[EM] Condorcet and other authors on Condorcet (and how does range voting fit in?)

[Warren Smith]

I just started looking in the library to answer the historical
question "what did Condorcet himself (and other authors about
Condorcetness) have in mind?"

Albert Wiele: "Democracy," St Martins Press NY 1999
on p133 defines "A condorcet-winner is that alternative that could
defeat every other alternative in a pair-wise contest."
Note: this can be interpreted as saying "range voting is a condorcet
system" or "not."
It is ambiguous.  For voting systems based on rank-order ballots,
though, it is unambiguous.
This is one example of a vastly prevalent phenomenon, which I have
pointed out before, of authors who just do not conceive that anything
besides rank-order ballots could possibly exist, and therefore do not
realize their definitions were ambiguous and hence inadequate.

I.McLean & A.B.Urken: Classics of Social choice (a sourcebook)
Univ. of Michigan Press 1995
gives excerpts from the writings of Condorcet himself (translated into English)
as well as other early luminaries such as Borda, Dodgson, etc.

ch7 pages 113-143 is
Condorcet "On the constitution and the functions of provincial assemblies" 1788.
p114 he discusses plurality voting, explains its problems.

p114-115 he says a system of repeated re-votes until somebody gets a
majority, or a 2/3 supermajority, is used "in several countries" but
disparages it as forcing voters to lie, and
taking a very long (unbounded) time, and requiring measures like
cutting off food to force the voters to finish (he evidently has in
mind the pope-election system, which C did not realize was
approval-style  voting, not plurality-style as C had indicated)

p122.  OK, Condorcet on this page reaches the end of his article
proper, and he still has, at no point so far, actually discussed or
even defined Condorcet voting.  But
there is an APPENDIX pages 122-148, which is actually longer than the
paper itself.
(Gag.)  Condorcet says on p115 of this appendix:
QUOTE
Examining the [form of election which I feel will led to the correct
result] would involve too lengthy a discussion [and] would exhaust the
reader [hence I place it in the appendix].
[That] only method which I consider accurate is also very complicated
and would in practice be dishearteningly time-consuming.  So rather
than suggest we immediately try it out in provincial and other
important elections, I prefer to illustrate a simpler version
which, while it may not actually determine the worthest candidate [by
which I guess C means
a Condorcet winner] at least ensures the the choice of a man that the
greatest plurality considers capable... [unlike plurality voting
itself, which as C had demonstrated on earlier pages, can elect the
worst and can fail to elect the best...]
END QUOTE

and with that he dives on p166 into
QUOTE
We suggest that each voter makes a list of the 20 candidates he
considers most worthy of the post.  If just one name is present on
more than half the lists, that candidate is elected.  If several names
are present on more than half the lists, then the one whose name is on
the most lists is chosen.  If [tie] then the candidate whose name
appears most often in the top 19 (or top 18...) is chosen. [note, so
evidently Condorcet has in mind ORDERED lists.]
If [still a tie] then [break it randomly].
END QUOTE
In the above quote, Condorcet does not say what to do if NO candidate
appears on more than half the lists.  So his description is
incomplete.  (Also the part he does give, contains redundancy.)  If
that flaw is ignored, or if we based on his preceding remarks on p115
assume the one on the most listings is elected, then observe that
Condorcet here basically
INVENTED APPROVAL VOTING!!!!!
C continues QUOTE
This method has several other advantages besides that of  being very simple.
First every voter can nominate his friends... and still have plenty of
room to include truly worthy men. [Such] partiality [does not hurt
this system much].
Second, a faction of less than half the voters could not force
election of a candidate opposed
by the others, and those others would not have to [dishonestly] band
together in "support" of
one to accomplish [such a defense]
END QUOTE.
ok, based on that C really does have in mind no election if nobody
gets majority-approval,
except C never explicitly admits it and had implied the opposite on
p115. (C appears to be a bit of an idiot, actually. And bad writer.)

