[EM] Condorcet exegesis

[Colin Champion]

Perhaps some people will be interested in another conclusion I came to 
from reading Condorcet's Essai. He proposed a method of breaking cycles 
which generated a lot of confusion until Peyton Young glossed it as a 
garbled account of the Kemeny-Young method. His reading has been widely 
accepted; Tideman (in his 2006 book) declared that "Condorcet's intent 
is decoded to my satisfaction" by Young.

Condorcet described his method twice: forwards in the Preliminary 
Discourse and backwards in the body of the work. Young only discusses 
the backwards version. In both cases Condorcet starts from a list of 
pairwise comparisons, sorted by margin. In the backwards version he 
writes: "We will successively discard from the contradictory set the 
preferences which have the smallest majority, and elect the candidate 
preferred by those which remain". Presumably he stops discarding when 
the residue is consistent; the flaw is that by this point there may not 
be enough comparisons left to determine a unique winner. Young noticed 
this and remarked that "It seems more likely that Condorcet meant to 
*reverse*, rather than to *delete* the weakest proposition". This is 
nonsense: no one writes "delete" when they mean "swap", and Young's 
reading doesn't fit the forwards version.

The forwards statement is clearer: "We thus obtain the following general 
rule, that whenever we are required to elect a candidate, we must take 
in turn all the pairwise preferences which have majority support, 
starting with the largest majorities, and make a decision according to 
these initial preferences as soon as they imply one, without worrying 
about the less probable later preferences." In other words, given a list 
sorted in decreasing order of margin, take an initial part which is 
small enough to be consistent but large enough to determine a unique 
winner. This has a corresponding flaw, which is that as you work through 
the list, you may be forced to include a comparison which contradicts 
those already present before reaching the point at which you have a 
winner. But there's nothing here which you can interpret as meaning 
"swap" rather than something else.

It seems to me as clear as daylight that Condorcet had an incomplete 
grasp of Tideman's Ranked Pairs. Tideman recognised the risk that a new 
pair may contradict the ones already in the list, and he saw what to do 
about it, namely throw it away.

CJC
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