[EM] Truncation (was re: Defeat Strength)

[Richard Lung]

Conservation of information requires all preferences be counted. That includes abstentions from some or none of the preferences, like a carte blanche. Counting non-preferences is a logical implication of allowing the voters to exclude, as well as elect candidates, because whether blank preferences come early or late on the ballot determines the relative importance of election or exclusion, in a (binomial) count.

A binomial count ballot looks just like any other preference vote, 1, 2, 3, etc, but is a preference (election) count and a reverse preference (exclusion) count. An election of 5 out of 10 candidates would more or less elect the first 5 prefered candidates, and less or more exclude the next 5 preferences. Preference 10 would count as much against a candidate as preference 1 would count for. But the voter could abstain from either preference, or both. 
Abstentions would go towards an unfilled vacancy, giving voters the power to leave a seat vacant from a less than satisfactory candidate line-up

The mathematical significance of such a binomial count is that it completes a dimension of choice. There could be a second dimension of choice, making possible a vector model, notably from physics. Physics observes conservation laws, including of information.

Regards,
Richard Lung.





On 10 Sep 2022, at 2:25 pm, James Gilmour <jamesgilmour at f2s.com> wrote:

I think there is a lot of misunderstanding in this discussion under the Defeat Strength heading, now Truncation.  I suspect it may arise from a confusion of "IRV" with "preferential voting".  IRV = Single Transferable Vote applied to a single-winner election (= Alternative Vote in the UK) uses preferential voting, but there are several (many?) other ways of counting the votes recorded on ballot papers marked with voters' preferences.  You could use a Borda count, or a Condorcet count, or several different 'social choice' methods.  All have different implications for the "meaning" of preferences and the "meaning" of truncation (i.e. where the voter has not marked a preference against one or more candidates).

What we are not at liberty to do is to take some aspect of the imputed philosophy of these other methods and say that it applies to IRV, or that it should apply to IRV.  IRV is IRV, and there is nothing in the Election Rules for an IRV count (attached) that says anything about the "meaning" of multiple blanks (no preferences against several candidates) other than that voter prefers the marked candidates to all and any of the unmarked candidates and that voter has no preference AMONG the unmarked candidates.  If the count proceeds such that the next IRV exclusion has excluded (eliminated) all of a voter's marked candidates, the Returning Officer declares that ballot paper 'non-transferable' and that voter takes no further part in deciding the outcome of the election.

James Gilmour


> -----Original Message-----
> From: Election-Methods [mailto:election-methods-bounces at lists.electorama.com] On Behalf Of Kristofer Munsterhjelm
> Sent: 10 September 2022 10:30
> To: Colin Champion <colin.champion at routemaster.app>; election-methods at lists.electorama.com
> Subject: Re: [EM] Trunaction (was re: Defeat Strength)
> 
>> On 9/10/22 10:48, Colin Champion wrote:
>>> On 09/09/2022 10:31, Kristofer Munsterhjelm wrote:
>>> 
>>> For truncation in particular, I think equal last means that unranked
>>> candidates provides information to the method that the voter desired
>>> those candidates to be considered worse than everybody else, while "I
>>> don't know" indicates that the voting method shouldn't care at all.
>>> 
>> I don t agree with Kristofer's statement.
> 
> I'm not taking a position, I'm just saying that that's what the "equal last" interpretation implies, and contrasting that to an interpretation where unranked means no opinion (kitten duel example).
> 
> I'm not entirely sure which I personally think is the better first-principles interpretation. Practically speaking, I think Forest is right when he says:
> 
>> As I understand it, the custom of treating truncation/abstention the
>> same as equal last rank is a practical expedient to ward off dark
>> horse upsets.
> 
> That is, counting unknowns as ranked below everybody else is a way to prevent a completely unknown candidate from winning, similar to the convention of filling in unrated candidates as zero in Range. This suggests that if honest performance is what we care about, unranked should be considered "no opinion".
> 
> On the other hand, there's something intuitively appealing about the Plurality criterion:
> 
> "If A is ranked first on more ballots than B is ranked at all, then A's probability of winning should be no lower than B's",
> 
> which is about a sort of cold start problem: if the data indicates that some people like A, but the data is less clear about B, then that should be taken to be in favor of A.
> 
> If complexity is no issue, there might be a soft quorum[1] analog that both satisfies Plurality and doesn't presume too much about the ranking of unknowns. But I don't know what it would look like.
> 
> -km
> 
> [1] For range voting: https://rangevoting.org/PuzzDLaplace.html
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