responding to both Forest and Kristofer...

well, i am not sure i said i was not satisfied with it.  but, in truth, i am not entirely satisfied with it.  but what i am fishing for are ideas to make it better.

what's a "valid" ballot?

i sure as hell am staying away from the term "beats-all candidate".  i don't think "pairwise champion" or even my neologism "consistent majority candidate" will do either.

the form of the language i wrote is in the form of the IRV language that was put on the ballot for voters to vote on.  i added a few defining terms.  but the real legislation will break out definitions into a section of the bill.  see page 6 in https://legislature.vermont.gov/Documents/2022/Docs/BILLS/H-0236/H-0236%20As%20Introduced.pdf

but the IRV template language (which is page 3 of https://legislature.vermont.gov/Documents/2022/Docs/BILLS/H-0448/H-0448%20As%20Introduced.pdf) looked more like this with some important definitions/clarification is at the bottom here.  That language is what I modified for the BTR-IRV but I am trying to see what it might look like for a straight Condorcet election.

"more than half of the ballots"???  as in an absolute majority??

the final legislation will actually put in needed definitions early in the language.  but this template is more abbreviated.

Now, I understand that we could spell out the pairing of candidates, but then it starts looking like a mathematics paper:

"The ballot shall list N candidates (including Write-in) and there shall be N(N-1)/2 unique pairings of candidates (including combined write-in).  In each pairing of two candidates, if the number of ballots ranking a selected candidate higher than the other candidate is less than the number of ballots marked to the contrary, then the selected candidate is marked as defeated.  The candidate who is not defeated in any pairing shall be elected."

What I am looking for is language without outside references (like references to the Schulze method or Tideman Ranked-Pairs), without neologisms, and can define the method procedurally in normal English.

I confess that what I want to do is present legislators with straight Condorcet language along with the BTV-IRV language to compare to the IRV language (below) in the same template form.

Thank you, everyone.

--

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

"Imagination is more important than knowledge."

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The IRV language slightly modified by me to define and clarify a couple of terms:

All elections of [office] shall be by ballot, using a system of ranked-choice voting without a separate runoff election. The presiding election officer shall implement a ranked-choice voting protocol according to these guidelines:
(1) The ballot shall give voters the option of ranking candidates in order of preference. Lower ordinal preference shall be considered higher rank and the candidate marked as first preference is considered ranked highest. Equal ranking of candidates shall not be allowed. Any candidate not marked with a preference shall be considered as ranked lower than every candidate marked with a preference.
(2) If a candidate receives a majority (over 50 percent of all ballots) of first preferences, that candidate is elected.
(3) If no candidate receives a majority of first preferences, an instant runoff retabulation shall be performed by the presiding election officer. The instant runoff retabulation shall be conducted in sequential rounds. A "continuing candidate" is defined as a candidate that has not been defeated in any previous round. Initially, no candidate is defeated and all candidates begin as continuing candidates.
(4) In each round, every ballot shall count as a single vote for whichever continuing candidate the voter has ranked highest. The candidate with fewest votes is defeated in the current round.
(5) The aforementioned instant runoff retabulation, eliminating one candidate each round, shall be repeated until only two candidates remain. The remaining candidate then receiving the greatest number of votes is elected.
(6) The [governing jurisdiction] may adopt additional regulations consistent with this subsection to implement these standards.

If it were up to me, I would use the fall-back method itself to seamlessly
finesse these niceties, and then remark that it obviously satisfies the
Condorcet and therefore Majority criteria. Here's the complete
definition/description of BTR-IRV in that succinct form:

Determine the winning candidate by loser elimination from the marked ranked
choice ballots as follows:

While there remain two or more uneliminated candidates, eliminate (by
crossing out and transferring votes from) the head-to-head loser of the
pairwise contest between the two candidates with the fewest transferred
votes. [In a pairwise contest the winner is the one ranked ahead of the
other on more ballots than not ... the other one is the loser of the
pairwise contest.]

After the eliminations are complete elect the remaining candidate.

