[EM] “Monotonic” Binomial STV

[Richard Lung]

HelloForest,

All the sciences that share the same structure of measurement are 
subject to formal inter-disciplinary comparisons. Evolutionary theory 
has been adapted by several disciplines, including speculation on the 
multi-verse. Transferable voting especially suits evolution, as Enid 
Lakeman observed, in How Democracies Vote.

Perhaps because I was too late to be educated in the New maths, it took 
me too long to tumble to the fact that a comparison of election method 
or “electics” with physics depends on a complex value election count. 
And that depends on an election, in at least two dimensions.

Binomial STV is a complete single dimension of choice. The operative 
word is complete, which makes possible its consistent binomial theorem 
expansion into exponentially higher orders of count, for unlimited 
analysis in depth.

The completeness also makes possible the combination of a second 
dimension into a complex number election count.

Binomial STV is a complete dimension, because it accurately rationally 
book-keeps, in keep values, all the voters preferential information. 
Other electoral systems do not do this. They make arbitrary or expedient 
rules to come to a result that does not well follow the voters wishes. 
They either exclude preferential information or they do not include it, 
in the first place. They use the preferences in ways not requested by 
the voters. In the case of traditional STV methods, they do try to 
always follow the voters preferences, but do so, less rationally 
accurately, only on an ordinal scale, in the exclusion count.

  Regards,

Richard Lung.


