# [EM] Condorcet and Participation

Markus Schulze markus.schulze at alumni.tu-berlin.de
Sun Oct 5 02:48:02 PDT 2003

```Dear participants,

this is Moulin's proof that participation and Condorcet
are incompatible.

Situation 1:

5 DBCA

Situation 2:

Suppose candidate B is elected with positive probability
in situation 1. When we add 6 BDAC voters then candidate B
must be elected with positive probability according to
participation and candidate D must be elected with
certainty according to Condorcet.

Situation 3:

Suppose candidate C is elected with positive probability
in situation 1. When we add 8 CBAD voters then candidate C
must be elected with positive probability according to
participation and candidate B must be elected with
certainty according to Condorcet.

Situation 4:

Suppose candidate D is elected with positive probability
in situation 1. When we add 4 DABC voters then candidate D
must be elected with positive probability according to
participation and candidate A must be elected with
certainty according to Condorcet.

Situation 5:

Because of the considerations in Situation 2-4 we get
to the conclusion that candidate A must be elected with
certainty in situation 1. When we add 4 CABD voters then
candidate B and candidate D must be elected each with
zero probability according to participation.

Situation 6:

Suppose candidate A is elected with positive probability
in situation 5. When we add 6 ACBD voters then candidate A
must be elected with positive probability according to
participation and candidate C must be elected with
certainty according to Condorcet.

Situation 7:

Suppose candidate C is elected with positive probability
in situation 5. When we add 4 CBAD voters then candidate C
must be elected with positive probability according to
participation and candidate B must be elected with
certainty according to Condorcet.

Markus Schulze

```