# Condorcet language: largest loss?

Steve Eppley seppley at alumni.caltech.edu
Mon Oct 14 21:18:06 PDT 1996

```I think there's room for improvement in the language used to explain
Condorcet's method.  The concept of "largest pairwise loss" is often
intuitively misunderstood to mean the largest margin in a pairwise
explain it?

I'm looking for a phrase that will better convey the idea of the
largest number of voters who prefer a pair-opponent in each
candidate's pair-losses.  Any suggestions?  How about "largest
number of opposed voters in any of a candidate's pairlosses"?
How about "amount of opposition in the candidate's pairloss
where his/her opposition is largest"?

* *

Months ago I asked what would happen to Condorcet's properties if
the "largest opposition" is found not only in pairlosses but in all
pairings, since this change would simplify the definition.  Mike O
replied that it wouldn't be a good idea, but my memory is fuzzy so
I'll need to hunt for that message thread to see which criteria would
be violated.

The following examples don't contrast the different properties well.
(I don't recall if Mike provided a "bad example" of Condorcet which
finds "largest votes against" in both wins and losses, so if I can't
find his example then I'd like to see one posted.)

Each matrix cell shows how many voters rank the candidate at the left
as more preferred than the candidate above.
An 'L' suffix in a matrix cell indicates a pairing loss for the
candidate above.
An '=' suffix in a matrix cell indicates a pairing tie for the
candidate above.
The LOL row shows the largest opposition in a pairing loss.  This
is plain Condorcet.
The LO row shows the largest opposition including both pairing wins
and losses.  This is "Condorcet(LO)".

Example 1. "Simple spectrum"
46: R>M>L                 R    M    L
20: M               R         46   46L
34: L>M>R           M    54L       66L
L    34   34
---- ---- ----
LO   54   46   66        M wins: 46
LOL  54    0   66        M wins:  0

Example 2. "Truncation"
46: R                     R    M    L
20: M               R         46   46L
34: L>M>R           M    54L       20
L    34   34L
---- ---- ----
LO   54   46   46        M and L tie: 46
LOL  54   34   46        M wins:      34

Example 3. "Reversal"
46: R>L>M                 R    M    L
20: M               R         46   46L
34: L>M>R           M    54L       20
L    34   80L
---- ---- ----
LO   54   80   46        L wins: 46
LOL  54   80   46        L wins: 46

The only result difference between the two methods in the familiar
46/20/34 series is in the truncation case, where the voters who
truncated are penalized by Condorcet(LO) by having M and L tie with
LO=46.  (If the //Plurality tie-breaker is used, L wins.)

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)

```