[EM] Clones in Circular Ties
DEMOREP1 at aol.com
DEMOREP1 at aol.com
Mon Feb 7 14:47:30 PST 2000
The below assumes that each choice gets a YES majority of all of the voters
on a YES/NO vote.
A simple circular tie in a single winner case --
35 ABC
34 BCA
31 CAB
100
66 A > 34 B
69 B > 31 C
65 C > 35 A
A>B, B>C, C>A
If D is made a 100 percent clone of B, then there is
35 ABDC
34 BDCA
31 CABD
100
A > B and D, B and D > C, C > A, 100 B > 0 D
Going backwards, even the 2 or 3 choice cases can be deemed to have an
element of cloneness. Namely, the largest head to head defeat shows the
largest clone (noting that head to head comparisons may involve direct
opposites or real clones).
With 3 or more choices, eliminating one choice at a time may, of course,
cause a bad defeat (by such losing choice) to be removed.
Example
27 ABCD
26 BCDA
25 CDAB
23 DABC
101
75 AB 26
50 AC 51
27 AD 74
76 BC 25
53 BD 48
78 CD 23
A > B, B > C, C > D, D > A
--
Rearranging--
Highest defeat
78 CD 23
76 BC 25
75 AB 26
74 DA 27 lowest worst defeat
53 BD 48
51 CA 50
Lowest defeat
407 199 Totals 606
Is D the largest clone ?
Note the DA line.
If D is eliminated, then there is
76 BC 25
75 AB 26
51 CA 50
202 101 Totals 303
If C is eliminated, then A beats B.
Would a circular tie winner always be near the median in a vertical
arrangement if the highest defeated clones lose ???
Another somewhat obvious tiebreaker would have the highest YES votes choice
be the winner (if there is no Condorcet winner).
I note again that any tiebreaker must be rather obvious to get adopted into
law for real public elections.
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