On Fri, May 7, 2010 at 4:27 PM, Peter Zbornik <[email protected]> wrote: > The proportional ranking needed is not P>VPa>VPb>Ma>Mb>Mc>Md, > but P>[VPa, VPb]>[Ma, Mb, Mc, Md]. > Let us call this required ranking for "boundary conditions".
Schulze's method can do that too. Step 1: Elect the Schulze single seat method winner as President Step 2: Elect a 3 person council using Schulze-STV, but the President must be a member Step 3: Elect a 7 person council using Schulze-STV, but the President + VPs must be members. I think this is what you meant by your unified method? Schulze rankings is just Schulze-STV, except you elect councils that increase in size by one each iteration, and members elected in previous iterations must be members of subsequent councils. > Example (from an email by Schulze): > "40 ABC > 25 BAC > 35 CBA > The Schulze proportional ranking is BAC. > However, for two seats, Droop proportionality, requires that A and C are > elected." > > The "unified" method for two seats without boundary conditions would select > BA (i.e.Schulze STV) Schulze-STV meets the Droop criterion, so would elect A and C in a 2 seat race. Schulze-rankings elects B and then A as you say. There are 2 steps: *** Work out A's score vs C: *** We split the voters in 2 groups Voters who prefer B to A: 60 Voters who prefer C to A: 35 There are no options in which group each voter can be placed, as no voter is eligible for both groups. The smallest group has 35 voters so, A better than than C gets 35 votes *** Work out C's score vs A *** Again we split into 2 groups Voters who prefer only B to C: 0 Voters who prefer only A to C: 0 Voters who prefer both to C: 65 Thus we split the third group into 2 parts, as they can be placed in either group. Voters who prefer B to C: 32.5 Voters who prefer A to C: 32.5 The smallest group has 32.5 voters so, C better than A gets 32.5 votes Thus the result is A gets 35 votes and C get 32.5 votes, so A wins the 2nd seat. Anyway, I think the rankings method can be generalised to allow groups of candidates to be elected at once, rather than electing them one at a time. ---- Election-Methods mailing list - see http://electorama.com/em for list info
