[EM] Range voting fails IIA

[Abd ul-Rahman Lomax]

At 09:53 PM 11/7/2006, Chris Benham wrote:
>The claim that Range meets IIA (and Clone Independence) rests on the
>assumption that the
>voters' ratings are "absolute", based on some standard that is
>independent of  the candidates.

Yes. More accurately, it simply rests on the assumption that voters 
will not change their vote based on the introduction of a new 
candidate, with the possible exception of inserting a rank. We assume 
that in a ranked election, for the purposes of considering IIA, 
voters will not change their ranks.

They might, for example for strategic reasons. But we must assume 
that they do not do this.

The equivalent in a Range election is that voters don't change their 
ratings. It is only strategic Range voting that would reasonably 
cause such a change.


>According to this assumption, Range doesn't reduce to FPP when there are
>two candidates.

That's correct. I presume that "reduce to FPP" means that all the 
other candidates disappear. Since some voters may have expressed weak 
votes, it can happen that a majority of voters express a weak 
preference, whereas a minority have expressed strong preference, and 
thus the choice of the minority prevails. So?

(Yes, I agree that there is a kind of problem here, and the problem 
is intrinsic to Range, but the solution is a ratification vote when 
there is doubt about the appropriateness of the Range winner due to 
certain conditions. The problem, though, is much more complex than a 
simple criterion will address.)

>Range promoters like to move the goal posts around. For example one who
>has claimed that
>Range meets IIA also makes it clear that he expects that voters will
>always vote at least candidate
>max. and at least one min.

One suggested strategy or method of determining votes has been 
confused, once again, with the method itself. If voters follow that 
strategy, which does consider candidate space, *as I wrote*, then 
their ratings will change with the introduction of a new candidate. 
But this is true of many other methods which are considered to satisfy IIA.

However, maybe not. I could not find, easily, any description of what 
methods satisfy it and what do not, and, it appears, there is some 
considerable confusion about exactly what this criterion means. I'm 
assuming that the criterion has an *objective* meaning that does not 
require information not on the ballot. If it does require such 
information, then we should know exactly how such information is to 
be collected. By glossing this over, the problems in application are 
avoided, and ready assumptions that are not actually true can easily be made.

Lack of rigor in definition, I'd say. *As written and with one 
reasonable interpretation, Range satisfies IIA." You can make other 
interpretations, especially those that involve internal voter process 
which is not clearly defined, and then conclude otherwise.