Re: [EM] Condorcet and Participation, Moulin's proof

[Chris Benham]

Michael Ossipoff wrote:

> Sure, Condorcet fails Participation. And of course it would be better 
> to not fail Participation. But Partilcipation isn't about a strategy 
> dilemma. It's about an embarrassment. You know that no method can 
> aviod embarrassments of some kind or other. You know, that goes back 
> to Kenneth Arrow. 


My intention in drawing attention to that proof  was to provide 
ammunition in favour of  Condorcet, not against it. Condorcet's 
Participation failure
apparently requires there to be four candidates in a cycle, which I 
don't consider to be a practical concern.

> But I use Partilcipation when comparing Approval to IRV. Some say 
> that's dishonest, to use Participation when my favorite method, 
> Condorcet, fails Participation.


I would say that it is somewhat misleading and inconsistent, and  
counter-productive to the goals of  educating people and promoting the 
Condorcet criterion.

> But it isn't, because, unlike Condorcet, IRV has no redeeming 
> qualities to outweigh its Participation failure. 


To be charitable, that is an absurd exaggeration made purely for the 
sake of being provocative. A more intelligent and appropriate attack on IRV
could be made along the lines that it's Participation failures are much 
more severe than Condorcet's because they are possible in relatively
common-place scenarios with just three candidates and no cycle. (This 
seems to be  Auros/M.Harman's main objection to IRV.)

So it seems to me that some weakened form of  the Participation 
criterion that captures one of  IRV's problems versus Condorcet might be of
some use/interest.

Chris Benham





>  
>

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Re: [EM] Condorcet and Participation, Moulin's proof

[Michael Ossipoff]

Sure, Condorcet fails Participation. And of course it would be better to not 
fail Participation. But Partilcipation isn't about a strategy dilemma. It's 
about an embarrassment. You know that no method can aviod embarrassments of 
some kind or other. You know, that goes back to Kenneth Arrow.

For me, the great strategy guarantees that Condorcet offers far outweigh the 
harmless, non-strategy-related embarrassment of Participation-failure.

But I use Partilcipation when comparing Approval to IRV. Some say that's 
dishonest, to use Participation when my favorite method, Condorcet, fails 
Participation. But it isn't, because, unlike Condorcet, IRV has no redeeming 
qualities to outweigh its Participation failure.

Mike



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[EM] Condorcet and Participation, Moulin's proof

[Chris Benham]

 [EM] Condorcet and Participation

*Markus Schulze * [EMAIL PROTECTED] 


/Sun Oct 5 02:48:02 2003/

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Dear participants,

this is Moulin's proof that participation and Condorcet
are incompatible.

Situation 1:

  3 ADBC
  3 ADCB
  4 BCAD
  5 DBCA

Situation 2:

  Suppose candidate B is elected with positive probability
  in situation 1. When we add 6 BDAC voters then candidate B
  must be elected with positive probability according to
  participation and candidate D must be elected with
  certainty according to Condorcet.

Situation 3:

  Suppose candidate C is elected with positive probability
  in situation 1. When we add 8 CBAD voters then candidate C
  must be elected with positive probability according to
  participation and candidate B must be elected with
  certainty according to Condorcet.

Situation 4:

  Suppose candidate D is elected with positive probability
  in situation 1. When we add 4 DABC voters then candidate D
  must be elected with positive probability according to
  participation and candidate A must be elected with
  certainty according to Condorcet.

Situation 5:

  Because of the considerations in Situation 2-4 we get
  to the conclusion that candidate A must be elected with
  certainty in situation 1. When we add 4 CABD voters then
  candidate B and candidate D must be elected each with
  zero probability according to participation.

Situation 6:

  Suppose candidate A is elected with positive probability
  in situation 5. When we add 6 ACBD voters then candidate A
  must be elected with positive probability according to
  participation and candidate C must be elected with
  certainty according to Condorcet.

Situation 7:

  Suppose candidate C is elected with positive probability
  in situation 5. When we add 4 CBAD voters then candidate C
  must be elected with positive probability according to
  participation and candidate B must be elected with
  certainty according to Condorcet.

Markus Schulze




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