On 01/03/2022 22:25, Forest Simmons wrote:
> Richard,
>
> I enjoy all of the connections you make including with quantum 
> mechanics ... understanding is a network of connections anchored in 
> the ideas most familiar and intuitive to us.
>
> My PR idea for Binomial Bucklin is based on the idea once articulated 
> by Kevin that Bucklin can be thought of as a procedure for arriving at 
> a reasonable approval cutoff ... i.e. a DesignatedStrategyVoting 
> version of approval just as Instant Runoff can be considered a DSV 
> version of Plurality .... a procedure for finding a reasonable 
> candidate for whom to cast your one and only vote.
>
> And just as Approval can be adapted for PR in the form of PAV, 
> Sequential PAV, or even the Martin Harper Lottery, so also should 
> Binomial Bucklin have similar possible modifications to various PR 
> versions.
>
> Best Wishes,
>
> Forest
>
> El mar., 1 de mar. de 2022 1:09 p. m., Richard Lung 
> <voting at ukscientists.com> escribió:
>
>     Hello Forest,
>
>     Yes, with Binomial STV, a blank ballot paper is the same as None
>     Of The Above. That would count as a whole vote against any
>     candidate. But any blank preferences go towards a fraction of a
>     vote, counting towards a quota for an empty seat, by the usual
>     Gregory method, expressed in keep value terms.
>
>     I had to introduce this feature, to establish the relative
>     satisfaction or dissatisfaction with the candidates. To take an
>     extreme example, an extremely disaffected voter might vote
>     preference 10 out of ten candidates, against some especially
>     detested candidate, and leave the rest blank. Preference 1 would
>     help to elect a non-candidate.
>
>     I take it this case would be untypical, and preference entropy
>     would weigh in favor of election counts, reinforced by low
>     exclusion counts. Binomial STV has formally equal election and
>     exclusion counts, like physics laws that are formally
>     time-reversible. But in practise, they go one way, except on the
>     quantum (very small) scale.
>
>
>     Bucklin method sounds like a method used once in British Columbia
>     in about 1951. Enid Lakeman, in How Democracies Vote, explained
>     how it is not proportional representation, as was mistakenly
>     suggested during the BC Citizens Assembly referendums. One faction
>     could take all the seats with  51% of the votes. And Bucklin seems
>     to still employ ordinal scale (only calculating by more or less)
>     displacements or transfers of candidates votes.
>
>     Binomial STV is essentially Gregory method PR, expressed in keep
>     values, that allow accurate calculating quota-deficit candidates,
>     as well as quota-surplus candidates. And also applied to counting
>     exclusions, as well as elections. This allows for a keep value
>     order of popularity. All kinds of STV have theoretical limitations
>     but transfer well from vote to count. Adding a rational exclusion
>     count should be worthy of further investigation, including real
>     world examples.
>
>     Binomial STV is a uniquely scalable system, capable of consistent
>     exponential expansion of the count, according to the binomial
>     theorem, offering unlimited representation, perhaps of the
>     exponential growth of human knowledge.
>
>     Regards,
>
>     Richard Lung.
>
>
>     On 01/03/2022 00:58, Forest Simmons wrote:
>     > "...It follows that if the abstentions add up to a quota, a seat is > not taken...." > > Kind of like NOTA ...
>     none of the above. > > I'm trying to think how I would design a
>     method in the spirit of > Binomial STV .... elections vs
>     exclusions ... preferences vs reverse > preferences. > > Perhaps
>     some variant of Bucklin that gradually collapses ballot > rankings
>     inward (ER Whole?) when not enough top or bottom votes exist > to
>     meet quotas for further inclusion or exclusion ... taking special
>     > care to insure both monotonicity and clone independence in the >
>     process, if possible. > > I think collapsing has more potential
>     for monotonicity than does > elimination, and I'm glad that
>     Binomial stv keeps all of the players > in the game until the
>     final count, like Bucklin does. > > -Forest > > > > El dom., 27 de
>     feb. de 2022 4:54 p. m., Richard Lung > <voting at ukscientists.com>
>     <mailto:voting at ukscientists.com> escribió: > > > On 28/02/2022
>     00:45, Richard Lung wrote: >> >> Thanks for your thoughts, Kevin,
>     >> >> In this simple instance, the election and exclusion quotas
>     cancel. >> But I would be lost without it, in multi-member PR
>     cases of >> involved transferable voting. There are a few examples
>     in my >> e-books, (The Super-Vote supercharged..., Elect and
>     Exclude..., FAB >> STV...) free from Smashwords, in epub format,
>     and pdf versions free >> from archive. org where putting "Richard
>     Lung" in quotes in the >> text box should come up with about 19
>     titles. >> >> The square root may not be strictly necessary, which
>     may be why I >> keep forgetting it. But it keeps the average keep
>     values on a par >> with the election and exclusion keep values.
>     The square root is for >> the correct form of the geometric mean,
>     -- an important average. >> >> Yes, you are right, there is some
>     other rule not stated -- All the >> abstentions are counted. in
>     more complex elections, they have to >> be, so as not to distort
>     the relative importnce of the election >> and exclusion counts. It
>     follows that if the abstentions add up to >> a quota, a seat is
>     not taken. This provides an incentive to >> nominate good
>     candidates, who work for the voters rather than their >> nominees.
>     >> >> So, a candidate is not necessarily electable. More-over a
>     large >> enough quota like Hare, with a small number of seats
>     would also be >> prohibitive of election, given the voters free
>     choice. >> >> Regards, >> >> Richard Lung. >> >> >> >> On
>     27/02/2022 19:30, Kevin Venzke wrote: >>> Hi Kristofer/Richard,
>     >>> >>> I wonder not just about the square root, but also if the
>     quota >>> has some additional role in the method, perhaps when
>     there are 4+ >>> candidates. >>> >>> Because this expression: (
>     quota / keep ) * ( exclude / quota ) >>> Appears to simplify to: (
>     exclude / keep ) >>> >>> This creates the appearance that the
>     quota has no effect on the >>> outcome. >>> >>> Richard stated
>     that final values below unity are electable. It >>> looks like
>     there will always be an electable candidate, unless >>> it's a
>     complete tie, or perhaps if there is some other rule not >>> yet
>     stated here. >>> >>> It seems to me that the 3-candidate 1-winner
>     case of this method >>> is monotone. It would help to see a
>     four-candidate election >>> resolved, too. >>> >>> Kevin >>> >>>
>     Le dimanche 27 février 2022, 07:41:20 UTC−6, Kristofer >>>
>     Munsterhjelm<km_elmet at t-online.de> <mailto:km_elmet at t-online.de> a
>     écrit : >>>> On 27.02.2022 14:04, Richard Lung wrote: >>>>> Thank
>     you, Kristofer, >>>>> >>>>> >>>>> for first example. >>>>> >>>>>
>     The quota is 100/(1+1) = 50. >>>>> >>>>> Election keep value is
>     quota/(candidates preference votes) >>>>> >>>>> Exclusion keep
>     value equals quota/(candidates reverse >>>>> preference vote):
>     >>>>> >>>>> Geometric mean keep value ( election keep value
>     multiplied by >>>>> inverse exclusion keep value): >>>> Geometric
>     mean: >>>> >>>> A: square root of (50/51 x 2/50) ~ 0.198 B: square
>     root of >>>> (50/49 x 1/50) ~ 0.143 C: ~= infinity (or very high)
>     >>>> >>>> So B wins, having the lowest keep value. Is this
>     correct? >>>> >>>> (You seem to have omitted the square root in
>     your calculations, >>>> but it shouldn't make a difference.
>     Without the square root, A >>>> and B's values are 0.0392 and
>     0.0204 respectively.) >>> Hi Kristofer/Richard, >>> >>> I wonder
>     not just about the square root, but also if the quota >>> has some
>     additional role in the method, perhaps when there are 4+ >>>
>     candidates. >>> >>> Because this expression: ( quota / keep ) * (
>     exclude / quota ) >>> Appears to simplify to: ( exclude / keep )
>     >>> >>> This creates the appearance that the quota has no effect
>     on the >>> outcome. >>> >>> Richard says final values below unity
>     are electable. It seems >>> like there will always be an electable
>     candidate, unless it's a >>> complete tie, or perhaps if there is
>     some other rule not yet >>> stated here. >>> >>> Kevin >>> >>> >>>
>     Le dimanche 27 février 2022, 07:41:20 UTC−6, Kristofer >>>
>     Munsterhjelm<km_elmet at t-online.de> <mailto:km_elmet at t-online.de> a
>     écrit : >>>> On 27.02.2022 14:04, Richard Lung wrote: >>>>> Thank
>     you, Kristofer, >>>>> >>>>> >>>>> for first example. >>>>> >>>>>
>     The quota is 100/(1+1) = 50. >>>>> >>>>> Election keep value is
>     quota/(candidates preference votes) >>>>> >>>>> Exclusion keep
>     value equals quota/(candidates reverse >>>>> preference vote):
>     >>>>> >>>>> Geometric mean keep value ( election keep value
>     multiplied by >>>>> inverse exclusion keep value): >>>> Geometric
>     mean: >>>> >>>> A: square root of (50/51 x 2/50) ~ 0.198 B: square
>     root of >>>> (50/49 x 1/50) ~ 0.143 C: ~= infinity (or very high)
>     >>>> >>>> So B wins, having the lowest keep value. Is this
>     correct? >>>> >>>> (You seem to have omitted the square root in
>     your calculations, >>>> but it shouldn't make a difference.
>     Without the square root, A >>>> and B's values are 0.0392 and
>     0.0204 respectively.) > ---- Election-Methods mailing list - see
>     https://electorama.com/em > for list info > epresentatio
>
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