Remark: this procedure never eliminates a candidate with more than half of
the initial votes (or transferred votes at later stages), nor does it ever
eliminate any candidate that is unbeaten pairwise. In other words, neither
a Majority Candidate nor a so called "Condorcet Candidate" can lose under
these rules.

As you can see, this concise approach obviates the need for breaking apart
the description of the method into steps 1, 2, 3, and 4.

The details of the construction and precinct summation of the pairwise and
win/loss/tie matrices should be relegated to the technicalities section
along with tie breaking rules, etc.

El mié., 1 de sep. de 2021 8:29 a. m., robert bristow-johnson <
rbj@audioimagination.com> escribió:

Oh, but I am not looking for the Condorcet loser and, with this straight-ahead Condorcet language, I don't want sequential rounds (but simultaneous runoffs).  If I was doing sequential rounds, then I think Bottom Two Runoff is the simplest language for a Condorcet method.

But for straight-ahead Condorcet I want it to satisfy the simple rule: "If the number of ballots marked ranking Candidate A higher than Candidate B exceeds the number of ballots marked to the contrary, then Candidate B is not elected."

What language is complete yet simpler and clearer and more concise than:

"The candidate, who is the Condorcet winner, is elected if the rankings on all of the ballots indicate that this one candidate defeats, by simple majorities of voter preferences, all other candidates when compared in turn with each other individual candidate.  A selected candidate defeats another candidate by a simple majority when the number of ballots marked ranking the selected candidate higher than the other candidate exceeds the number of ballots marked to the contrary."

Assuming a CW exists, I want language that is better (simpler, more concise) than that to identify the CW.  Perhaps I gotta get more procedural about this:

"Given the number of candidates as N, including combined write-in, then the number of possible candidate pairings is N(N-1)/2.  For each pairing of candidates, the defeated candidate is whom that the number of ballots marked ranking the other candidate higher than the defeated candidate exceeds the number of ballots marked to the contrary.  The candidate, who is the Condorcet winner, is whom that is not shown as defeated in any pairing is elected."

Is that better?  I just don't know.  Maybe this BTR-IRV thing is the most concise language to get for a Condorcet method.  I'm just fishing around for good, concise, yet complete language that is plausible or credible for legislation.  Not that I am all that sanguine about the Vermont legislators will buy it, but I thought maybe I would try.

I dunno.

--

r b-j

--

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

"Imagination is more important than knowledge."

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Here's one quite simple formulation for you.

(1) If one of the candidates is preferred over any other candidate in a pairwise comparison, based on which one of the two candidates is ranked higher in each ballot, then that candidate will be elected.

(2) If there is no such candidate, then ...

(Note1) A candidate that is not ranked at all in a ballot is considered to be ranked below all those candidates that are ranked in the ballot.

BR, Juho

On 9/1/21 5:12 PM, robert bristow-johnson wrote:

I thought that was strange, too. I was interpreting Forest's "valid
ballot" as "any ballot", which then leads to that conclusion. It kinda
works if we disallow equal rank, but there's no reason we should.

Perhaps this could work:

• A candidate is considered to be the victor of a head-to-head against
  another candidate if the first candidate is ranked ahead of the second
  candidate on more ballots than the second is ranked ahead of the first.

• If, on a ballot, a candidate is left unranked, that candidate is
  considered to be ranked below every ranked candidate.

Your "marked to the contrary" definition would also work, I think.

Yes, that seems to be a bit on the verbose side.

I also think that the best candidate Condorcet methods (if you want a
pure Condorcet method) would be one where the Condorcet criterion is
automatically satisfied, rather than the method having to be prefixed by
"if there is a CW, elect that candidate, otherwise..."

So possibly something like minmax or Ranked Pairs. Not Black or
"Condorcet else IRV".

However, you then have to deal with not only defining whether X beat Y,
but also how decisively X beat Y. Winning votes resists strategy better,
but margins is considerably easier to define.

-km

...

I hope so.  It was meant to reduce word count.

It's almost as concise as the original that I posted.  But putting in math into the legislative language is a bit iffy.

