[EM] Summability and proportional methods
Richard Lung
voting at ukscientists.com
Fri Jun 9 13:56:30 PDT 2017
Every stage of an STV count sums the whereabouts of all the votes in
their process of transfer. So it is not "scary" on that account. Gregory
method is a standard statistical technique called weighting in
arithmetic proportion. Statisticians are not thereby a scarified
profession. Of course, traditional STV counting does have anomalies. And
that is why I developed its generalisation in Binomial STV.
No need for the retrograde steps you mention.
from
Richard Lung
On 08/06/2017 17:33, Jameson Quinn wrote:
> Most proportional voting methods are not summable. Transfers,
> reweightings, and otherwise; all of these tend to rely on following
> each ballot through the process. This makes these methods scary for
> election administrators.
>
> I know of 3 ways to get summability: partisan
> categorization, delegation, and second moments. List-based methods
> (including partially list-based ones like MMP) use partisan
> categorization. GOLD voting
> <http://wiki.electorama.com/wiki/Geographic_Open_List/Delegated_%28GOLD%29_voting> does
> it by giving voters a choice between that and delegation. Asset voting
> and variants use delegation.
>
> The other way to do it is with second moments. For instance, if voters
> give an approval ballot of all candidates, you can record those
> ballots in a matrix, where cell i,j records how often candidates i and
> j are both approved on the same ballot. This matrix keeps all the
> information about the two-way correlations between candidates, but it
> loses most of the information about three-way correlations. For
> instance, you can know that candidates A, B, and C each got 10 votes,
> and that each pair of them was combined on 5 ballots, but you don't
> know if that's 5 votes for each pair, or 5 votes for the group and 5
> for each. Note that those two possibilities actually involve different
> numbers of total votes --- 15 in the former, 20 in the latter. In
> order to fix this, you can instead make separate matrices depending on
> how many total approvals there are on each ballot --- a "matrix" for
> all the ballots approving 1, one for all those approving 2, etc. Thus,
> in essence, you get a 3D matrix instead of a 2D one.
>
> Once you have a matrix, you can essentially turn it back into a bunch
> of ballots, and run whatever election method you prefer. The result
> will be proportional insofar as the fake ballots correspond to the
> real ballots. How much is that? Well, I can make some hand-wavy
> arguments The basic insight of the Central Limit Theorem (CLT) ---
> that second moments tend to dominate third moments as the number of
> items increases --- would seem to be in our favor.
>
> I think this could be an interesting avenue of inquiry. But on the
> other hand, the math involved will immediately make 99% of people's
> eyes glaze over.
>
> If this is not possible, then the only 2 ways towards summability are
> partisan categorization and delegation. GOLD uses both. For a
> nonpartisan method, I don't think there's any way to be summable
> without forcing people to delegate; and I think that forced delegation
> is going to be a deal-breaker for some people.
>
> So I'm frustrated in trying to design a nonpartisan proportional
> method that's as practical as GOLD and 3-2-1 are for their respective
> use cases.
>
>
> ----
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--
Richard Lung.
http://www.voting.ukscientists.com
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