[EM] Participation criterion: a thought

[Kevin Venzke]

Diana,

 --- Diana Galletly <dag1000 at eng.cam.ac.uk> a écrit : 
> It struck me this evening that surely the participation criterion is
> just a rather sharp, clear-cut case of the consistency criterion.  With
> consistency we have set 1 and set 2, both of whom declare A as the winner,
> and then the amalgamated set that will declare A as the winner if consistency
> is satisfied.
> 
> With participation we have set 1 who declared A as the winner, and then a
> newly-discovered ballot box, or 3 extra people who chose to vote, all of
> whom ranked A first, who are identical to the previous set 2.

I don't know whether you're right or not about the relationship between
Participation and Consistency.  But in most Participation failure examples
I've seen, the same candidate is not the winner in both sets.  For example,
for MCA:

5 A>B>C
4 B>C>A

add in: 2 C>A>B

The winner of the two sets of votes are A and C.  Combined, the winner is B.

So perhaps Consistency is an easier-to-satisfy version of Participation?
Seems to be what you're saying.


Kislanko said:
> We've known that consistency is not possible in any ranked-ballot method for 50 
> years.

Does Kislanko not consider Borda to be a "ranked-ballot method"?  Or what does
this statement refer to?


Diana said:
>>So why the great recent worry about participation ? (myself included, I
have to admit!  The statement of the participation criterion sounds much
more important and generally worrying than the statement of the consistency
criterion.)  If I'm right in my belief that participation is a subset of
consistency then I no longer see it as a bugbear to worry about overmuch.<<

I think it would be extremely desirable to meet Participation, but I don't
see how it can be done without being very simple.

For the last couple of weeks I've been trying to come up with the smallest
possible modification to Approval that would still meet Participation, but
I still haven't got anything.

Can anyone come up with anything here?


Kislanko said:
>I don't even know what is meant by "participation." The only so-called definition I've 
>seen is "suppose another bunch of voters show up and vote the same way as one voter does".

I don't know what the point of posting that was.

Markus recently wrote:
"Participation" says that adding a set of identical ballots
   on which candidate A is strictly preferred to candidate B
   must not change the winner from candidate A to candidate B.

I would note that we can't easily define Consistency by changing a couple of words
in the above definition.  We have to evaluate the method's winner for the new
ballots, not simply see who's ranked first, for instance.

Kevin Venzke
stepjak at yahoo.fr


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