[EM] Cardinal Rating Condorcet Loser Elimination

[Dgamble997 at aol.com]

Rob Speer wrote:

>Didn't we hear this same debate, oh, a week ago? And the week before
>that? It seems like every thread on this list eventually turns into
>"Weak centrist!" "Condorcet winner!" "Weak centrist!" "Condorcet winner!"

>Unless someone's providing some new information (like, say, the results
>of an experiment to _find out_ whether people prefer a weak centrist or
>a Condorcet non-winner), there is no value to repeating the argument.

What I was trying to do in my original post was give details of a method 
which gives high utility centrist, low first preference vote- winner ( as in 
Condorcet ) and low utility centrist, low first preference vote- loser ( as in IRV 
).

Take the following examples:

Low utility centrist:

48 1.00A > 0.3B
5   1.00B > 0.5C
47 1.00C > 0.3B

Pairwise comparisons using utilities 

A versus B   48 v  19.1  A wins
A= 48 @ 1.00 =48.00    B = 5 @ 1.00 + 47 @ 0.3 = 19.1

A versus C   48 v 49.5   C wins
A= 48 @ 1.00 = 48.00    C = 5 @ 0.5 +  47 @ 1.00 = 49.5

B versus  C   19.4 v 47   C wins
B= 5 @ 1.00 +  48 @ 0.3 = 19.4   C = 47 @ 1.00 = 47.00

B is the Condorcet loser and is eliminated.

B votes transfer to C at a utility of 1.00 giving:

       1st    2nd
A     48     48
B      5      ---
C     47     52

C is the winner ( as in IRV).



High utility centrist:

48  1.00A > 0.95B
5    1.00B > 0.5C
47   1.00C > 0.95B

A versus B   48 v 49.65   B wins
A = 48 @ 1.00 = 48.00   B = 5 @ 1.00 + 47 @ 0.95 = 49.65

A versus C   48 v 49.5     C wins
A = 48 @ 1.00 = 48.00    C = 5 @ 0.50 + 47 @ 1.00 = 49.5

B versus C   50.6 v 47     B wins
B = 48 @ 0.95 + 5 @ 1.00   C = 47 @ 1.00

A is the Condorcet loser and is therefore eliminated.

A votes transfer to B at a utility of 1.00 giving:

    1st    2nd
A  48     -----
B  5       53
C  47     47

B is the winner ( as in Condorcet ).

David Gamble

 


    
    

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