So this is actually fascinating.  Observe, Condorcet actually appears
to be admitting up front that
(1) Condorcet voting is too complicated to describe in his article,
and would, if he had tried, "exhaust the reader" (even though, e.g.
Schulze Condorcet is far more  complicated than Condorcet Condorcet)
(2) Condorcet voting is "very complicated" and would in practice be
"dishearteningly time consuming" which is very close to an admission C
himself regards his own idea as impractical.
(3) Condorcet therefore indicates we need a more-practical very simple
alternative and proceeds to fill that bill by inventing APPROVAL
VOTING!!

Amazing eh?  OK, now let's move on to C's appendix.
He reiterates his anti-plurality election examples and discussion of
repeated revotes.
(C has absolutely no idea how to eliminate redundant writing.)
C on p124 defines (rather horribly) Borda voting, and p125
gives three example elections where Borda voting fails to elect a
Condorcet winner.
C just regards it as obvious Borda is wrong in such examples, hence he
sees no need to argue WHY he is wrong.
Finally at long last, on p126 C gets to the idea of defining what is a
Condorcet method!
QUOTE
Thus the only method remaining to be examined is that by which we have
been judging the others.  Each voter ranks the candidates in order of
merit. From his ranking, we can easily extract his opinion of the
relative merits of each candidate [by which, I assume, C really meant
"pair of candidates"] and by collating all the individual opinions we
can discover the candidate considered best by the plurality.
END QUOTE

This is, as is common with Condorcet, an imprecise description.  Furthermore,
observe that, within the considerable play this imprecise description
allows, RANGE VOTING IS A CONDORCET METHOD provided "ranks in order"
were changed to "scores
numerically between 0 and 99" which is something C never considered
the possibility of anywhere in this article.  So I continue to contend
that it is NOT CLEAR whether Condorcet
(had this possibility been brought to his attention) have considered
range voting to be a Condorcet method.

C continues p127
QUOTE
But on closer examination, we find that even with just three
candidates, this method can apparently give a totally absurd result,
which in practice means no result at all
END QUOTE
and then he gives to illustrate a Condorcet cycle example election.
Note, again,. with range voting, this would not have even been an
issue.  As far as I can tell from these direct quotes from Condorcet
p126-127, C would apparently have considered range voting to be the
perfect voting method, meeting all his desiderata and avoiding his
"absurdity"!!!

On p128 C wonders what to do about "contradictory propositions"
i.e. cyclic preference structures, and argues the right winner would
be the "most probably correct one" which is a concept he doe not
explicitly define, though he does give one election example with a
cycle, in which "the first [proposition] is most probably correct"
(since it has a greater margin) and hence C selects a winner in that
one example election.
But then

p128 QUOTE:
If 3 candidates... 3 propositions.
If 4, then 6 propositions.
If 5, then 10
If 6 then 15...
For 20 candidates there would be 190 propositions and for 100 candidates there
would be 4950.  This [my] method is quite impracticable unless the number
of candidates is limited.
ENQ QUOTE

How exactly to consider the Mare's nest of 190 contradictory "propositions"
in the 20-candidate case to find the "most probable" noncontradictory
result? C does not give us any clue.  But

QUOTE CONTINUES
   But... [I see] nothing wrong with limiting the number of candidates
[by a nomination procedure which gets rid of a ton of them having low
support]... this is not really a restriction
END QUOTE

And Condorcet then suggests as a nomination procedure, basically the
approval voting
idea he'd introduced earlier, now used in a multiwinner fashion.
So his ultimate suggestion up to p129 is basically, do approval
voting, select the top finishers
according to some cutoff he does not describe, then hold a second
election among them alone using a Condorcet method.

One form of this would simply be "approval with separate top-2 runoff"
of course, which is not really what modern Condorcetists consider a
"condorcet method" at all, but C apparently would have liked it.

