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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.<br>
No need for the retrograde steps you mention.<br>
from<br>
Richard Lung<br>
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On 08/06/2017 17:33, Jameson Quinn wrote:
<blockquote
cite="mid:CAO82iZzq+y-sLFN+2p2fgEQPB_ejp=EhnNtZny0mUb0EyPnOOg@mail.gmail.com"
type="cite">
<div dir="ltr">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.
<div><br>
</div>
<div>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. <a moz-do-not-send="true"
href="http://wiki.electorama.com/wiki/Geographic_Open_List/Delegated_%28GOLD%29_voting">GOLD
voting</a> does it by giving voters a choice between that
and delegation. Asset voting and variants use delegation. </div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>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.</div>
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<pre class="moz-signature" cols="72">--
Richard Lung.
<a class="moz-txt-link-freetext" href="http://www.voting.ukscientists.com">http://www.voting.ukscientists.com</a>
Democracy Science series 3 free e-books in pdf:
<a class="moz-txt-link-freetext" href="https://plus.google.com/106191200795605365085">https://plus.google.com/106191200795605365085</a>
E-books in epub format:
<a class="moz-txt-link-freetext" href="https://www.smashwords.com/profile/view/democracyscience">https://www.smashwords.com/profile/view/democracyscience</a>
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