[EM] Condorcet cyclic drop rule

Blake Cretney bcretney at postmark.net
Sun Apr 1 12:33:32 PDT 2001

Subject: [EM] Correction about Ranked Pairs(margins) 
Date: Thu, 29 Mar 2001 07:19:46 -0000
From: "MIKE OSSIPOFF" <nkklrp at hotmail.com>
> When Mr. Condorcet made his proposals, he specified that defeats be
> measured by defeat-support. And that's the only defeat measure that
> confers compliance with the defensive strategy criteria.
> Ranked-Pairs(defeat-support) is something that Condorcet proposed,
> and it meets all 4 of the majority defensive strategy criteria,
> as does Cloneproof SSD.

Of course Condorcet didn't really propose Ranked-Pairs
(defeat-support).  That method was invented recently by Mike, based on
the method Tideman invented around 1985.  Condorcet wrote in the

Subject: Re: [EM] Condorcet cyclic drop rule
Date: Wed, 28 Mar 2001 03:26:23 -0000

> Defeat Support is what Condorcet himself specified. Norm & Markus
> posted quotations about that. They're in the archives for last year.

Unfortunately, at the time of that discussion, I didn't have access to
a Condorcet translation, so I had to rely on others to give quotes.  I
currently have a book though: 

Iain Mclean, Fiona Hewitt, 1994
"Condorcet:  Foundations of Social Choice and Political Theory"
Edward Elgar Publishing Limited

It isn't a complete translation of his works.  Unfortunately, one
important section is merely described, instead of being presented as a
translation.  However, I think it proves my case.

Here are some back-ground quotes.  These are by Condorcet (although
they are translated).  He uses the term plurality as we might use the
term majority today.

For example, p 137 "An Essay on the Application of Probability Theory
to Plurality Decision-Making" 1785

> The Proposition `A is better than B' therefore obtains 41 
> votes to 40.

p 126
> the first of which has a plurality of 37 votes to 23, and 
> the second a minority of 29 against 31

p 136
> it would seem more reasonable to judge these propositions, 
> not according to the preceding hypothesis, but according 
> to the degree of plurality they have obtained.

The preceding hypothesis is that of Borda.  I present these to show
that Condorcet talks about the "degree of plurality" as being the
deciding point.  He seems to speak of pluralities as a pair of values,
however.  Norm's argument was that at the time plurality strength
would have been measured by the number on the winning side, and he
gave a quote from a French dictionary of the time in support of this. 
Norm reasoned that Condorcet must have meant winning-side voters by
"degree of plurality".

I argued that since no one had come up with an example where Condorcet
had considered incomplete rankings, he hadn't.  So, even if he did say
to only use winning-side voters, this wouldn't have mattered because
he wasn't comparing margins to winning-votes.  

These quotes show, first, that he intended voters to use ballots:

p 111 "On Ballot Votes" 1784
> Clearly, once the list of candidates in order of merit has 
> been submitted, we can extract from it each voter's 
> judgement on the relative merits of any two candidates.

And that he expected these ballots to be complete:

p 123 "Essay..."
> In general, therefore, we should replace this method with 
> one in which each voter simultaneously shows his preferences 
> among all the candidates by placing them in order of merit.

"This method" is the traditional plurality method.

The preceding was just to give some back-ground to the discussion.  To
see that Condorcet's argument is based on margins, consider the
following quote

> We must now look at the case in which a decision is made with the
> possible plurality.  If we suppose each vote to have a probability
of 9/10 of 
> being correct, then for 10 candidates, we only require a plurality
of four 
> votes to have, even in the worst possible case, a probability of
99/100 of 
> having made a good choice.

You might wonder what on earth he is talking about.  Where did this
probability come from?  According to the translators (p35), he clearly
presents what he means:

v=chance of truth -- note that v doesn't stand for votes, it stands
for verite
e=chance of error 1-v
h=votes for majority 
k=votes against majority

p = v^(h-k) / [v^(h-k) + e^(h-k)]

The book introduces this as a "formulae of classical probability", of
course, adapted by Condorcet for his use.  It assumes that voters have
some equal chance of being correct, and that they act independently.

The point is that Condorcet's formula, called Condorcet's jury
theorem, relies on margins, h-k.  So, Condorcet not only specifies
margins, but his whole probabilistic argument makes no sense, unless
you realize he is talking about margins.

Blake Cretney

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