[EM] Re: Approval, IGB, and Participation

[Kevin Venzke]

Chris,

I hope it's OK if I post this to EM.

 --- Chris Benham <chrisbenham at bigpond.com> a écrit : > Kevin,
> You recently posted:
> 
> "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."
> 
> Doesn't Approval pass Participation ?! 

Yes.  (I said "still meet" Participation.)  But I haven't been able to add any 
kind of ranking functionality that preserves Participation.  I would've thought
it would be a simple matter to make a method which says "the Approval winner
wins, unless Condition X applies," but it seems to me that such methods fail
weak FBC (which seems to suggest Participation failure).  That is, there may be
incentive to disapprove candidates insincerely (inconsistent with any cutoff).

It's hard to use pairwise comparisons in a harmless way.  Suppose there is a
majority defeat A>B.  Should B be barred from winning?  Perhaps only if it means
A can win?  In the former case, as a voter I'm not sure I want to help sink B
if it won't guarantee anything to A.  In the latter case, some voters may have 
incentive to make sure B isn't "offered" a victory that has to be passed on to A.
That's so even if B is their favorite.

I'm still a little skeptical that DAC meets Participation, but then the method
is so bizarre that I shouldn't be so surprised if it at least has Participation
to brag about.  Perhaps it passes because one essentially casts approval votes
for sets of candidates, and there are no pairwise rankings.  Still, DAC has to
ignore votes at times to avoid eliminating all candidates, and that looks
suspicious to me.

> Hasn't Diana Galletly spotted that Consistency
> and Participation are the same thing? From Condorcet.org:

I don't think they're the same thing.  For Participation, the same candidate
doesn't have to win in both sets.  Participation is harder in that sense.
But perhaps Consistency is harder in that the winner of the set has to be
evaluated, not just its ranking order.  Consistency doesn't require that the
new set consist of identical ballots.

>   Pass: Approval <http://condorcet.org/emr/methods.shtml#Approval>, 
>  Average Rating <http://condorcet.org/emr/methods.shtml#Average%20Rating>, Borda
> <http://condorcet.org/emr/methods.shtml#Borda>  (CB: I don't know why no Purality.)

Seems like Plurality should be there.

> On the subject of "Improved Generalised Bucklin" and Participation, is no news good news?

I guess you could say that.  That IGB is more complicated than I first thought, makes
it hard for me to think up a scenario.  I suspect I can make a three-candidate failure 
example, but I may have to write a program to do it for me.  I want to do something 
similar for DAC, as well.

Can you remind me what IGB does when it finds multiple majorities at a given stage?
And is it the same procedure going forwards (finding the first finalist) as
backwards (eliminating losers)?  Does the procedure work with (e.g.) three majorities?


Kevin Venzke
stepjak at yahoo.fr


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