IRO and Condorcet

Mike Ossipoff dfb at
Fri Nov 22 11:50:24 PST 1996

Yes, the single-winner method that Hallett proposed in
_Proportional Representation_ (1926) was a pairwise method,
and meets Condorcet's criterion.

What Hallett's method amounts to, as he explained (I believe 
it was at the end of the chapter or section preceding the
one where he introduced the rules), was that if there's
an alternative that pairwise-beats each one of the others, then
it wins. Otherwise the winner is the alternative that Hare-Ware
(IRO) would choose.

Hallett's actual rules for the count were incredibly complicated.
I don't know why or how his rules produce the desired result, but
I take his word for it. No doubt the reason for the complicated
count rule was a desire to minimize count labor in a
non-computerized count.


Of course Dodgson, Young, Copeland, Hallett, & the 2 methods
named after Nanson, all meet Condorcet's criterion, which
makes them all much better than IRO (Hare-Ware).

Incidentally, Dodgson, as I remember, proposed that, in a
circular tie, it be determined which alternative could be
made into a beats-all winner by reversing the fewest individual
prefrences, and then the members of the committee (the voters)
be advised that they could resolve the circular tie if they'd
reverse those preferences.

Dodgson also used that standard for evaluating the results of
other methods.

I was told that Young's method is like Dodgson's but that
Young elects the alternative that would be Beats-All by
_ignoring_ (rather than reversing) the fewest individual
pairwise preferences. Of the two, Dodgson & Young, I prefer
Young. Someone said that Young's method is also known as
Nanson's method, in Australia, where Nanson was the 1st
to propose it. Not being in Australia, I don't know
the details of that proposal, or whether it was identical
to the simple definition of Young's method.

In some U.S. books, the term "Nanson's method" is used for
a different method. A method that meets Condorcet's criterion,
but which isn't done as a pairwise method. That method's rule
is to repeatedly eliminate from the ranks the alterntive having
the lowest Borda point score, as computed by the rankings as
they exist at that time.


As I said, all of these methods meet Condorcet's criterion,
and respect the basic democratic principle on which
Condorcet's criterion is based:

If the number of voters indicating tht they prefer A to B
is greater than the number indicating that they prefer B
to A, then if we choose A or B, it should be A.

But none of those methods meets GMC (Generalized Majority
Criterion, or respects the basic democratic principle upon
which that criterion is based. Since I'm now writing to
people not on EM, let me repeat that basic democratic
principle (after which I'll define GMC):

If a majority of the people voting on a particular single-winner
choice election indicate that they'd rather have A than B,
then if we choose A or B then it should be A.


That principle is obvious & natural but none of the abovementioned
pairwise methods & Condorcet-Criterion methods respects that
principle--they can violate it unnecessarily. Only Condorcet(EM)
will never unnecessarily violate that principle. Condorcet(EM)
is the method that chooses as winner the alternative with fewest
votes against it in a pairwise defeat by another method.

Strictly speaking, the other pairwise methods that I mentioned
aren't "Condorcet's method", because Condorcet didn't just
propose the general pairwise methods: He proposed a particular
class of such methods that looked at the worst defeat of each
alternative. Dodgson & Young might sound like interpretations
of Condorcet's proposal, except that they don't go by
worse defeat; they go by _overall_ margin of defeat. So
Condorcet(EM) is the only version of Condorcet being proposed
at the present time.

GMC (Generalized Majority Criterion):

definition: An alternative is "majority-rejected" if there's
another alternative that is ranked over it by a majority of
all the voters.

A method meets GMC if & only if a majority-rejected alternative
can never win unless every alternative is majority rejected.


GMC is for comparing choice rules, and, strictly speaking
, instead of just saying "every alternative" it should
say "...every alterntive in the set from which that choice
rule is to choose".  So, when a certain choice rule, such
as the rule to choose the alternative with fewest votes
against it in a pairwise defeat, is used to choose from
the Smith set, the overall method is defined by the Smith
set & that choice rule, but GMC is for rating that choice
rule. But obviously if it's felt that only alternatives in
a certain set, like the Smith set, should be considered, then
, with that understanding, any method that uses a GMC-complying
method to choose from that set is doing the best possible 
in terms of GMC & the insistance on choosing from that set.


I've argued emphatically against Copeland's method, which
has a serious problem that the other pairwise methods don't
have, a dependence on how many candidates various parties are
able to run in a particular election.  So though Copeland may
still be better than IRO, it isn't as good as Dodgson, Young,
& Nanson, and probably isn't as good as Hallett's method.

But Condorcet(EM) is better than all of those, becaue
of its compliance with additional standards, principles
& criteria, and because its count of "votes-against" is what
transparently satifies the requirement that one's 2nd-place
ranking of a compromise should fully help it beat anything
ranked higher or not ranked, but shouldn't count for it against
one's 1st choice. Votes-against does that, transparently.


For the U.S., I'd argue against any other method while arguing
for Condorcet(EM). But regarding proposals in another country,
I don't feel that it would be right to criticize pairwise proposals
in in another country, and I'm not critical of the use of Hallett's
country in Australia, or the proposal of Young's method there.

[By the way, Tom mentioned that a pairwise method was being proposed
at an Australian university. Which pairwise method is it?]


Lastly, though I've mentioned this on EM & ER, I'd like to say
it again here, since others are on this group-reply list:

Not only does IRO not respect either of the 2 basic democratic
principles that I named, but more than that can be said.

All the pairwise methods respect the principle that says:

If the number of voters indicating that they'd rather have A
than B is greater than the number indicating that they'd rather
have B than A, then, if we choose A or B, it should be A.

Well, it isn't just that IRO doesn't respect that principle,
though lots of other methods do. Here's what else:

IRO is the only method that will violate that principle even
if every voter ranks, alone in 1st or 2nd place, the alternative
whose election wouldn't violate that principle.

[By "only method", I mean "only rank-balloting method"]


Mike Ossipoff


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