[EM] The quota and the quotient

[Andy Dienes]

Let me answer your question with another question, I say, to fight fire
with fire.

The Indicated Vote, being an analytic continuation of the single vote, can
be seen as a contravariant functor from the internal preference to the
external preference. Examination of each (the internal) yields a measure
group; the measure group never crossing (though sometimes touching) into
the strategy space, with each Indicated Vote being summaried independently
and no regard for the external.

This process of coenumeration is not unlike Boltzmann's Demon (a phenomenon
prevalent in Statistical Mechanics causing much grief to purveyors of the
discipline, but we shall not get into that here) where the analytic
continuation of preferences makes the measure group ``smooth out'' the
external preference. As water shakes off a duck, so too does the internal
preference shake off the Indicated Vote.

If I understand correctly, the quota, count, and keep value can all be
regarded as by-products of the summaried internal preference, leveraging (a
lever is a classical simple machine) the ability of holomorphicity to
renumerate the quantities. All that is needed is to define the appropriate
chart and atlas, and whoopee! We are on our way. Grothendieck nearly had
this vision in the late 1960s, as communicated in a letter to the King of
Spain, but the assassination of Zayn Thimbleau threw a wrench (or should I
say, lever) into any burgeoning reform efforts... I digress.

My question to you remains: at what point in the coenumeration process does
the rationality (or lack thereof) fail contravariance? Are they one and the
same, or is there an omitted variable?

Best,
Andy

On Fri, Jul 29, 2022 at 1:37 PM Richard Lung <voting at ukscientists.com>
wrote:

>
> The quota and the quotient
>
>
>
> Binomial STV combines a rational election count with a rational exclusion
> count. The election count is conducted, in the normal way, in order of the
> voters preferences. The exclusion count is conducted in exactly the same
> way (symmetrically), but with the preferences in reverse order.
>
> The election count elects candidates. The exclusion count excludes
> candidates.
>
> But some candidate may be both elected and excluded. ("Schrodingers
> candidate" as Forest Simmons might say, tho this term is poetic license,
> here. Binomial STV does, however, like quantum physics, deal in
> probabilities.) Their election keep value can be compared with their
> exclusion keep value.
>
> The keep value is the quota divided by a candidates vote, including
> preference transfers.
>
> The election keep value is divided by the exclusion keep value. If this
> over-all keep value, or quotient, is still unity or less than unity, the
> candidate is relatively elected, by the quotient. That is as well as
> positively elected by the quota.
>
> If two such candidates are so placed, for one remaining seat, the
> candidate with the lower quotient is elected or wins.
>
> The quota is a more powerful measurement than the quotient, because the
> ratio scale is more powerful than the interval scale. Occasionally the
> quotient may arbitrate, when election and exclusion quotas conflict.
>
> Does this seem consistent, or not inconsistent, to you?
>
> Regards,
>
> Richard Lung.
>
>
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20220730/abdfd9cf/attachment-0001.htm>