I am actually fiddling around with creating plausible language for RP.  But right now I am trying to show to legislators how simple in concept Condorcet is.  So I am less concerned with the fallback language in case there is no CW.

Then I will present the BTR language (which is "one where the Condorcet criterion is automatically satisfied") as the other alternative for legislators to consider.  Now, complete legislative language will be several pages with definitions and the like, but this template (which fits on 1 page) is pretty much exactly like the template that the IRVers had put on the ballot (well it wasn't on the actual ballot, but in an addendum to it) for Burlington to adopt and sent to the legislature.  So, within that template, is how I want to compare Hare-IRV, BTR, and straight-ahead Condorcet (the latter is the simplest).

I am still convinced that my original language is the most concise that is also sufficiently complete.  Repeating it here, just for all of our information:

All elections of [office] shall be by ballot, using a system of ranked-choice voting without a separate runoff election. The presiding election officer shall implement a ranked-choice voting protocol according to these guidelines:
(1) The ballot shall give voters the option of ranking candidates in order of preference. Lower ordinal preference shall be considered higher rank and the candidate marked as first preference is considered ranked highest. Equal ranking of candidates shall be allowed. Any candidate not marked with a preference shall be considered as ranked lower than every candidate marked with a preference.
(2) If a candidate receives a majority (over 50 percent) of first preferences, that candidate is elected.
(3) If no candidate receives a majority of first preferences, a Condorcet-consistent retabulation shall be performed by the presiding election officer. The candidate, who is the Condorcet winner, is elected if the rankings on all of the ballots indicate that this one candidate defeats, by a simple majority of voter preferences, every other candidate when compared in turn with each other individual candidate. A selected candidate defeats another candidate by a simple majority when the number of ballots marked ranking the selected candidate higher than the other candidate exceeds the number of ballots marked to the contrary.
(4) If no Condorcet winner exists in step (3), then the candidate with the plurality of first preferences is elected.
(5) The [governing jurisdiction] may adopt additional regulations consistent with this subsection to implement these standards.

Now, I am not too worried that guideline (4) is crappy.  It's just a placeholder for the fallback method.  This fallback method is short and simple.

What I want is for the language to be complete in description (maybe not procedurally complete, but that is what guideline (5) is for).

Then, after completeness, I want, for the most part, normal English language and usage.  No special words (other than the word "Condorcet"), nor jargon, nor acronyms.

Then conciseness.  Make this template short as reasonably possible.

Complete, normal language suitable for legislation, and conciseness.  I still think the language above is better than the suggestions so far, but I can be convinced that something else is better.

--

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

"Imagination is more important than knowledge."

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On 9/12/2021 11:49 AM, robert bristow-johnson wrote:
-snip-

-snip-

Here's simple language to explain the concept:

Count all the head-to-head majorities using the information in the voters' orders of preference.

Construct the order of finish by processing the majorities one at a time, from largest majority to smallest majority, placing each majority's more-preferred candidate ahead of their less-preferred candidate in the order of finish.

I also recommend providing two simple examples: The first example with a Condorcet Winner and three candidates (perhaps named Left, Center and Right).  The second example with no Condorcet Winner and three candidates (perhaps named Rock, Scissors and Paper).

If one believes it's essential to include the rock-paper-scissors exception in the "simple concept" language, here's more complete language:

[...]

Construct the order of finish by processing the majorities one at a time, from largest majority to smallest majority, placing each majority's more-preferred candidate ahead of their less-preferred candidate in the order of finish (unless their less-preferred candidate has already been placed ahead of their more-preferred candidate).

Condorcet himself did NOT define his voting method as "First check whether a candidate defeats all others head-to-head, etc."  Here's what he actually wrote in his 1785 essay, after his meandering analysis of some 3-candidate cyclic examples:

    Il résulte de toutes les réflexions que nous venon de faire,
    cette règle génerale, que toutes les fois qu'on est forcé d'élire,
    il faut prendre successivement toutes les propositions qui ont
    la pluralité, en commençant par celles qui ont la plus grande,
    & prononcer d'après le résultat que forment ces premières
    propositions, aussi-tôt qu'elles en forment un, sans avoir égard
    aux propositions moins probables qui les suivent.

