Condorcet and Irrelevance of Alternatives

[David Catchpole]

On Thu, 27 Aug 1998, Norman Petry wrote:

> David,
> 
> Welcome to the list.  You wrote:
> >for the following system (and therefore that IA is not satisfied for
> 
> The point you may be missing is that we usually use criteria to evaluate
> voting _methods_, not particular "systems" of ballot configurations.  You

I apologise for my misuse of the word "system". I do know I should have
used the word such as "case" (such is misnomenclature...). However I do
say that a criteria has worth even if it is a certainty that it cannot be
satisfied in some non-tied cases.
 
> better than those that don't, partly because they provide a degree of
> independence from irrelevant alternatives, as you pointed out.  We can go

Condorcet gives us *absolute* independence where it exists. We can
still pursue a high degree of IIA if it does not, albeit a non-absolute
degree.

> further, though, and say that even if there are cycles, it is often possible
> to identify at least _some_ candidates who are completely irrelevant -- this
> motivates the use of MIIAC.
> 

In a single-winner Condorcet election, if a paradox of voting has
occurred, no such irrelevant candidate exists- only occasionally
indifference between particular "links" in the chain or cycle.

> Of course, IIAC can always be satisfied by some *unreasonable* methods.
> According to Lorrie Cranor,
> 
> "A voting system is independent from irrelevant alternatives if it always
> produces the same results given the same profile of ordinal preferences.
> This criterion has consequences in two areas: it prohibits voting systems
> that take into account cardinal preferences or ordinal preferences beyond
> each voter's first choice, and it prohibits voting systems that include
> elements of randomness." -- Lorrie Cranor, "Vote Aggregation Methods"
> 
> Therefore, unless we're prepared to live with plurality voting, we're going
> to have to forget about trying to use IIAC as a means of assessing voting
> methods.

PLURALITY GIVES INDEPENDENCE OF ALTERNATIVES? Hello!; IIA is precisely the
concept of an independence to splitting. Guess what the *BIG* problem with
plurality is?

Sorry for being a little rude, but I get a bit riled up when I see a
completely illogical statement. I'm your typical lefty, I guess...