[EM] Can anyone help with straight-ahead Condorcet language?

[Steve Eppley]

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:
> This is the clear, concise yet complete kind of language we need!
>
> My only suggestion is to repeat in the non transitive case the 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 at alumni.caltech.edu <mailto:seppley at alumni.caltech.edu>> escribió:
>
>     On 9/12/2021 11:49 AM, robert bristow-johnson wrote:
>     -snip-
>     > 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.
>
>     -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).
>
>
> 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."
>
>
>     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
>
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