Chapter 8 pp145-150 is Condorcet: "A survey of the principles
underlying the draft constitution" 1792.

on p146-147, Condorcet basically appears to be inventing and proposing
as a nomination procedure (used in multiwinner fashion), BUCKLIN
VOTING!!
He apparently then has in mind a second separate election conducted
with Condorcet voting
but is not explicit about it.

p149, Condorcet says voters should sign their ballots "there can be no
drawback in making each voter answerable for their choice." Oh.





On 5/17/10, Abd ul-Rahman Lomax <abd at lomaxdesign.com> wrote:
> At 10:12 PM 5/16/2010, Dave Ketchum wrote:
>>On May 16, 2010, at 6:11 PM, Abd ul-Rahman Lomax wrote:
>>>At 02:16 PM 5/16/2010, Dave Ketchum wrote:
>>>>On May 16, 2010, at 9:24 AM, Abd ul-Rahman Lomax wrote:
>>>>>At 06:34 PM 5/15/2010, Dave Ketchum wrote:
>>>>>>>Some objections to Condorcet could be:
>>>>>>>1. It is not expressive enough (compared to ratings)
>>>>>>Truly less expressive in some ways than ratings.
>>>>>>    This is balanced by not demanding ratings details.
>>>>>>    And more expressive by measuring differences between each pair
>>>>>>of candidates.
>>
>>The base topic is Condorcet.  It would take a book to respond to all
>>your extensions such as IRV.  Likewise I see no benefit in adding
>>Borda - Range/score is an adequate source for ratings.
>
> Dave, you apparently don't understand a good deal of what you read.
> That's okay, take your time.
>
> My point was about your use of "demanding ratings details," which is
> not intrinsic to range methods. In particular, I've been pointing
> out, Borda is a ranked method that is a Range method, and it becomes
> full range if the method simply allows one to equal rank any two (or
> more) candidates without disturbing the points given to other candidates.
>
> The most fully expressive ballot is a Range ballot, of course, and
> the higher the resolution, the higher the allowed expression.
>
> The simplest way to understand this is through this progression:
>
> Plurality. Vote for one, candidate with the most votes wins.
> Approval. Vote for one or more, candidate with the most votes wins.
> Range. Vote for one or more, fractional votes allowed, candidate with
> the most votes wins.
>
> What distinguishes Range from Ranked methods is the allowance of
> fractional votes. However, once it is possible to vote fractions, and
> particularly if the resolution (fractional increment) is fine enough,
> a Range ballot can fully express ranking, which is a Range ballot
> interfaces with a ranked ballot. Borda is a range method that is a
> ranked method, and the connection is that the number of unique
> ratings is equal to the number of candidates, thus a Borda ballot has
> adequate resolution; however, typically, Borda ballots prohibit
> assigning the same rating to more than one candidate, and all ratings
> are assigned or the vote is diluted. If overvoting and empty ranks
> are allowed, Borda is simply Range (N-1), where N is the number of
> candidates.
>
>>   I used care in
>>mentioning ranking to avoid complications such as you add - and
>>clearly included equal ratings and rankings.  Your extensions could be
>>useful if they contributed value, but not if they just complicate.
>
> You have not understood the "extensions," which may be because your
> lack of understanding causes them to seem complex.
>
> All this stemmed from your complaint or comment that range methods
> "demand" ratings details. They don't. You can vote a Range ballot as
> Borda, generally. Just spread the votes across the range. It's
> trivial if the number of ratings allowed is the number of candidates.
>
> But you seem to assume that "Range" involves some particular number
> of ratings; you cited Range 99, when, quite likely, Range will be
> implemented with much less than 100 ratings (0-99 in Range 99).
>
>
>
>>>>>"Demanding" is an odd word to use for "allowing." "Condorcet"
>>>>>doesn't really refer to ballot form, though it is often assumed to
>>>>>use a full-ranking ballot. In any case, a ballot that allows full
>>>>>ranking, if it allows equal ranking and this causes an empty space
>>>>>to open up for each equal ranking, is a ratings ballot, in fact.
