[EM] "Condorcet winner" versus "winner of Condorcet's method" (was Re: 2018 Chess Candidates Tournament)

[Richard Lung]

I've added a chapter on Condorcet method to my book on FAB STV: Four 
Averages Binomial Single Transferable Vote, published last week.
From
Richard Lung.

On 29/03/2018 09:03, robert bristow-johnson wrote:
>
>
>
> ---------------------------- Original Message ----------------------------
> Subject: [EM] "Condorcet winner" versus "winner of Condorcet's method" 
> (was Re: 2018 Chess Candidates Tournament)
> From: "Steve Eppley" <SEppley at alumni.caltech.edu>
> Date: Wed, March 28, 2018 11:52 am
> To: election-methods at lists.electorama.com
> --------------------------------------------------------------------------
>
> > @Ross Hyman: Ding Liren was not a Condorcet
> > winner in that chess tournament, because a
> > Condorcet winner is an alternative that
> > defeats all other alternatives pairwise.
> > Ding Liren didn't defeat all other players;
> > he won only one game.
>
> yes, i would not call that the CW.
>
>
> > Some people might prefer a weaker,
> > non-standard definition of Condorcet winner:
> > a candidate that's undefeated pairwise. (Like
> > Ding Liren.)  In public elections the two
> > definitions (if implemented by two voting
> > methods) would behave the same with regard to
> > the incentives on candidates, potential
> > candidates, voters, parties, donors, etc.,
> > because ties are rare when there are many
> > voters, as there are in public elections.
>
> and the reason for that is that with an electorate of decent size 
> (like at least hundreds of voters) the probability of a tie in any 
> pairing of candidates is very low.
>
>
> > Don't be misled the way many people have
> > been, especially mathematicians not familiar
> > with the social choice theory literature.
> > They wrongly believe "Condorcet winner" means
> > the winner according to Condorcet's method,
> > and thus that Condorcet's method simply
> > elects the candidate that defeats all others
> > pairwise, and is indecisive when no such
> > candidate exists.  "Condorcet winner" is a
> > term of art (a.k.a. jargon).  Unlike Borda
> > winner, which is not a term of art and merely
> > means the winner according to Borda's method,
> > and Black's method, which is not a term of
> > art and merely means the winner according to
> > Black's method, etc.
> >
> > Because sometimes there is no candidate that
> > defeats all others pairwise, the confusion
> > has caused a number of writers to wrongly
> > claim Condorcet's method is often indecisive
> > and therefore unsuitable for elections.
>
> i just read what i see here and what i see in the EM wiki and in 
> Wikipedia.  i hadn't thunk there was a "Condorcet's method" but that 
> there are a few decisive methods that are "Condorcet compliant", which 
> means these methods will elect the CW **if** a CW exists (and i really 
> think that in most public elections with a ranked-order ballot, that a 
> CW will exist virtually all of the time, and most of the time, i'll 
> bet that the IRV method will also elect the CW, but not always).
>
> > (In simulations with random voting, the frequency
> > of scenarios in which no candidate defeats
> > all others increases asymptotically to 100%
> > as the number of candidates increases to
> > infinity, and as the number of voters
> > increases.)  But the voting method Condorcet
> > promoted in his famous 1785 essay is very
> > decisive:
> >
> > CONDORCET'S METHOD (copied from page lxviii
> > of his 1785 essay):
> >
> > Here's its 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."
> >
> > The phrase "this general rule, for all the
> > times when one is forced to elect" meant he
> > was referring to a very decisive voting method.
> >
> > A "proposition" is a pairwise statement like
> > "x should finish ahead of y."  It has the
> > plurality if the number of voters who agree
> > with it exceeds the number of voters who
> > agree with the opposite proposition.
> >
> > "Taking successively commencing with the
> > largest" means considering the propositions
> > one at a time, from largest to smallest.
> > (Like MAM and Tideman's Ranked Pairs do.
> > However, MAM and Ranked Pairs measure size in
> > different ways: MAM measures the size of the
> > majority, whereas Ranked Pairs subtracts the
> > size of the opposing minority from the size
> > of the majority.
>
> that's RP-margins.  there is also RP-winningVotes.  how does this 
> method from Condorcet differ from RP-winningVotes?
>
>
> >  The word "plurality" can
> > mean either of those: either the larger
> > count, or the difference between the larger
> > count and the opposing count.)
> >
> > The "result" is an order of finish, like "x
> > finishes ahead of y, y finishes ahead of z,
> > etc."  It's a collection of pairwise results,
> > each of which is obtained either directly
> > from a proposition that has a plurality, or
> > transitively from a combination of pairwise
> > results obtained directly.  An example of a
> > pairwise result obtained transitively is the
> > pairwise result "x finishes ahead of z"
> > obtained transitively from "x finishes ahead
> > of y" and "y finishes ahead of z."  By
> > definition, an order of finish is an
> > ordering, and is thus transitive and acyclic.
> >
> > "Without regard for the less probable
> > propositions that follow" means disregarding
> > propositions that conflict (cycle) with the
> > results already obtained from propositions
> > that have larger pluralities.
>
> I cannot see how that differs from Ranked Pairs.
>
>
> >  For example,
> > disregarding "z should finish ahead of x"
> > after having obtained the pairwise results
> > that "x finishes ahead of y" and "y finishes
> > ahead of z."
> >
> > Note: No language in the definition of
> > Condorcet's method refers to an alternative
> > that defeats all others pairwise. (Nor to an
> > alternative that's undefeated pairwise.)
> > Although it can be deduced that Condorcet's
> > method will elect an alternative that defeats
> > all others, it will also elect an alternative
> > even when no alternative defeats all
> > others... in other words it's very decisive.
>
> so this historical "Condorcet's method" always elects a single-winner 
> and, **if** a pairwise champion exists, it will elect that pairwise 
> champion.  so "Condorcet's method" is Condorcet-compliant.
>
>
> > People who write about "Condorcet completion"
> > rules -- first check whether there exists an
> > alternative that defeats all others and then,
> > if no such alternative exists, proceed in
> > some other way to find the winner -- have
> > misunderstood Condorcet's method,
>
> or, perhaps we haven't heard of Condorcet's "method".  but if they 
> apply "Condorcet completion" rules to another Condorcet-compliant 
> method that doesn't need completion rules (such as RP or Schulze), i 
> think that reflects the same misunderstanding.
>
>
> > which is
> > already "complete" (very decisive when there
> > are many voters, because when there are many
> > voters it's rare that any two majorities are
> > the same size, and rare that any pairings are
> > ties).
>
> yup.
>
> thanks for the information, Steve.
>
>
> --
>
> r b-j                         rbj at audioimagination.com
>
> "Imagination is more important than knowledge."
>
>
>
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