[EM] Looking for a little voting insight...

[D CarySys]

On Tue May 2 22:31:33 PDT 2006,  Matthew Welland wrote:

> I don't follow the logic perfectly but looking at the example it seems that 
> intuitively "A" is the choice that would leave the least number of people 
> unhappy and since no-one has contradicted you I will go with that.

B's worst defeat is by a margin of 6, A's worst defeat is by a margin of 8.  So in some senses, the Minimax choice of B as the winner leaves fewer people unhappy:

  1. The most people voting against B in any pair-wise matchup was 18.  All other candidates have higher corresponding numbers (19 for A).
  2.  B's worst defeat can be reversed by ignoring preferences of (disenfranchising) 6+1 voters.  All other candidates have higher corresponding numbers (8+1 for A).
  3.  B can become the Condorcet winner, reversing all (both) of its losses, by adding 6+1 votes.  All other candidates have higher corresponding numbers (8+1 for A).
  4.  B can become the Condorcet winner, reversing all (both) of its losses, by ignoring some preferences of (disenfranching) 6+1 voters.  All other candidates have higher corresponding numbers (8+1 for A).

Items 2 and 3 above are a direct result of B being the Minimax winner using margins.  Item 1 is  a direct result of B being the Minimax winner, either using magins with strict preferences and no truncated ballots, or using winning votes.

On the other hand, there were 24 voters that ranked B lower than at least one of the candidates (A or C) that pair-wise beat B.  Item 4 above says that only preferences of 7 of those voters would have to be ignored to make B the Condorcet winner.  But each of those 24 voters might feel his/her preferences were among the 7 and therefore be unhappy with the result.  The corresponding number for A is only 19 voters.


On Wed May 3 11:29:21 PDT 2006, Dave Ketchum wrote: 

> i am getting rusty as to details, but noting strength of defeats 
> needs more thought - here he looks only at strength of victor, not at 
> magnitude of difference.  25>5 is stronger than 26>24.

In the example, all ballots fully and strictly ranked all candidates -- no explicit equal rankings and no truncated rankings resulting in implicit equal rankings. In such a case, both the Schulze and Minimax methods are insensitive to whether strength of victory is measured in terms of margins or winning votes, avoiding the complications of that issue and keeping the focus on the key differences of the two methods.

-- David Cary

		
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