DEMOREP1 at aol.com DEMOREP1 at aol.com
Fri Jul 19 20:39:51 PDT 1996

```In Condorcet's Theory of Voting by H. P. Young (American Political Science
Review, Vol. 82, No. 4, P. 1231 (Dec. 1988)), Professor Young interprets
Condorcet's writings to the effect that Condorcet suggested that the relative
winners in a cycle situation would be determined by finding the "most
probable combination of opinions" (where Condorcet used the word "opinion" to
be a series of pairwise combinations on the alternatives). The article points
out that Condorcet in his 1785 work gave no example with 4 or more candidates
and that the language that Condorcet used to resolve ties is cryptic.

The article suggests the following to me as a possible tie breaker.

Assume 4 Candidates in a Condorcet tie- C1, C2, C3 and C4.

If the "most probable" alternative is C1>C2>C3>C4, then
C1>C2, C1>C3, C1>C4, C2>C3, C2>C4 and C3>C4.

However, in a cycle by definition, one or more of the six combinations shown
will not actually happen.
If the six combinations are rearranged, then
(1 on 1) C1>C2
(2 on 1) (C1>C3 and C2>C3)
(3 on 1) (C1>C4 and C2>C4 and C3>C4).

If all of the (3 on 1) combinations are done for the 4 candidates, then one
of the candidates will be defeated the worse (i.e. the votes against such
candidate will be highest). Such candidate should be ranked last.

In like manner, if all of the (2 on 1) combinations are done for the 3
remaining candidates, then one of the candidates will be defeated the worse
(i.e. the votes against such candidate will be the highest). Such candidate
should be ranked next to last.

In like manner, with the two remaining candidates one will beat the other.

Example (left rows over top columns)
a    b      c     d
a      -     12   15   17
b     13    -     16   11
c     10     9    -     18
d       8   14     7     -

b>a, d>b, a>c, b>c, a>d, c>d-- tie having b>a, a>c, c>d, d>b
Tot  31   35   38   46 (total votes against)
Total against d is highest- d should be 4th

a    b      c
a      -     12   15
b     13    -     16
c     10     9    -
Tot  23   21    31

Total against c is highest- c should be 3rd

a    b
a      -     12
b     13    -
Total against a is highest- a should be 2nd, b should be 1st.

Thus the result would be b>a, (b+a)>c, (b+a+c)>d or the combined bacd.

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