IRO, monotonicity

[Markus Schulze]

Mike Ossipoff wrote (23 Oct 1998):
> I haven't found those articles you cited yet, but I did
> find something by Nurmi. He seemed to consider nonmonotonicity
> an undesirable thing, so he couldn't have too high an opinion
> of IRO, could he?
>
> He said:
>
> "The Monotonicity Criterion is undoubtedly one of the basic
> criteria of democratic decisionmaking.  The idea of counting
> votes in an effort to determine group preference assumes that
> the more support an alternative has, the better the chance it
> has of being chosen as the socially most perfect alternative.
> Surely this sounds like a reasonable requirement. Indeed, it
> seems to be at the heart of the idea of letting the people
> choose."
>
> Could the person who said that like IRO?? Are you sure
> he likes IRO?

It is true, that Nurmi criticizes the nonmonotonicity of IRO.
On page 78 of "Comparing Voting Systems," he writes:

"The monotonicity criterion is undoubtedly one of the basic
criteria of democratic decision making. The idea of counting
votes in an effort to determine group preferences assumes that
the more support an alternative has, the better chances it
has to be chosen as the socially most prefered alternative.
As we have seen in procedures lacking the monotonicity
property, additional support may turn out to be harmful for
an alternative. Thus, one can build a strong case for monotonic
procedures in contrast to non-monotonic ones."

Nevertheless his book ends with the conclusion, that IRO is
better than Condorcet criterion methods. On page 123, he
writes:

"The fourth level in the preference misrepresentation hierarchy
consists of procedures that are most difficult to manipulate in
the sense that the informational requirements for a successful
manipulation are most stringent: in typical cases one has to
know the entire preference orderings of most -if not all- voters
to benefit from the misrepresentation of one's own preference
ordering. A procedure that most clearly represents systems at
this level is Coombs' method. But typically the Hare system also
requires a profound knowledge of the preference profile to
enable a successful preference misrepresentation."

On page 172-173, he writes:

"We have already paid attention to the fact that speaking of
manipulability in the sense of individual preference
misrepresentation is likely to blur the issue to the extent
that this property is considered as a dichotomous one. Even
though all the procedures are manipulable in this sense, there
are essential differences between them concerning the
difficulty of manipulation or the amount of information one
has to possess about other people's preferences in order to
benefit from preference misrepresentation. E.g. Hare's
procedure is extremely difficult to manipulate and some
empirical evidence gives strong support to this claim."

On page 192, he writes:

"Some procedures are inherently difficult to manipulate even
with an extensive knowledge of other people's preferences.
When no such arrangements can be made, it would seem that the
approval voting is the optimal method when primary attention
is on the agenda-manipulation possibilities. If, on the other
hand, individual preference misrepresentation is to be feared,
then Hare's, Coombs' or plurality runoff procedures would
seem appropriate."

Markus Schulze