[EM] General PR question (from Andy Jennings in 2011)
kathy.dopp at gmail.com
Thu Oct 9 12:52:58 PDT 2014
On Thu, Oct 9, 2014 at 10:09 AM, Toby Pereira <tdp201b at yahoo.co.uk> wrote:
> The method is:
> Voters cast approval ballots. If a particular candidate receives n votes,
> then if this candidate is elected, each voter of that candidate will get a
> representation of 1/n from that candidate. Each voter who did not vote for
> that candidate gets 0 representation from them. So the total representation
> received from that candidate will be 1.
> A voter's total representation is the sum of the representation they receive
> from each elected candidate. Assuming that each elected candidate has
> received at least one vote, then for c candidates, the sum of the
> representation of all voters will be c. The arithmetic mean will always be
> c/v (for v voters).
> Full proportionality is achieved if every voter has representation of c/v.
> The measure of a set of candidates is the total of the squared deviation
> from c/v of the voters' representation (lower being better). But also,
> because the variance of x is mean (x^2) - (mean x)^2, where in this case x
> represents voters' representation levels, (mean x)^2 will always be the same
> - it will be (c/v)^2 - so we can remove it from the equation.
> This means that the winning set of candidates will be the set that minimises
> the sum of the squares of the voters' representation levels. [end of
> Because the best result is based on the sum of the squared of the
> representation levels, then if faction A has 2 seats and faction B 0 seats
> or they have 1 seat each, the relative proportionality of each of these will
> be unaffected by a small C faction.
Yes. I see. Do you think these three results *should* be equally
proportional according to your measure?
With nonoverlapping support:
# voters, winning candidate set
All three candidate sets for two winners for this scenario get the
same value of your measure: 0.021462585
>>> But what I mean is that if a large faction (with say 50% of all voters)
>>> divided into two (say 25% each) because of a single controversial
>>> who appears on half of that faction's ballots but not the other half,
>>> if that faction receives half the candidates (and the one controversial
>>> candidate is not elected), then it will be measured as unproportional
>>> because each faction will have each contributed to 50% of the candidates
>>> will only be 25% of the electorate each.
>>I don't see the problem. Could you possibly provide an example where
>>you believe this is situation would be a problem?
> Let's say we have 4 to elect and the following approval ballots:
> 5 voters: A, B, C, D
> 5 voters: A, B
> 10 voters: E, F
> The 10 E, F voters will get both these candidates elected because they are
> half the voters and they get half the candidates. But for the other two
> candidates to be elected, if we elect AB, then each AB subfaction will have
> elected half of the candidates when they "should" only have elected a
> quarter, so this is seen as disproportional. AC would be seen as more
> proportional by your metric because while one subfaction would still have
> elected half of the elected candidates, the other would have elected a
> quarter, so it would be seen as more proportional overall. But this is an
> unbalanced allocation.
OK. I see what you mean. Yes. That does not seem like the best winning set.
>>How do you apply your method sequentially? Many sequential methods
>>I've seen are fundamentally unfair (IRV, for example that treats
>>voters' votes unequally) and can tend to produce undesirable results.
> Instead of finding the slate that minimizes squared deviation, you could
> elect them one at a time. So initially the candidate that has the most
> approvals. Then the most proportional two-candidate set that includes the
> first winner. Then the most proportional three-candidate set that includes
> these two and so on. It would save computing time even if it doesn't find
> the overall most proportional candidate set.
At first glance, that seems like a good algorithm. (I'm busy with
another project now, but it seems OK to me.)
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"A little patience, and we shall see ... the people, recovering their
true sight, restore their government to its true principles." Thomas
Fundamentals of Verifiable Elections
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