>>>>>It's Borda count converted to Range by having fixed ranks that
>>>>>assume equal preference strength. Then the voter assigns the
>>>>>candidates to the ranks. It is simply set-wise ranking, but the
>>>>>voter may simply rank any way the voter pleases, and full ranking is
>>>>>a reasonable option, just as is bullet voting or intermediate
>>>>>options, as fits the opinion of the voter.
>>>>
>>>>Assuming I LIKE A, B & C are almost as good, and I DISlike D:
>>>>
>>>>I can rate A=99, B=98, C=98, D=0 or rank A high, B&C each medium, and
>>>>D low (A>B=C>D).
>>>
>>>Dave, you are assuming that the ratings ballot has more ratings than
>>>candidates. That is precisely what I did not suggest. That's why I
>>>mentioned "Borda." It seems you are thinking of Range 99 as "Range,"
>>>when Range is a family of methods, with the range of ratings being,
>>>normally, from 1-N for Range N. With 4 candidates, the equivalent
>>>Borda ballot has four ranks (1st, 2nd, and "no vote" perhaps). If
>>>the ballot allows equal ranking, then, you really have a Range 3
>>>ballot. So your "simple ranking" would be A>B>C>D or A>C>B>D. With
>>>no equal ranking allowed, you must choose one of these, but the
>>>condition of the problem is that you have no basis for this. Is that
>>>hard, or what?
>>
>>Since the topic is Condorcet equal ranking can be allowed, and I
>>clearly indicate use of that.
>
> Yes, you did. However, you also assumed a very high resolution range,
> thus creating an appearance of some difficulty. Your stated condition
> can be expressed with a Range 3 ballot: A 3, B 2, C, 2, D, 0. In real
> terms, if the difference between A and B=C is 99 to 98, and if D is a
> viable candidate, there really is no difference at all, it is a
> formal expression of preference without significant substance.
> However, if D is not a viable candidate and is "Satan," then the
> ratings of B=C have been disturbed by the presence of D. It's a
> complex subject, in fact.
>
>>After describing B and C as equally ranked I used common symbology -
>>(A>B=C>D) - and am not used to the symbology you use below.
>
> Sure, you aren't. But the only difference is the existence of empty
> ranks. I'd have thought that obvious. I expressed an empty rank with a "."
>
> I wrote that it was the "same ballot." That means that the ranks are
> laid out on the ballot for you to specify. You can leave a rank
> empty. This is actually how Bucklin was implemented, and it is this
> that made Bucklin a Range method. The empty ranks have significance.
> They indicate a preference strength. The problem with pure
> preferential ballots is that they show no preference strength. A>B>>C
> is just A>B>C.
>
>>>Now allow equal ranking on the same ballot.
>
> I.e., a ballot with fixed ranks. IRV ballots are sometimes set up
> this way, with facility for ranking all candidates (making the ballot
> the same, effectively, as a Borda ballot), or for ranking a fixed
> number. But preferential interpretation of that ballot means that an
> empty rank is meaningless, it is simply skipped, as if it did not
> exist. In Borda/Range, it has meaning.
>
>>>  Yes, you have a choice,
>>>with the simplest ballot rules: You can rank them A>B=C>.>D (D
>>>perhaps not being on the ballot, but I'll show the bottom rank), or
>>>as A>.>B=C>D.
>
> Do you understand the notation now? The first example, A>B=C>.>D
> means just what you said. But you could also have ranked them
> A>.>B=C>D, which would mean something a little different. Instead of
> liking B and C almost as much as A, you, rather, dislike B and C
> almost as much as D.
>
>>>  It's a trade-off, and which one you pick depends on
>>>two factors: how strongly do you want to prefer A, and how strongly
>>>do you want to act against D? Strongly preferring A indicates you
>>>put both middle candidates in third rank, strongly acting against C
>>>indicates you might put both middle candidates in second rank. In
>>>addition, there are the probabilities to consider, which may
>>>outweigh the preference strength issue. Is it possible for A to win?
>>>If so, indication is that you should rate B and C lower. Is it
>>>possible for D to win? If so, then you might want to rate B and C
>>>higher.
>
> And then I've introduced a real consideration: strategy. There is a
