[EM] General PR question (from Andy Jennings in 2011)
Kathy Dopp
kathy.dopp at gmail.com
Thu Oct 2 10:44:14 PDT 2014
on further reflection, because the terms in the sum involve only
proportions, perhaps each term in the sum Sum(Absolute(v_i/v - s_i/s))
needs to be weighted by the proportion of voters each term represents,
i.e. also multiplied by v_i/v to make the winning set of most
proportionate candidates the set minimizing: Sum(v_i/v
*Absolute(v_i/v - s_i/s)), which would make the formula a little more
complicated. Even without weighting terms, the formula picks the most
proportionate winning candidate set in the examples we've been looking
at in this email thread, so perhaps I'm overthinking it now.
On Thu, Oct 2, 2014 at 1:31 PM, Kathy Dopp <kathy.dopp at gmail.com> wrote:
> OK. Here's the formula that will *always* work to evaluate how
> proportional fair any election result is, given any set of voter
> groups and the combination of approval votes each group casts:
>
> Sum(Absolute(v_i/v - s_i/s))
> or
>
> Sum(|v_i/v - s_i/s|)
>
> Where v_i and s_i are, respectively the number of voters in group i
> and the winning candidates group i voted for (for any group voting for
> the same combination of voters)
>
> and where v is the total number of voters and s is the total number of seats.
>
> Thus, for an approval vote election, one fairly simple way to find the
> most proportionately fair set of winning candidates would be to find
> the set of candidates who minimize this sum of absolute values of the
> differences between the proportion of the voters in each voting block
> that votes for the same combination of candidates out of all voters,
> and the proportion of seats that this group contributes to electing.
>
>
> I am convinced this method of counting approval ballots will never
> fail to assign the most proportional outcomes to select the winning
> set of candidates. If there are more than one set of candidates with
> the same minimum sum, perhaps toss a coin.
>
> I actually like this proportional voting method very much because it
> strictly adheres to finding the most proportionately fair set of
> winning candidates, the vote tallies are easily precinct summable and
> auditable, the vote casting method is easy and gives voters more
> choice and flexibility to express themselves, and the method is fairly
> (equally) counted for all voter groups. However, perhaps the summing
> method with its proportions and differences in tallying the votes of
> all voter groups voting for the same candidates is a little too
> complex for some voters to comprehend.
--
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
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