[EM] “Monotonic” Binomial STV

[Forest Simmons]

Thanks, Richard. That's very helpful and tantalizing!

El sáb., 26 de feb. de 2022 4:21 a. m., Richard Lung <
voting at ukscientists.com> escribió:

>
> Thank you, Forest,
>
> Your example is the kind of example that Riker gave.
>
> Here the quota equals 50 = 100/[1+1].
>
> Original profile:
>
> Election Keep value is quota/candidate vote:
>
> for A  50/35
>
> B:  50/33
>
> C:   50/32
>
> Exclusion keep value = quota/candidate reverse vote:
>
> for A:  50/33
>
> B:   50/32
>
> C:  50/35
>
> Final (geometric mean) keep values, divide election keep value by
> exclusion keep value.
>
> (This is equivalent to multiplying by the inverse exclusion keep value, as
> a make-shift second opinion election keep value.)
>
> for A:  50/35 x 33/50. And take their square root ~ ,971
>
> for B: 50/33 x 32/50.  As above, gives ~ .9847
>
> for C:  50/32 x 35/50. ... gives ~ 1.0458
>
> Keep values below unity are technically electable. A wins, with lowest
> keep value.
>
> New profile:
>
> Election divided by exclusion keep values:
>
> A: 50/37 x 31/50. Take square root of 31/37, for ~ .9153
>
> B: 50/31 x 32/50. As above, ~ 1.016
>
> C:  50/32 x 37/50. As above, ~ 1,075
>
> Again, A is elected as before, and with a yet lower keep value, as the
> extra preferences for A warrant.
>
> Regards,
>
> Richard Lung.
>
>
> On 26/02/2022 01:30, Forest Simmons wrote:
>
> Richard,
>
> Here's an example of monotonicity failure in conventional single winner
> STV as I understand it:
>
> Original profile of ballots:
>
> 35 A>B>C
> 33 B>C>A
> 32 C>A>B
>
> C eliminated and A wins.
>
> New profile: two members of B faction defect to A faction:
>
> 37 A>B>C
> 31 B>C>A
> 32 C>A>B
>
> Now B is eliminated and C wins.
>
> How does Binomial STV avoid this monotonicity failure?
>
> Thanks!
>
> -Forest
>
> El jue., 24 de feb. de 2022 10:36 a. m., Richard Lung <
> voting at ukscientists.com> escribió:
>
>>
>> “Monotonic” Binomial STV
>>
>>
>>
>> I was told (hello Kristofer) that I could not say that binomial STV is
>> “monotonic” unlike traditional or conventional STV. But I gave my
>> reasons why I could say this, and they were not contradicted or even
>> answered. It is not tabu or forbidden to say, and say again, what there is
>> good reason to believe is true, whatever the prevailing view.
>>
>> In conventional STV, the transfer of surpluses, over a quota, to next
>> preferences is monotonic. There is “later no harm” unlike the Borda count.
>> The intermediate Plant report quoted a non-monotonic test example from
>> Riker, to justify their rejection of STV. This was based solely on the
>> perverse outcome of a different candidate being last past the post, for
>> elimination.
>>
>> Riker made the unsupported claim that STV is “chaotic.” >From a century of
>> STV usage, he did not provide a single real case of this. The record is
>> that STV counts well approximate STV votes, all things considered.
>>
>> A paper that tried to provide some doubt, of STV as a well-behaved
>> system, drew not on a conventional STV election of candidates, but on NASA
>> using STV for outer space engineers to vote on a set of best trajectories
>> (I forget where).
>>
>> Traditional STV is not “chaotic”. It is not even wrong. It is just an
>> initial or first approximation of binomial STV, a zero order binomial STV.
>>
>> Zero order STV is a uninomial count that does not clearly distinguish
>> between an election count or an exclusion count. In 1912, HG Wells said of
>> FPTP, we no longer have elections we only have Rejections. From first order
>> Binomial STV, the two counts, election and exclusion counts, are clearly
>> distinguished and both made operational.
>>
>> Binomial STV does not exclude candidates during the count. It uses an
>> exclusion count, to help determine a final election. This exclusion count
>> is exactly the same or symmetrical to the (monotonic) transfer of surplus
>> votes in an election count.
>>
>> In both election and exclusion counts, Gregory Method or the senatorial
>> rules are expressed in terms of keep values, which enable proper
>> book-keeping of all preferences. Keep values can keep track of all the
>> preference votes, including abstentions. So, no perverse results are
>> possible from the chance exclusion of preferences from this or that
>> candidate last past the post. This is also why binomial STV is one complete
>> dimension of choice.
>>
>> Binomial STV has “Independence of Irrelevant Alternatives.” For instance,
>> it makes no difference what level the quota is set, to the order of the
>> candidates keep values, their order of election. It is just that bigger
>> quotas raise the threshold of election.
>>
>> Regards,
>>
>> Richard Lung.
>> ----
>> Election-Methods mailing list - see https://electorama.com/em for list
>> info
>>
>
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