> serious problem with assuming that ratings on a range ballot should
> simply reflect relative "like" or "dislike." The fact is that we make
> choices based on real possibilities, not merely on absolute
> preferences. And it's necessary unless there is some way for a method
> to "amplify" our preferences once irrelevant alternatives have been
> removed. That is, in a way, what preferential methods do, though it
> isn't normally described that way, and doing it without
> discrimination means that trivial preferences are given the same
> weight as strong ones. The paper from Voting Matters, latest issue,
> that used a Range ballot allowed what might be called a "sincere
> absolute range expression," with other data that, if I understand the
> paper correctly, caused "expansion" of the voting power over a
> narrower set, thus allowing the kind of vote that could be:
>
> A:100
> B:51
> C:49
> D:0
>
> Where A was the Messiah, and D was the Antichrist, and B and C are
> the real candidates. If I get it correctly, the voter's additional
> expression would cause the B and C votes to be expressed with full or
> appropriate strength. In Dhillon-Mertens Rational Utilitarianism --
> which is Range voting -- the voter does this, and might vote A:100,
> B:99, C:1, D:0. The absolute utilities have been modified by real
> election probabilities.
>
> Unless one, for example, thinks of D as a frontrunner, in which case
> one might well vote A:100, B:99, C:98, D:0.
>
> Bucklin with runoff can handle this case reasonably well.
>
>>In ranking all I can say is to rank B&C above D and below A..
>>
>>Go back to the example and see B and C each rated 98 because I DO NOT
>>want them to lose to D.
>
> Yes. And that's what I described. But you made the decision more
> complex by imagining a high-resolution Range method. If D is not a
> realistic outcome, you then may have over-rated B and C. Essentially,
> you rated A, B, and C all the same, for most practical purposes.
>
>
>>>If the frontrunners are A and D, *it matters very little where you
>>>rank B and C*
>>
>>True, but ranking them below A and above D gave what insurance was
>>possible.
>
> Depends on the canvassing method. Bucklin is cool because you can
> express any significant first preference with very little harm, yet
> still vote maximum strength for your second or third choices.
> Bucklin/Runoff even allows you to postpone the lower choice decisions
> to a runoff, unless you see a danger of your least favorite winning
> in the primary.
>
>>>If you have trouble deciding to go for low ranking or high ranking,
>>>there is an option that might be allowed in Bucklin or Range: half-
>>>ranking. The way that A low-res Range 3 ballot might be shown would
>>>be a list of candidates, with three options for each candidate. If
>>>you mark more than one option, your vote would be, with range,
>>>half- assigned to one rank and half to the other. (or a third, etc., if
>>>you mark more than two, but with this particular ballot you could
>>>just neglect the middle rank vote, it would end up the same). With
>>>Bucklin analysis, same, except that in the counting rounds, a
>>>"middle rank" would be counted after the higher rank and before the
>>>lower.
>>
>>Huh?
>
> Yes, you don't understand. It's been explained before, you either
> didn't read it (which is fine) or you didn't understand then, either.
>
> Take a three-rank Bucklin ballot. Suppose a voter votes for a
> candidate in both second and third rank. When is the vote counted?
> The only law I've seen that considered this specified that the vote
> was counted in the higher rank. That's arbitrary, but better than
> tossing the vote. It could have been that it would be counted at the
> lower rank. The problem with Bucklin and voting machines was that
> both the votes would be counted, unless the ballot was arranged
> properly so that such overvotes would be impossible. This requires
> that the ballot be arranged so that each candidate is, as it were, an
> independent race, vote-for-one-rank-only.
>
> But with hand counting or more sophisticated machine counting, the
> vote could be counted as if it were in rank 2.5. That would mean that
