[EM] Two approval ballot methods using approval opposition

[Kevin Venzke]

Chris,

--- Chris Benham <chrisbenham at bigpond.com> a écrit :
> >A philosophical question would be whether there is any justification
> >for electing someone other than the Approval winner when we're using
> >approval ballots. 
> >
> And  the philosophical answer would be that it isn't. A  fundamental 
> standard is that  the results
> of  the voting method must be justifiable on the assumption that the 
> votes are sincere.
> You can't do nothing except collect approval information and then elect 
> someone who isn't the
> Approval winner because you make some "guess"  about voters' rankings 
> based on the assumption
> that there is a political spectrum.

My assumption isn't part of method's mechanics, though. The "tied at
the top" rule and the concept of approval opposition don't depend on
there being a spectrum.

Here's how this reads approval ballots with respect to ranking:

If X isn't approved, conservatively assume that this candidate wouldn't
be ranked above anyone. Equal-last ranking.
If X is approved but not Y, then this voter prefers X to Y.
If X and Y are both approved, then it isn't clear whether this voter
prefers X to Y, Y to X, or both equally.

You seem to criticize that I don't assume the answer is "both equally" 
as Approval does.

tCMAO says: Given the above assumptions, narrow the field to every
candidate who *could* be the Condorcet winner, and pick a winner based
on the AO rule.

I am sure that if I run Condorcet-effiency simulations comparing Approval
and tCMAO, and *don't* assume that there's an underlying spectrum or
any particular correlation among different candidates' supporters,
tCMAO will come out worse than Approval.

But I'm fairly sure that if I use distance-based preferences to create
full rankings, truncate in the middle somewhere and approve those above
it, tCMAO will do nearly as well as Approval if not better.

Consider again:

25 A
25 AB
25 BC
25 C

If we imagine a 1D spectrum, it's unavoidable that the A and C voters
have an unexpressed preference for B over the other. (Remember, this
is just a thought experiment, not a justification.)

The AO mechanism can be justified without assuming there's a spectrum.
Mike Ossipoff characterized MMPO as electing the "least unpreferred"
candidate (with respect to another candidate). Isn't that much more 
meaningful here, where each candidate must either be "preferred" or
"not preferred" absolutely?

> The least bad of  these three methods, MAMAO, fails   Irrelevant Ballots.
> 
> Modifying one of your examples slightly, we see that the other two fail 
> the Plurality criterion.

MAMAO fails Plurality, too, whenever it doesn't pick a majority favorite.

It is pretty easy to show that using approval ballots, the only way
to avoid failing Plurality is to elect the approval winner.

Kevin Venzke



	

	
		
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