In case your French is rusty, here's a literal translation to English:

    The result of all the reflections that we have just done,
    is this general rule, for all the times when one is forced to elect:
    one must take successively all the propositions that have
    the plurality, commencing with those that have the largest,
    and pronounce the result that forms from these first
    propositions, as soon as they form it, without regard
    for the less probable propositions that follow them.

Here's how I interpret the terms in Condorcet's definition:

By "for all the times when one is forced to elect" Condorcet meant this is his voting rule for any single-winner election.

By "propositions" Condorcet meant propositions of the form "x shall finish ahead of y."  Votes that rank x over y constitute support for "x shall finish ahead of y" and opposition to "y shall finish ahead of x."

By "propositions that have the plurality" he meant the propositions supported by a relative majority. (Which could be less than half the votes if some voters express indifference.  His essay assumed no indifference.)

To "take successively" a collection means to take one thing at a time, in some order.  This has two possible interpretations: (1) Each thing may be one item (one proposition) in the collection, or (2) each thing could be a subset of the collection if there's a way to order the possible subsets so that the subsets can be taken one at a time.  The simpler and more natural interpretation is one proposition at a time, and that's how I interpret it.  It follows that "commencing with those that have the largest" means "from largest majority to smallest majority."

By "less probable propositions that follow" Condorcet meant propositions with smaller pluralities. (Either less support, or less support-minus-opposition.)  Because their pluralities are smaller, they follow later in the order of succession (which I usually call the order of precedence).  Condorcet's majority rule heuristic was: The larger the number of people who think x is better than y, the more likely it is that x is better than y.

By "pronounce the result that forms from these first propositions" I think it's clear Condorcet meant to include results implied by transitivity.  For example, if the two largest majorities support "Scissors shall finish ahead of Paper" and "Rock shall finish ahead of Scissors," he would place Scissors ahead of Paper and Rock ahead of Scissors in the order of finish.  An order of finish is transitive, and by transitivity he has also placed Rock ahead of Paper, "without regard for the less probable" "Paper shall finish ahead of Rock" proposition that follows.

With those interpretations, it's straight-forward to translate the English literal translation of Condorcet's method to the simple concept language I suggested above, repeated here for convenience:

Construct the order of finish by processing the majorities one at a time, from largest majority to smallest majority, placing each majority's more-preferred candidate ahead of their less-preferred candidate in the order of finish (unless their less-preferred candidate has already been placed ahead of their more-preferred candidate).

--Steve

This is the clear,  concise yet complete kind of language we need!

My only suggestion is to repeat in the non transitive case he same slightly
redundant clarification that you employed in the simpler case ... "... in
the order of finish ..." [see inline below]

El lun., 13 de sep. de 2021 10:10 a. m., Steve Eppley <
seppley@alumni.caltech.edu> escribió:

I suggest adding here the same slightly redundant phrase with which you
finished the simpler case:

" ... in the order of finish ."

OR

" ... in said order."

Forest,

My advice about the language is to not repeat the "in the order of finish" phrase, which you called "the same slightly redundant clarification."  I believe the one slight redundancy is enough, because the language in the rock-paper-scissors exception uses the same "place ahead of" relation that the earlier part of the sentence uses.

Here are some related concepts that might also be useful, especially if the audience is legislators or other people experienced with parliamentary rules of procedure:

Preferences are relative.  For example, a voter who prefers Trump over Biden might also prefer John Kasich over Trump.  A voter who prefers Biden over Trump might also prefer Bernie Sanders over Biden.  All of a voter's relative preferences, also called head-to-head preferences, are implied by his/her order of preference.  Note that a voter's top-ranked choice depends on which candidates chose to compete: if a voter's true favorite doesn't compete -- perhaps because the voting method is prone to spoiling -- then his/her order of preference misleadingly makes it appear that a candidate who does compete is his/her favorite, but we can say for sure only that s/he ranks that candidate over the other candidates who chose to compete. (A voting method that effectively eliminates spoiling would most reliably elicit each voter's true favorite.)

