IPDA criterion (was Re: [EM] Approval meets IIA?)

[Steve Eppley]

Markus Schulze wrote:
-snip-
> Here is a very similar desideratum (Steve Eppley's "independence 
> from Pareto-dominated alternatives"; IPDA):
> 
>    Candidate x is weakly Pareto-dominated if and only if 
>    there exists a candidate y such that at least one
>    voter ranks y over x and no voters rank x over y.
> 
>    IPDA says that the election outcome must not change if 
>    a weakly Pareto-dominated alternative is deleted from
>    the set of nominees and from the votes.
> 
> Your example demonstrates that Approval Voting violates
> IPDA when the voters vote in the manner presumed by you.
> However, the fact that also Tideman's ranked pairs method
> and my beatpath method violate IPDA demonstrates that
> this criterion is stronger than one might think on first
> view.
-snip-

Right.  And although one could tweak a voting method so it 
first eliminates from contention every weakly Pareto-
dominated candidate, this patch wouldn't be robust.  For 
one thing, we probably also want to defeat the "99 against 
1" candidates in most scenarios. (Not necessarily, though: 
the lone supporter might be very passionate, while the 99 
opponents are nearly indifferent.)  For another thing, some 
joker would notice the strategic incentive to rank the 
dominated candidate over the dominating candidate, to make 
the tweak ineffective.  Also, the tweak probably sacrifices 
some other criterion, such as monotonicity. (But don't 
construe this to mean that I think monotonicity is as 
important as other criteria.)

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)