RE Condorcet(x( ))
DEMOREP1 at aol.com
DEMOREP1 at aol.com
Tue May 21 15:03:04 PDT 1996
A way to treat tie rankings in Condorcetish methods is to note that (a) at
any choice level, a voter has a total of one vote and (b) tie rankings cover
more than 1 choice level.
Example-- A voter votes A> (B=C=D) > E
The (B=C=D) involves a tie for the 2nd, 3rd and 4th choice levels. Since a
voter has a total of one vote at any choice level, there is---
1st one vote for A
2nd 1/3 vote for each of B, C and D
3rd 1/3 vote for each of B, C and D
4th 1/3 vote for each of B, C and D
5th one vote for E
The general case is that with K candidates in a tie, each candidate gets 1/K
vote at each of the involved choice levels.
Thus- since Condorcet head to head pairings compare the votes received at all
choice levels, x would seem to be 1.
Example- in the above- if B and D are being compared, each obviously gets 1
vote each from such voter (by combining the three 1/3 votes each).
If x=1, then equal rankings take on an aspect of approval voting (in which
choice levels are ignored and each candidate voted for gets one vote-- in the
above all five candidates would get one vote each in approval voting).
However (a)- can any voter give more than one *effective* vote to any two
candidates being compared in a Condorcetish method ?
Thus, does x equal 1/2 between any two of the candidates that have equal
rankings? Having x = 1/2 results in the total votes for the candidates being
equal to the number of ballots. [If x = 0, the total votes for the candidates
are less than the number of ballots. If x =1, the total votes for the
candidates are more than the number of ballots (due to the above approval
voting effect.]
However (b), if a tie breaker is based on limited choice levels (such as the
first, then the first plus second, then the first plus the second plus the
third, and so forth), then there would be fractional votes.
The math complexities of equal rankings may well require that equal rankings
not be allowed. How many voters, politicians and supreme court judges would
understand a Condorcetish method with fractional votes ?
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