[EM] Participation criterion: a thought

[Diana Galletly]

People are likely to note that I will often apologise in advance for my
ideas, as experience shows that, 24-48 hours later, I will suddenly see
why I am mistaken.  On occasion I'm not, and that's when I tend to do
decent research.  I provide this disclaimer now because otherwise I'll
probably preface every mail with "I'm probably wrong, but" and that gets
wearing after a while.

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.

So any method that fails consistency is surely also going to fail
participation, so it's no great surprise that Condorcet methods fail
participation.

Where's the error in my logic?

Diana.