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

On 10.09.2022 15:25, James Gilmour wrote:

I understood Colin's response to be about what methods should do in
general, similar to say, a criterion definition. The logic of such a
general argument is something akin to:

• Suppose that a voter faces some particular situation.
• Then it's reasonable that the method should interpret the ballot or
  the voter's response in a way that's consistent with some property.
• Method X does or does not do this.
• Therefore this part about X is good/not so good.

So Colin is saying that it's reasonable that a method should give a
voter an option to, in effect, mark a number of candidates as unknown,
so that if the method has to decide between these candidates, it will
not rely on that voter's ballot.

Such arguments are unconcerned with the algorithm that implements any
particular method.

We could check whether IRV does or doesn't pass certain criteria,
though. E.g. I can say that Condorcet compliance is a reasonable
extension of majority rule and adding a Condorcet preround never makes a
method more strategically susceptible (for certain definitions thereof),
and that this is a point against IRV. Or you could say that IRV passes
both LNHs which very few other methods can, and that's a point in its favor.

As long as we have some notion of whether some philosophy or criterion
is desirable or not, we can indeed check if IRV follows it. Now it may
be that the designers of STV never intended it to follow that philosophy
or pass that criterion, but that's not really relevant when determining
whether a method is fit for purpose according to one's own standards, or
those of some electorate.

-km

We realize that you think that.  It's quite apparent.

So where is the source of that confusion.  The document you had attached says "This method of filling a single vacancy is commonly called the Alternative Vote. It also known as Preferential Voting or Instant Run-off Voting."

Now, let's exclude the cardinal methods: Score, STAR, Approval from these "several different 'social choice' methods" to remove these from the semantics.  We are talking about ordinal methods; these are methods that use only a ranked-order ballot.

As far as I can tell, there are four basic classes of ranked-order methods:

1. Borda count
2. Bucklin voting
3. Hare STV (IRV etc., FPTP is a degenerate case)
4. Condorcet (several methods, some invented by persons present)

I don't know any others.  Within each method, what do each of those marked ballots mean?  That is not the same question as asking "How are these ballots tabulated?"

No, that is misinformation.  And we can prove it using simple logic and comparing the manner that the ranked ballot is tabulated using these different ordinal methods.

In each of those methods, if Candidate A is ranked higher than Candidate B, then that voter intends to vote for Candidate A, not B, if it were a simple two-person FPTP election.  That's all that can be inferred of the voter's intent from the marks on the ballot.

This is also true; in each of these methods, if Candidate A is ranked and Candidate B is not ranked.  We know, from the marks on that ballot, that the voter intends to vote for Candidate A, not B, if it were a simple two-person FPTP election.  That can be and is all that can be inferred of the voter's intent from that marking of the ballot.

I define "the truth" to be an accurate description of reality.  The above two paragraphs are true.

Then the next thing to do is consider more than one unranked candidates.  Some, not all, ranked-choice (or ordinal) methods allow for equal ranking of candidates.  That difference is relevant to the specific method, but all methods (in jurisdictions that don't force voters to rank each candidate) allow for any number of unranked candidates.  In the case where equal ranking is allowed, there is no operational difference between those candidates being unmarked and those candidates being equally ranked at the very bottom.

That means, in ordinal (ranked-choice) voting, that unranked candidates are consistently interpreted as being tied for the lowest, bottom ranking.  But there is no difference, in voter intent, between the same ballot in an ordinal method that disallows equal ranking versus being in an ordinal method that allows equal ranking.  What the voter's expressed preference is essentially the same.  The voter intends to vote for any of the ranked (or higher-ranked) candidates and not for that unranked (or bottom-ranked) candidate in any simple two-candidate FPTP election.

All that disallowing equal rankings means that, if not ranking is also disallowed, the voter would be forced to choose between unranked candidates, which unranked candidate is preferred over which other unranked candidate.  But, still, any of those previously unranked candidates that now the voter is forced to rank, will be ranked lower than any of the previously ranked candidates.  In a simple two-candidate FPTP election, the intent of the voter is unchanged between any of the previously ranked candidates and any of the previously unranked candidates.  We know who the voter is voting for.

