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

Steve Eppley seppley at alumni.caltech.edu
Mon Sep 20 15:31:23 PDT 2021

```Robert,

I wasn't attempting to provide complete language for legislation.  I was merely responding to your request for simple language to explain the concept.  You had written: "But right now I am trying to show to legislators how *simple* in concept Condorcet is."  And it appeared to me that your email focused on Ranked Pairs.

I don't know whether you were asking for language to describe Tideman's Ranked Pairs (which uses margins... subtracting the sizes of opposing minorities from the sizes of the majorities) or Maximize Affirmed Majorities (MAM, which does not subtract the opposing minorities).  My recollection is that some people in the EM list use the name Ranked Pairs to mean both (which I think is a bad idea).  Another recollection is that most people in EM acknowledged long ago that majority size is better than margins.  So I guessed you wanted simple language to explain the concept of MAM.

I don't use the word "majority" as a shorthand for margin of victory.  It has the common meaning.  The fact that there's no need to mention subtraction of the size of the opposing minority when explaining the concept of MAM is one more reason to prefer MAM over Tideman's Ranked Pairs.

I don't think there's an ambiguity about "from largest majority to smallest majority."  It's the order of precedence in which the head-to-head majorities are processed.  If there is an ambiguity, an example should make its meaning clear.

You ask about the terms "larger majority" and "smaller majority" but those terms do not appear in the language I suggested.  Assuming you're referring to the "largest majority to smallest majority" order of precedence, then No, those terms have nothing to do with margins.

Regarding Condorcet's intent... the word plurality (pluralité in French) has (and had) two meanings: it can mean the larger of two numbers (size of the majority), and it can mean the larger number minus the smaller number (margin of victory).  So I think the paragraph I cited from his 1785 essay doesn't by itself imply whether he had majorities or margins in mind.  Earlier in his essay, his analysis of the probability that a jury's decision is correct indicates he had margins in mind in the jury context.  I don't recall whether his analysis or examples of voting scenarios made it clear whether he had margins in mind in the voting context too, and I don't have time to reread his essay.  When Keith Michael Baker translated the cited paragraph to English in his 1982 book "Condorcet: From Natural Philosophy To Social Mathematics" he translated it as majority but didn't explain why not margins.  If I had to bet, I would bet Condorcet had margins in mind.

Whether Condorcet meant majority size or margin shouldn't matter to us, since there appears to be no reason to believe he considered the question as we have.  I have no reason to believe he considered the consequences of indifference or strategic voting, which is what led many people in the EM maillist to the conclusion that sizes of majorities is better than margins.  In particular, criteria such as Truncation Resistance and Minimal Defense, which MAM satisfies but margins methods do not.

You ask whether my long description would be needed in the legislation.  I think something like it should be in an appendix or preface or exhibit.  Examples too.

You also ask about what I assume is part of your wording: "If more ballots are marked ranking Candidate A over Candidate B than the number of ballots marked to the contrary, then Candidate B is not elected."  You ask: "How do we turn that maxim into concise procedural language?"  I think it's a bad maxim, due to majority cycles.  That maxim can defeat all candidates.  Why is it of interest?

Other language I strongly recommend avoiding: "pairwise defeats," "defeat strength," "beat pairwise," "defeators," etc.  The only defeat that should be mentioned is the concept that everyone already knows: not finishing in first place, or not getting elected.  It's confusing and potentially misleading to overload the word "defeat" by defining a new kind of defeat, and totally unnecessary.  It's confusing because a candidate said to be defeated "pairwise" can finish in first place.  It won't confuse people like you and me who are immersed in this stuff, but I'm pretty sure it will confuse people we want to teach.

I see no need to define new terms.  Familiar terms, using their familiar definitions, will suffice and are preferable.

I don't see the point in drafting legislation before persuading legislators or activists to support the concept.  My hunch is that most legislators will be repulsed by a good voting method because it would end the two party system that elected them and would induce competition they don't want, so the way forward is with citizens' initiatives and by persuading private organizations to use it. (They can use it for electing board members and it can also replace the Robert's Rules procedure for voting on motions.)  Detailed legislative language would be needed for citizens' initiatives, but I think that can wait until enough activists have been persuaded to pursue it using citizens' initiatives.

In the software I've written for MAM, the code related to tiebreaking seems the most complex part of the algorithm.  (It uses the Random Voter Hierarchy algorithm -- the generalization of Random Dictator for voting methods that allow indifference -- to construct a strict ordering of the alternatives.  It carefully employs that ordering to distinguish between same-size majorities, so that one majority at a time is processed.  It also employs that ordering at the end in the case where, due to one or more pairwise ties, the majorities don't suffice to construct a strict order of finish.)  It's complex in order to strictly satisfy criteria such as independence of clones.  In the context of large public elections, where it's unlikely that any pair will be a tie or that two majorities will be the same size, tiebreaking is unimportant and maybe it would be better in the legislation to use coin flips or some other familiar tiebreaker.  The voting method can be completely
deterministic if people don't mind using some kind of seniority order for tiebreaking, such as the chronological order in which the candidates qualified for the ballot.

--Steve

On 9/14/2021 9:16 PM, robert bristow-johnson wrote:
> From what you translated from French, it looks like Condorcet was describing Ranked Pairs.  I wonder if Nicolaus Tideman would see it that way.
>
> Okay, Steve, all this explanation of the RP concept is good, but the question is if it is needed in the legal language or if your proposition is good enough by itself:
>
>>     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).
> Is that a well-defined procedure that instructs exactly how the "processing the majorities" are done?  What is a "larger majority" or "smaller majority"?  Do you mean margins?
>
> This is similar to the RP alg that I have been working on (but sorta set aside for now).  Each candidate has a list of "defeators" who are other candidates who have defeated the subject candidate or has defeated someone else who has defeated the subject candidate.  In order of largest margin (or whatever "defeat strength") to smallest, when considering adding a runoff pair to the list of "locked" runoff pairs, one looks at the defeated candidate in that pair under consideration.  If the defeated candidate is already in the list of defeators of more preferred candidate, then that runoff pair is not locked and is ignored.  If the defeated candidate is not on the defeator list, then the pair is locked and the preferred candidate and all of the preferred candidate's defeators are merged onto the defeated candidate's defeator list.
>
> But putting this all into C code is one thing, putting it all into legislation is another.
>
> I just don't think that the short instruction in that one paragraph is enough to fully define RP in legislation.
>
> For "straight-ahead Condorcet", I hadn't thought that Condorcet created a method. I just thought it was applying this Condorcet criterion universally (that means for every possible pairing of candidates):
>
>> "If more ballots are marked ranking Candidate A over Candidate B than the number of ballots marked to the contrary, then Candidate B is not elected."
> How do we turn that maxim into concise procedural language?
>
>> On 09/13/2021 1:10 PM Steve Eppley <seppley at alumni.caltech.edu> wrote:
>> 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).
>>
>> 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).
>>
> --
>
> r b-j . _ . _ . _ . _ rbj at audioimagination.com
>
> "Imagination is more important than knowledge."
>
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