[EM] STV anomaly - Part of my vote went to someone who was not on my list

[Markus Schulze]

Dear Jim Ronback,

the main aim of STV is to achieve Droop proportionality.
Suppose S is the number of seats and V is the number of
voters. Then "Droop proportionality" says:

   If W > 0 voters strictly prefer every candidate
   of a given set of N1 candidates to every other
   candidate, then at least min {ceil((S+1)*W/V)-1; N1}
   candidates of this set must be elected.

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In your example, V = 10000 voters and S = 4 seats.

W = 5100 voters strictly prefer each of the N1 = 4
candidates {A,B,C,D} to every other candidate.
min {ceil((4+1)*5100/10000)-1; 4} = 2.
Therefore, Droop proportionality says that at least
2 candidates of {A,B,C,D} have to be elected.

W = 4900 voters strictly prefer each of the N1 = 4
candidates {E,F,G,H} to every other candidate.
min {ceil((4+1)*4900/10000)-1; 4} = 2.
Therefore, Droop proportionality says that at least
2 candidates of {E,F,G,H} have to be elected.

The fact that the Meek method chooses {A,B,F,G} is in
agreement with Droop proportionality.

Markus Schulze