cannot be
determined as above.  The mean would be calculated by summing the
number of candidates each voter voted for that were elected and
dividing by the number of voters.  The terms of this sum would be zero
for many voters and less than c for all voters who did not vote for
all the elected candidates. The mean would be less than c/v, not as
described above.

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>> The proportionality measure of a set of candidates is the average squared deviation from c/v for the voters' total level of representation (lower deviation being better). There's also a score voting version.
>>
>>
>>If we look at the following approval election with two to elect:
>>
>>
>>10 voters: A, B, C
>>10 voters: A, B, D
>>
>>
>>Monroe would be indifferent between any set of two candidates, even if it favours one faction over the other. My metric would rate AB and CD as the most proportional.
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Since the example above shows 20 voters voted for both A and B, and
only 10 voters voted for both C and D, such a metric for
"proportional" representational calculation fails to elect candidates
that the most number of voters would be happy about and the least
dissatisfied with.

 I have never seen the word "proportional" voting used in this fashion
before, so have always supported the notion of "proportional" voting,
until now, when I see that using this metric, although strictly
proportional, would be undesirable IMO.

-- 

Kathy Dopp
Town of Colonie, NY 12304
 "A little patience, and we shall see ... the people, recovering their
true sight, restore their government to its true principles." Thomas
Jefferson

Fundamentals of Verifiable Elections
http://kathydopp.com/wordpress/?p=174

View my working papers on my SSRN:
http://ssrn.com/author=1451051