Dear Peter Zbornik,
the fact, that the Schulze single-winner election method
satisfies the majority criterion, is a direct consequence
of the fact that every pairwise victory is stronger than
every pairwise defeat.
Similarly, the fact, that the Schulze proportional ranking
method satisfies the proportionality criterion for the
top-down approach, is a direct consequence of the fact
that every link H[A(1),...,A(n-1),x,y] from an outcome
{A(1),...,A(n-1),x} in agreement with the proportionality
criterion to an outcome {A(1),...,A(n-1),y} in disagreement
with the proportionality criterion has a strength of more
than N/(n+1) and that every link H[A(1),...,A(n-1),y,x]
from an outcome {A(1),...,A(n-1),y} in disagreement
with the proportionality criterion to an outcome
{A(1),...,A(n-1),x} in agreement with the proportionality
criterion has a strength of less than N/(n+1). This means
that every path from an outcome in agreement with the
proportionality criterion to an outcome in disagreement
with the proportionality criterion has a strength of
more than N/(n+1) and that every path from an outcome
in disagreement with the proportionality criterion to an
outcome in agreement with the proportionality criterion
has a strength of less than N/(n+1). This means that every
outcome in agreement with the proportionality criterion
disqualifies every outcome in disagreement with the
proportionality criterion.
Markus Schulze
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