[EM] Condorcet completed by SC reversed-rankings IRV elimination

Chris Benham chrisbenham at bigpond.com
Fri Jan 16 14:18:21 PST 2004

  I propose and reccomend this single-winner  Condorcet  compliant method:
Plain ranked-ballots, equal preferences and truncation ok.
1: Eliminate all candidates who are not members of the Schwartz set.
2: If  more than one candidate remains, then based on the symetrically 
completed (SC) and reversed rankings,
eliminate the candidate picked by the Alternative Vote (aka IRV).
Repeat steps 1 and 2 until only one candidate (the winner) remains
In terms of criteria mentioned by Woodall, it has in common with Winning 
Votes  that it  meets the Plurality Criterion,
and because of this (combined with meeting  Condorcet) also fails 
 Mono-add-top, Mono-raise-random,
Mono-sub-top, Mono-raise-delete, and Mono-sub-plunp.  
(These criteria are defined here: 
 http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf  )
Unlike  WV, this method  meets  Symetric Completion, and  I  believe 
that that allows it to meet my
Decisiveness Fairness Standard, which means means meeting Kevin Venzke's 
 "Earlier-no-harm" and "Earlier-no-help"
criteria  (introduced here: 

This method makes use of IRV's great resistance to Burying  (aka 
"offensive order-reversal"), so that in this respect  I believe
(with some evidence) that it performs  better than Winning Votes.
Some examples (I copied from somewhere):
Sincere preferences are:
44: A>B>C
14: B>C>A
14: B>A>C
28: C>B>A
100 ballots. B is the CW.

The A voters try to "Bury" B:
44: A>C>B
14: B>C>A
14: B>A>C
28: C>B>A
and it backfires.  A is eliminated and  C wins. Schulze, Tideman, 
Simpson, Raynaud, LeGrand all pick A.
C has the highest Borda score. (Borda is not fit to be used, but is 
allowed to comment.)

An example from  a  James Green-Armytage posting on  Sun.Aug.17,2003

Sincere preferences
46: A>B
44: B>A
5: C>A
5: C>B

"It is extremely clear here that C seriously does not deserve to win, as he
is ranked last by 90% of the voters. Also, it is clear that A deserves to
win, albeit by a narrow margin.
Now, if the method is Condorcet (minimax, Schwartz / minimax, ranked
pairs, or beatpath), and if everyone voted sincerely, A would win.
However, if the 44 B>A voters strategically vote B>C (offensive order
reversal), a cycle is formed, in which the defeat of B is now the defeat
of least magnitude, and so B wins."

46: A>B
44: B>C
5: C>A
5: C>B

A:B = 51:49
A:C = 46:54
B:C = 90:10

"This is already very unfair, and a clear subversion of the democratic
What can the offended A>B voters do about this? Assuming that the other
preferences are constant they have no way of electing A. Their only
option, other than allowing B to steal the victory, is to truncate or
order-reverse themselves, leading to the election of C." 

46: A
44: B>C
5: C>A
5: C>B

A:B = 51:49
A:C = 46:54
B:C = 44:10

"The B-->C defeat is the defeat of least magnitude, and so C wins.
The only hope of A voters is that their truncation will deter the B voters
from their order reversal.
Thus the A and B voters have entered a game of chicken. A voters swerving
is their voting sincerely and allowing B to win. B voters swerving is
their voting sincerely and allowing A to win. The car crash is the
election of C. 
The outcome is unpredictable. It is quite possible that C will be elected,
despite the fact that he so clearly does not deserve to win. This is not a
pleasant scenario at all from the point of view of democracy, utility,
majority rule, public trust in government, etc."

In the above example, with the B voters trying to Bury A, and the A voters responding
by truncating, B is eliminated and A wins.

Chris Benham

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