Normative principles of elections- Condorcet and Irrelevance of Alternatives (plus a brief hello and an STV clarification)

[Mike Ositoff]

On Thu, 27 Aug 1998, David Catchpole wrote:

> On Wed, 26 Aug 1998, Mike Ositoff wrote:
> 
> I guess it's hard to always have everyone agreeing, but I believe the
> criterion of irrelevant alternatives actually does allow for the criteria
> below.
> 
> The fact is that if a Condorcet winner exists, that winner
> satisfies IA, and vice versa. This is a good point about Condorcet,
> in case people are just being defensive without provocation.

Condorcet's method, in all of our versions, and every proposed
method that I've heard of, fails IIAC. I didn't mean to seem
defensive. I quite agree that the Condorcet winner is a good
choice. But compliance, or noncopliance, with IIAC is a 
property of a method. Maybe Condorcet doesn't violate
IIAC, can't violate it, when it elects a Condorcet winner.
If so, I very much appreciate your pointing that out, because,
as you said, that's a useful thing to say to someone who
brings up Arrow's theorem to argue against single-winner
reform. That matter hadn't occurred to me--thanks for
pointing it out.

> 
> I personally disagree with the vagueness of just plain "majority rule", 
> believing that more focused principles of majority rule need to be
> developed. As for the concept of strategy- IA has a large-scale
> positive effect on the behaviour of actors in an election.

Therea are a number of precisely-defined criteria that are
about majority rule. One such criterion that I consider
important, partly because of its consequences, is GMC, the
Generalized Majority Criterion. In its ordinary version, I
word it: "Never avoidably elect an alternative that has
another alternative ranked over it by a majority of all the
voters". Obviously that isn't a desirable thing to do, a
clear violation of majority rule. That has always seemed to
me to be what majority rule means in a multicandidate race.
Anyway, I don't know that majority rule is a vague concept;
it's undesirable to violate the expressed wishes of a majority,
avoidably.

Another wording that I've used is: 

If a majority of all the voters have indicated that they'd
rather have A than B, then, if we choose A or B, it should
be A. It's desirable to not avoidably violate that.

Someone has defined a slightly more complicated, but useful
version of GMC: If some aternative, A, has a majority 
beat-path to alternative B, but B doesn't have one to A,
then don't elect B. This is quite similar in its consequences
to the simpler GMC, but it doesn't require a subcycle
of alternatives that all beat eachother by majorities to
disqualify eachother from winning.

When I said "majority rule", I was naming a principle, and
wasn't offering it as a criterion. Since majority rule
isn't intended as a criterion, it can't really be faulted
for not being a precisely stated criterion. I regard a
criterion as a precise yes/no test for use in measuring
adherence to a principle.

By the way, isn't someone going to tell me what "normative"
means?? I found it in a dictionary, but it wasn't clear to
me what that definition would mean as used by voting
system authors.

> 
> I would appreciate it if you gave me examples of IA contradicting other
> ubiquitous criteria, as I am a relative newcomer to the "field"; however, I

Well I'll tell you what: You show me a method that meets 
IIAC, and then I'll show you some desirabale criteria that
it violates. I would now, except that I don't know of a
method that meets IIAC.

Again, though, I appreciate your pointing out that Condorcet's
method complies with IIAC when it elects a Condorcet winner;
as I said, that hadn't occurred to me.



> believe that the concept of IA itself is a particularly dominant one- that
> the outcome of the election reflects the values of the electorate 
> independent of the presence of any losing candidates.
> 
> 
> > I'm always interested in suggestions about flaws, including this
> > one, but I have to admit that I've never known what "normative"
> > means. But as for principles that (almost) everyone can agree on,
> > we Condorcet advocates base our whole advocacy on such principles:
> > 
> > Majority rule
> > Getting rid of the lesser-of-2-evils problem (LO2E)
> > Avoiding the need for defensive strategy
> > 
> > (The last 2 are the same, really, and both are closely
> > related to the first)
> > 
> > ***
> > It would be good to comply with IIAC (Irrelevant Alternatives Critrerion),
> > but it isn't possible, at least not without giving up other
> > more important properties.
> > 
> > ***
> > 
> > Mike Ossipoff
> > 
> > 
> > 
> 
>