And I did none of that above.

and tautologies are tautologies.  That's true, but is what some might label an empty truth.

Well, "nothing in the Election Rules for an IRV count that says anything about the 'meaning'", but the Election Rules do not have the ability to remove the operational implication of the relationship between the ranked and unranked candidates.  In any ranked ballot, the meaning is the same: That voter prefers any ranked candidate over any unranked candidate.  And that is operationally equivalent to the same ballot where unranked candidates are tied for the lowest preference.

That's about the function of the election.  It still changes nothing about the meaning of the marked ballot.  And the meaning of the marked ballot is as I said above: If A is ranked higher than B or if A is ranked and B is unranked, if the election was a simple two-candidate First-Past-The-Post election, that voter is voting for A and not voting for B.

James, you may have a doctorate.  You may live on the island where the notion of the single-transferable vote was birthed.  But when you keep repeating:

... then you are betraying your misunderstanding.  Not mine.

And when you claim:

That's true.  But when you claim:

That's false.  The unmarked preferences do mean something more.  They means that the voter prefers (and would vote for) any of the marked candidates over any of the unmarked candidates.

And that is operationally equivalent to equally-ranking all of those unmarked candidates at the very lowest ranking level on the ballot.

--

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

.
.
.

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@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

<ERS-Alternative-Vote-Election-Rules.pdf>

Election-Methods mailing list - see https://electorama.com/em for list info

On 11.09.2022 13:40, Juho Laatu wrote:

I consider those to be roughly equivalent. What equal-rank means to me
is something along the lines of "with the time I've given myself, I
can't see a difference between these candidates, and I think it's more
worthwhile for other ballots to decide".

Unless two candidates are identical, every voter probably has an ever so
slight preference between the two that he could discover given enough
effort. But a voter equal-ranking simply says that it's not worth it.
(It's sort of related to the idea of the absolute threshold or JND.)

-km

Your approach seems to be close to the tradition of voters estimating the utility of each candidate, and then putting them in linear order, based on those identified utilities. That is a good approach. No chances given to influence the elections any more than that. Everyone understands that approach, and can vote accordingly with full strength of one's vote.

The "unmarked treated as equal last" rule could be seen as adding to this the idea that all given opinions should be positive and not negative. The unmarked candidates must thus be at zero level. (There are also other, more practical reasons behind the "equal last" practice. It may be good not to give totally unknown candidates any "unearned" points.)

One could indeed "force" voters to always rank all the marked candidates (i.e. explicitly marked ties not allowed) without losing much. There is always a small difference, and if not, one can always flip a coin. In some ballot formats equal rankings are natural, and in some others unnecessarily complex.

I don't actually see any practical benefits in the "A B" approach or other "no opinion" additions . It is an interesting theoretical area of study to see what kind of additional information we could use (up to free form algorithms), but for large competitive single winner elections with independent voters the basic approach of ranking + "equal last" seems to be a stable basis. (Different strength preferences (A>>B>C) might be useful somewhere - or seriously - maybe not really :-) .)

(Different defeat strength measurements may treat those pairwise ties in different ways, but that's another story.)

Juho

Well written and well argued!

And each additjonal explanation reveals more clues of how to construct an
algorithm embodying these lofty principles!

On Sat, Sep 10, 2022, 2:33 PM Richard Lung voting@ukscientists.com wrote:

On 9/11/22 16:31, Juho Laatu wrote:

I would probably say that we can define honesty for ranked ballots and
for von Neumann-Morgenstern utilities, but anything beyond that and it
gets really hard. And if we can't define honesty, then methods can get
away with externalizing their burden on the voters the way Range does.

As for different strength prefereces, it feels kind of like "neither
this nor that". I'd rather have an automatically normalized rated ballot
(if utilities are important) or MJ-style grades or plain rankings (if not).

(Personally, I'd imagine what voters can reliably answer lies somewhere
between rankings and vNM utilities. Just where, I don't know, though.)

-km