Circular tie solutions should be obvious

Sun Feb 20 13:50:19 PST 2000

I wrote-

Is there still support for the single step tiebreaker using the fewest votes 
against in the worst defeat (especially with 4 or more choices in a circular 
tie) ?
D- Seeing no responses-- I note another simple circular tie example with 5 


Arranging the pairings high to low--

82 DE 18
81 CD 19
80 BC 20
79 AB 21
78 EA 22

63 CE 37
61 BD 39
60 DA 40
59 BC 41
57 EB 43

Which choice is the biggest clone ?
Obviously E- a clone of D
See the DE diagonal.

If E is removed, then

81 CD 19
80 BC 20
79 AB 21

61 BD 39
60 DA 40
59 AC 41

Still a circular tie.

D is now the biggest clone.

If D is removed, then

80 BC 20
79 AB 21

59 AC 41

C is now the biggest clone (and defeated by both A and B)

If C is removed, then

79 AB 21

Of course, in real elections there might/would be more diffusion of votes (as 
if ALL the U.S. President candidates in the last year were on one ballot).

The misleading nature of clones can be seen by adding F, a 100 percent clone 
of E, after each E.

100 EF 0
with the same other pairings as E---

82 DF 18
78 FA 22 (especially)

63 CF 37
57 FB 43

In real elections some voters will, of course, rank a copycat clone ahead of 
the original (in politics, music, movies, TV shows or whatever).

I mention again- a minority can rank its favorites early, then such minority 
can stop voting or rank the lesser of the perceived evils ahead of the 
greater perceived evils.

Borda fans- take note what happens when clones are added.  Borda R.I.P. ???

Both Condorcet and Borda appear somewhat not to have detected the clones 
lurking in circular ties (???) (although Condorcet with his comments about 
probability in high/low pairings came very close).

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