[EM] An improved Condorcet Hare hybrid and its generalization to STV

Chris Benham cbenhamau at yahoo.com.au
Sat Mar 31 22:40:11 PDT 2018

On 30/03/2018 4:41 AM, Ross Hyman wrote:
> V_A>B is the number of ballots that rank A above B. V_A is the number of ballots that rank A at the top.
> M_A,B = (V_A>B - V_B>A)/(V_A>B + V_B>A)
> S_A = sum_B M_A,B V_B is the score for candidate A.
> So long as there is no majority winner, eliminate the candidate with lowest score.  Recalculate V_A's and S_A's.  (M_A,B’s do not need to be recalculated.)Repeat until there is a majority winner (that is one with more top votes than
> the quota = total votes/2.)

I'm a bit confused by this Mathese.   In the second line, what does the 
"M" stand for?  Does the "/"  mean divided by?

> Example 6 A2, A1, B, C
> 1 A1, A2, B, C
> 5 B, C, A1, A2
> 4 C, A1, A2, B
> Condorcet Hare hybrid eliminates A1 then C and elects A2.
B>C 6-4,   B=A1 5-5,   B=A2 5-5,    C>A1 9-1, C>A2 9-1,    A1>A2 10-0

In your example B is the only candidate that is pairwise undefeated, so 
if the "Condorcet Hare hybrid" is
happy with that (rather than insisting that among uneliminated 
candidates the winner must pairwise beat
all the rest) then no candidate will be eliminated and B will be elected.

Otherwise Hare and the "Condorcet Hare hybrid" will first eliminate A2 
(because it is the only candidate voted
top on zero ballots) and then A1 and still elect B.

> A1 is the more sensible winner since more voters prefer A1
> to A2 than A2 to A1.

In your example A2 is voted below A1 on every ballot, so certainly of 
those two "A1 is the more sensible winner".
Is there a typo in your example ?

Chris Benham

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