Left or right loser

[DEMOREP1 at aol.com]

Prof. Young gives the following example of his (Young's) interpretation of
Condorcet's comments (that I quoted in the original Left or right loser
posting)--
         Table 1- 13 voters
           a         b          c
a        --        8            6
b        5        --           11
c        7          2          --

Prof. Young's comments- Let us apply this rule [Condorcet's comments that I
quoted in the original Left or right loser posting] to the situation in Table
1.  First we are to choose the three propositions having a majority, namely b
> c with eleven votes, a > b with eight votes, and c > a with seven votes.
Since these three propositions form a cycle, however, we delete the
proposition with the smallest plurality, namely c > a.  This leaves the
combination b > c and a > b (and implicitly a > c), which implies the ranking
a > b > c. 
---
My comment- It appears that Prof. Young says that Condorcet's  tiebreaker is
different from anything written about on the EM list.
----
Prof. Young goes on with a 4 candidate cycle example--
25 Voters
         a       b         c         d
a     --       12      15       17
b    13        --      16       11
c    10         9       --       18
d     8         14       7        --

In step 2 of Condorcet's algorithm one would select the six propositions
having greatest majorities.  In descending size of majority, these are c > d
[18 > 7] , a > d [17 > 8], b > c [16 > 9], a > c [15 > 10] , d > b [14 > 11]
, b > a [13 > 12].  According to a literal reading of [Condorcet's] step 3,
one would first delete the proposition b > a, as it has the smallest majority
in its favor.  But this does not result in an "opinion" because one cycle
still remains: b > c, c > d, d > b.  Therefore one would delete the
proposition d > b, as it has the next- smallest majority in its favor.  All
cycles are now eliminated.  But there is a difficulty: in the resulting
partial order both a and b are undominated.  Either one of them could be
interpreted as the top- ranked candidate, so the outcome is indeterminate.
----
My comment-- b beats a head to head 13 to 12.
--- 
Prof. Young goes on with his own idea about reversing the lowest
proposition(s) to eliminate any cycles.
---
The general problem is, of course, that the pairings of the candidates
involved in a cycle can be looked at in 2 simple ways (noting truncation
possibilites)--
Votes For at left in high to low order
L1 > R1
L2 > R2
L3 > R3
L4 > R4
L5 > R5
etc. (That is, L1> L2> L3, etc.)
 or
Votes Against at right in high to low order (assuming some truncations such
that the left number of votes plus the right number of votes may not be the
same in all pairings)
L3 > R3
L1 > R1
L2 > R2
L5 > R5
L4 > R4
etc. (That is, R3> R1> R2, etc.)

I suggest that all Condorcet fans take a look at-- Condorcet's Theory of
Voting by H. P. Young, 82 American Political Science Review 1231 (Dec. 1988).