> it is not counted in the second round, but before the normal third
> round. This would allow finer ranking. Otherwise the possible
> information is discarded. Which is better? In any case, the voters
> should know how such a vote will be counted.
>
> This interpretation of such overvotes could turn a three-rank Bucklin
> ballot into a five-rank one, with no fuss or extra ballot space taken
> up. Indeed, it would convert a two-rank ballot to a three-rank one.
> And I don't think it would be at all difficult to understand.
>
>>>There are other reasons for defining what such "overvotes" mean,
>>>basically to avoid discarding ballots that have an apparent meaning.)
>>>
>>>It is, in general, easier to rank candidates if the equal ranking
>>>option exists. The issue, then, is how such equal ranking is to be
>>>interpreted. IRV rules typically toss the vote. Not allowed. But, in
>>>some small level of progress, in the U.S., the ballot simply is
>>>considered exhausted at that point, the higher ranked candidate
>>>still have their votes (which, if the lower ranked votes, where the
>>>overvoting was, are being counted, the higher ranked candidates have
>>>been eliminated. But at least the whole ballot hasn't been tossed.)
>>
>>Why say this?
>
> Why not?
>
> How overvotes are handled is an important topic. It's the "equal
> ranking" topic, really, which certainly is relevant to Condorcet
> counting methods.
>
>
>>>>The example ratings of A, B,&C do the most I can to make any of them
>>>>win over D; the example rankings do the most I can to make A win, D
>>>>lose, and give B&C an equal chance.
>>>>
>>>>In Condorcet I ranked A over B and C over D but could not express the
>>>>magnitude of these differences.  In Score I must rate with numeric
>>>>values that include the differences.
>
> You are showing, Dave, that you have completely missed the point.
> Again, you use "must." No, a Range ballot can simply be a list of
> ranks. On a real ballot, you would not enter numbers at all, but the
> voting positions might have numbers attached. With low-res Range,
> they might have names. I've described a Bucklin ballot that is a true
> and complete Range 4 ballot, it would have names like
>
> Favorite(s)
> Preferred
> Acceptable
> Less than Acceptable
> Rejected
>
> Sort the candidates into these five categories. The top three
> categories are approval votes if you place the candidate there. The
> lower two categories are disapproved categories and are used for
> Condorcet analysis and runoff determination, probably.
>
> The magnitude of preference between two candidates is expressed on
> this ballot by the rank distance. On this ballot, the rating step
> between ranks can be expressed as 0.25.
>
> Bucklin is a method which steps down what can easily be seen as a
> Range ballot, adding in approvals when the sliding down of Approval
> cutoff reaches candidates. Classic Bucklin had only three ranks, and
> was equivalent to a Range 4 ballot with the ratings of 0 and 1
> combined (into 0). Any approved candidate was rated at or above
> midrange (which sets midrange as the average expected election value,
> classic approval voting strategy).
>
> The theory can get somewhat complex, but the actual voting was very
> simple. I'm suggesting tweaks for the use of Bucklin in runoff
> voting; these tweaks would make it Condorcet compliant, or so close
> to compliant that the difference would be merely theoretical and very
> unlikely to show up in actual elections. (Depends on the runoff
> rules, but I've suggested that any Condorcet winner should be
> included in a runoff, and the ballot contains good data for the
> determination of that.)
>
> The above ballot, with an explicit Rejected rating (which would also
> be assumed, I'd prefer, for any non-rated candidate), can become even
> finer in expression of the "overvoting" scheme is followed. By using
> multiple rank expression, the five single ratings become nine
> possible ratings. My opinion is that this is more than adequate. But
> the voter does not need to pay attention to these complications
> unless the voter needs the flexibility.
>
>
>>...
>>
>
>


-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)
and
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