Positive Involvement; No-Show

Markus Schulze schulze at sol.physik.tu-berlin.de
Fri Jul 3 09:49:52 PDT 1998

Dear Demorep,

you wrote (25 Jun 1998):
> For the folks who do NOT live on the various criteria (such as me),
> I ask how many criteria are out there in internet land ?  Perhaps
> some expert in such criteria may want to post them.

Of course, there are only six important criteria: Pareto, Autonomy,
Neutrality, Non-Dictatorship, Invulnerability by Exaggeration, and
Independence from Irrelevant Alternatives.

Unfortunately, it is impossible for an election method to meet
all six criteria simultaneously. Thus, some criteria have to be
relaxed. If you investigate the currently discussed criteria, you
will find, that Monotonicity, Positive Involvement, No-Show, Local
Independence from Irrelevant Alternatives, Complete Independence
from Clones, and Truncation Resistency are relaxations of the
Independence from Irrelevant Alternatives Criterion.

The consequence of the above mentioned incompatibility is the
fact, that every sensefull and democratic election method,
that is not unnecessarily random, is manipulatable

1) by exaggeration or
2) by additional candidates and by giving wrong preferences.

If you want to know, how many criteria an election method should
meet, then my answer is: It should meet Pareto, Autonomy,
Neutrality, Non-Dictatorship, and Invulnerability by Exaggeration.
And it should meet Independence from Irrelevant Alternatives
as much as possible.

Markus Schulze

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