Ok, I think I have an example which shows the vote management resistance. Assume the following
2 Seats to be filled and 3 candidates A1: Popular candidate (party A) A2: Other candidate (party A) B: Party B candidate Honest rankings are A1's personal supporters 12: A1>B>A2 26: A1>A2>B Party A's supporters 12: A1>A2>B 13: A2>A1>B Party B's supporters 27: B Standard PR-STV Quota = 30 Round 1 A1: 50 A2: 13 B: 27 A1 elected with 20 surplus (15 for A2 and 5 for B) Round 2 A1: 30(-20) Elected A2: 28(+15) B: 32(+5) B elected Result: (A1,B) wins Assuming vote management. Party A tells all supporters to vote A2>A1>B Round 1 A1: 38 A2: 25 B: 27 A1 elected with 8 surplus (2.5 for B and 5.5 for A2) Round 2 A1: 30(-8) A2: 30.5(+5.5) B: 29.5(+2.5) A2 is elected Result: (A1,A2) Vote management has paid off Schulze's method A1's personal supporters 12: A1>B>A2 26: A1>A2>B Party A's supporters 12: A1>A2>B 13: A2>A1>B Party B's supporters 27: B Compare (A1,A2) against (A1,B*) B is the test candidate. 12 prefer A1 to B (Assign to A1's group) 0 prefer A2 to B 51 prefer both to B (Assign 19.5 to A1 and 31.5 to A2) All groups are the same size of 31.5 Compare (A1,B) against (A1,A2*) A2 is the test candidate 38 prefer A1 to A2 (assign to A1) 27 prefer B to A2 (assign to B) 12 prefer both to A2 (assign 0.5 to A1 and 11.5 to B) All groups are the same size of 38.5 This means that (A1,B) beats (A1,A2) by 37.5 votes to 32.5 votes. Schulze's method under vote management A1's personal supporters 12: A1>B>A2 26: A1>A2>B Party A's supporters 25: A2>A1>B Party B's supporters 27: B Compare (A1,A2) against (A1,B*) B is the test candidate. 12 prefer A1 to B (Assign to A1's group) 0 prefer A2 to B 51 prefer both to B (Assign 19.5 to A1 and 31.5 to A2) All groups are the same size of 31.5 Compare (A1,B) against (A1,A2*) A2 is the test candidate 26 prefer A1 to A2 (assign to A1) 27 prefer B to A2 (assign to B) 12 prefer both to A2 (assign 6.5 to A1 and 5.5 to B) All groups are the same size of 32.5 This means that (A1,B) beats (A1,A2) by 37.5 votes to 32.5 votes. Thus, even under vote management A1,B wins. The condition seems to be that vote management will still payoff under Schulze if A1's personal vote + Party A's vote > A1's personal vote + Party B's vote thus if Party A's vote > Party B's vote, then party A can get the additional seat, but only if vote management is used. ---- Election-Methods mailing list - see http://electorama.com/em for list info