[EM] The quota and the quotient

[Forest Simmons]

Time to put aside that forgetful functor and hop up those cuddly categories!

El sáb., 30 de jul. de 2022 7:09 a. m., Andy Dienes <andydienes at gmail.com>
escribió:

> 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
>>
>
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