# Exaggerated opinions

Markus Schulze schulze at sol.physik.tu-berlin.de
Fri Apr 24 08:07:22 PDT 1998

```Dear Mike, dear David,

I don't believe, that it is possible to find a sensefull and
democratic voting method, that -simultaneously- uses absolute
preferences and is invulnerable by exaggeration. Let me explain:

I want to consider a situation with only two candidates
(A and B), where an absolute majority of the voters
prefers candidate A to candidate B.

Suppose, there is a voting method, that uses absolute
preferences and that is invulnerable by exaggeration.
Then there must be some situations, where candidate B is
elected, because otherwise this voting method would only
use relative preferences.

Suppose, we have a situation, where candidate B is elected.
As the used voting method is invulnerable by exaggeration,
candidate B must be elected, even if those voters, who
prefer A to B, exaggerate (i.e., they vote A=100% and B=0%).
In other words: Even if an absolute majority of the voters says,
that candidate A is absolutely perfect and that candidate B is
absolutely unacceptable, candidate B must be elected. Otherwise
the used voting method would use only relative preferences or
it would be manipulatable by exaggeration.

To my opinion, it is not possible, that B is elected, because
this would be a violation of the Neutrality Criterion (i.e.,
every candidate is treated equally), the Anonymity Criterion
(i.e., every voter is treated equally) or the Weak Monotonicity
Criterion (i.e.: If there are only two candidates (A and B) and
candidate A is elected, then he must be elected also if a voter
changes his opinion to the advantage of A. If there are only two
candidates (A and B) and candidate A is elected, then he must be
elected also if a voter changes his opinion to the disadvantage
of B.).

In short: I believe, that, if there are only two candidates (A and B)
and if an absolute majority of the voters prefers candidate A to
candidate B, then every sensefull democratic voting method would
necessarily elect candidate A. Otherwise that voting method would
be manipulatable by exaggeration or it would be unnecessarily random.

By the way: I don't think, that it is the task of a voting method
to protect a minority from an intolerant majority. I don't think,
that a democratic voting method can do that. To protect a minority,
that is the task of the constitution and not of the voting method.

Markus

```