Dear Peter Zbornik, I wrote (6 May 2010):
> The Schulze proportional ranking method can be > described as follows: > > Suppose place 1 to (n-1) have already been > filled. Suppose A(i) (with i = 1,...,(n-1)) > is the candidate of place i. > > Suppose we want to fill the n-th place. > > Suppose x,y are two hopeful candidates. Then > H[A(1),...,A(n-1),x,y] is the largest possible > value such that the electorate can be divided > into n+1 disjoint parts T(1),...,T(n+1) such that > > 1. For all i := 1,...,n: |T(i)| >= H[A(1),...,A(n-1),x,y]. > 2. For all i := 1,...,(n-1): Every voter in T(i) > prefers candidate A(i) to candidate y. > 3. Every voter in T(n) prefers candidate x > to candidate y. > > Apply the Schulze single-winner election method > to the matrix d[x,y] := H[A(1),...,A(n-1),x,y]. > The winner gets the n-th place. You wrote (6 May 2010): > The example below is intriguing. But I am afraid I fail > to understand this formulation of Schulze's proportional > ranking. I would be grateful if M. Schulze or someone > else, could give an example, which could help me get it. > Specifically, I didn't understand what H[A(1),...,A(n-1),x,y] > is. Is it a function, H[A(1),...,A(n-1),x,y]= > min(cardinality of T(i), 0<=i<=n+1 plus other criteria)?, > I didn't get the properties of T(n+1). Why are there n+1 > partitions of the electorate and not only n? H[A(1),...,A(n-1),x,y] is a real number. My mail above is supposed to be a definition for H[A(1),...,A(n-1),x,y]. There are n+1 partitions because there can also be some voters who prefer candidate y to every candidate in {A(1),...,A(n-1),x}. The voters in T(n+1) are those who prefer candidate y to every candidate in {A(1),...,A(n-1),x}. Markus Schulze ---- Election-Methods mailing list - see http://electorama.com/em for list info