[EM] HBH

[Kevin Venzke]

Hi Forest,

--- En date de : Lun 18.7.11, fsimmons at pcc.edu <fsimmons at pcc.edu> a écrit :
> > The "pecking order" is the Range order. Assume no
> ties.
> 
> I suppose that you could use the range order for the
> pecking order, but as you mention below that could 
> lead to some strategic distortions.
> 
> The pecking order I had in mind is more like implicit
> approval; if implicit approval (number of above zero 
> ratings) has no ties, that's all it is.

Oops. I understood this when I read it but didn't retain it.

> > I understand the Plurality argument. Still wrapping my
> head 
> > around the
> > monotonicity and compromise ones. 
> 
> The key to montonicity is that from the first time the
> eventual winner becomes the defending champ, she 
> has to defeat every challenger, i.e. all of the remaining
> candidates.  So if a winner W gets barely enough 
> increased support to change the proximity order by just one
> pair, say W is now closer to V, than W' 
> instead of vice-versa, then W' challenges V before W. 
> Whether or not W' or the current V weathers this 
> challenge doesn't matter, because W beat the current V
> before, and then beat W' and all of the other 
> remaining candidates later.
> 
> If the winner gets lots of increased support, just
> gradually add that support so that it makes this minimal 
> change in the order, and note that each time this kind of
> minimal change is made, the winner stays the 
> same.  If we wanted to get fancy, we would call this a
> homotopy argument.

Ok. I'll just trust it for now.

I was thinking a bit while trying to code it. In the 3-candidate case,
if there is a "Condorcet winner" in the HBH sense then he wins. Otherwise
we have one of two cycles as always.

I notice that no matter which cycle it is, the winner is going to be
whichever candidate is deemed further from the approval loser.

My first thought is that that sounds pretty bad. It sounds like the
approval loser is set up to spoil the outcome.

On the other hand, in order to have a cycle, everybody must have 
majority approval, which makes it very strange to think of there being
weak noise candidates as such... A candidate lacking majority approval
(who isn't the AW) has no effect. So it's hard to imagine appalling
outcomes... I'm pretty sure it can overrule a lone majority contest,
but it won't even violate minimal defense when it does...

Kevin Venzke