[EM] Approval, Pareto, & ICC

[James Green-Armytage]

Mike, you wrote:
>
>In many or most cases, there's some vaguness about Pareto's definition.
>Is 
>it about preference or voting? If it's about preference, then no method 
>meets it, or at least it isn't complete till someone adds stipulation
>about 
>how people vote. If Pareto is about voting, then it says that a candidate 
>shouldn't win if another candidate is voted over him/her by everyone. No, 
>they don't say it that way, and so I'm just trying to guess what they
>might 
>mean.
>And if they do say "voted over", then it would be necessary to supply a 
>definition of that too. Sometimes the academics don't seem to have their
>act 
>together very well. I'd supply my definition.
>Anyway, if Pareto is about voting, then of course Approval passes. I've
>read 
>in academic publications that Plurality, Borda, IRV, Copeland, etc. meet 
>Pareto. (Copeland is or was usually the only pairwise count method
>mentioned 
>in academic articles, though occasionally Condorcet (meaning PC) or
>Dodgson 
>is mentioned). Sequential Pairwise, the familiar parliamentary procedure,
> 
>is mentioned as the method that notably doesn't meet Pareto. So, most 
>likely, for most authors at least, Pareto is intended to be about voting, 
>though vaguely defined.
>
	I believe that Pareto is a criterion taken from the literature of welfare
economics. It deals primarily with preference. The basic idea is that if
there is some outcome A that everyone concerned prefers to another outcome
B, then B should not be selected. It's a very weak criterion. 
	The application of Pareto to ranked ballot voting methods seems fairly
straightforward. Assume that voters vote sincerely, and then ask whether
the method can ever choose a candidate who is Pareto-dominated.
	How to apply Pareto to approval? I suggest that we start by trying to
take the same approach as before: assume that voters vote sincerely. But
what is sincere voting in approval? It's not as easy to define as in a
ranked ballot method. Perhaps the most we can assume is that no voter will
approve a less-preferred candidate while not approving a more-preferred
candidate. Given that restriction, is it possible that a Pareto-dominated
candidate will be elected by approval voting? I think so. Consider this
example:

Sincere preferences and approval cutoffs:
60: A>B>>C
40: C>>A>B

	A and B are tied with 60 points each. Hence, assuming that the method
resolves ties randomly, B wins with 50% probability, in which case Pareto
is violated.

Sincerely,
James