Head-to-head majorities are what matter in the most widely used, most frequently used voting system: the Robert's Rules procedure for voting on motions.  Robert's Rules works like a single elimination tournament: it has a series of head-to-head matches (rounds of voting), which each eliminate one alternative of the pair being voted on (until eventually only one remains).  Under Robert's Rules, voters do not indicate their favorites; all votes express head-to-head relative preferences.  For example, suppose there's a motion M to change the status quo to m, and a motion M2 to change the status quo to m2.  There are three alternatives: m, m2 or the status quo.  To be more concrete, suppose the status quo is that your co-op's hot water heater temperature is set at 120F, motion M would set the temperature to 125F, and motion M2 would set it to 122F.  Presume the people whose favorite is 120 also prefer 122 over 125 (because for them cooler is better), and presume the people
whose favorite is 125 also prefer 122 over 120 (because for them warmer is better).  Suppose 40% favor 120 and 35% favor 125.  It follows that 25% favor 122.  It also follows that a 65% majority (40%+25%) prefer 122 over 125 and a 60% majority (35%+25%) prefer 122 over 120.  Robert's Rules would count both of those head-to-head majorities and elect 122.  The first round of voting would be a head-to-head vote between 122 and 125, which would count the 65% majority who prefer 122 over 125, and eliminate 125.  The second (final) round of voting would be the head-to-head vote between 122 and 120, which would count the 60% majority who prefer 122 over 120, eliminate 120, and elect 122.

There will be cases where the majorities' preferences are like rock/paper/scissors.  An example well known to legislators is the "killer amendment": a majority prefer m (the main motion M) over the status quo, a majority prefer m2 (the motion M2 to amend M) over m, and a majority prefer the status quo over m2.  M2 is called a killer amendment because the status quo wins... Robert's Rules doesn't count the majority who prefer m over the status quo. (It counts only the majorities who prefer m2 over m and the status quo over m2.)  When rock/paper/scissors preferences happen, it's because this is a collective property of the voters; it's not a property of a voting method.  Primitive voting methods that count at most one majority fail to reveal rock/paper/scissors preferences, but they still exist.  They're not obvious with Robert's Rules either, because Robert's Rules works like a single-elimination tournament, not a round robin tournament, and counts only some of the
head-to-head majorities... the fact that a majority prefer m over the status quo isn't revealed.

Constructing the order of finish by processing the majorities from largest majority to smallest majority is the best way to handle rock/paper/scissors cases.  Here's an example to illustrate:

    Assume the two majorities who prefer Scissors over Paper and Rock over Scissors are larger than the majority who prefer Paper over Rock.  With the largest-to-smallest order of processing, after Scissors has been placed ahead of Paper and Rock has been placed ahead of Scissors in the order of finish, this also implies Rock finishes ahead of Paper.  Later when the smaller majority's preference for Paper over Rock is processed, Paper cannot be placed ahead of Rock because Rock has already been placed ahead of Paper. 

Largest-to-smallest processing of the majorities is the proper way to handle rock/paper/scissors cases because it's consistent with the fundamental heuristic that led societies to use majority rule: /"The larger the number of people who believe x is better than y, the more likely it is that x is better than y, all else being equal/."  Rock/paper/scissors is a case where not all else is equal: the evidence provided by the smaller majority is outweighed by the evidence of the two larger majorities.  A flaw in the Robert's Rules procedure is that it neglects the sizes of all the majorities.  Its winner instead depends on the order in which the alternatives are paired: first m2 eliminates m, then the status quo eliminates m2 and the status quo wins... even in the case where a huge majority prefer m over the status quo. (If there are 4 or more alternatives, the flaw in Robert's Rules can even egregiously elect an alternative y when the voters unanimously prefer some x over
y.)  Largest-to-smallest processing of the round robin of majorities eliminates the flaw... so it also makes sense to revise Robert's Rules so it will elicit each voter's order of preference and count all the head-to-head majorities.

--Steve Eppley

On 9/13/2021 3:08 PM, Forest Simmons wrote: