[email protected] wrote:
Here's a link to Jobst's definitive posting on individual and social
utility:
http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2007-February/019631.html
Also, I would like to make another comment in support of Warren's
thesis that cardinal range scores are as meaningful or more so than
ordinal rankings:
Consider that Borda is a method based on rankings. Do the rankings
in Borda have the same meaning to the voter as the rankings in IRV
do? From Arrow's point of view they do; the ballots are identical in
format, and in either case (for a sincere vote) you simply rank A
ahead of B if you prefer A over B.
But now let's compare Borda with Range; Suppose that there are ten
candidates and that the Range ballots ask you to rate them on a scale
of zero to nine. On the Borda ballot you are asked to rank them from
one to 10.
Borda elects the candidate with the "highest" average rank (i.e. the
lowest average rank number). Range elects the candidate with the
highest average range score.
Now, tell me why Arrow worries about the supposed incommensurable
ratings on a scale of zero to 9, but sees no problem with the one to
ten ranking scale?
Doesn't that confuse the meaning of ranking (versus rating) in itself
with the meaning of ranking, as interpreted by the system? I could make
a ranked ballot system like IRV that would produce non-monotone results
given the ranked ballots that are input to it -- but I could also make a
rated ballot system, say "the winner is the candidate with the greatest
mode", that would also give non-monotone results (since if X is the
candidate with greatest mode, rating X higher may lower his mode).
Thus, if ratings and rankings are to have meaning, it would seem that
this meaning would be independent of the system in question. Otherwise,
the meaning would have to be considered with respect to the space of
possible voting methods that could use the ballot type in question, and
there would be very many outright weird voting methods on both ballot types.
If, then, meaning is independent of the method, then Borda's internal
workings (where it assigns a score to each ranking) doesn't mean that
Borda makes use of a rated ballot, but simply that Borda acts *as if*
the ranked ballot is a rated ballot. Because of this, it may produce
counterintuitive outcomes (e.g. failing the majority criterion). For
that matter, we know that every ranked ballot method can produce a
counterintuitive outcome (if we consider determinism, unanimity,
non-dictatorship, and IIA intuitive). However, in the
independent-of-method point of view, that doesn't make the ranked ballot
itself ill-defined.
To use an analogy, say you could instruct a robot either by giving
somewhat general commands (ranking), or by explicitly programming it
(rating). Now, if you were to find a theorem that there's no way to
construct the robot so that it never misunderstands any of your
commands, then that doesn't mean that the concept of a general command
is without meaning. It just means that there are hard limits to the
robot's understanding.
Of course, one could then argue what the meaning of a ranked ballot is.
I think this is easy enough: a ranked ballot is a compact representation
of a combination of preferences (prefers A to B, B to C, C to D, etc),
so that the combination is transitive.
(Using that definition, one could even design a "strategy-free" method
where voters are encouraged to submit full rank orders as defined: the
method would be random dictator but with a pre-stage that removes a
random subset of the candidates. That method would be nondeterministic
and not that good in practice, though.)
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