Hi Nicholas, At no point is he adding simultaneously different groups of voters. He is reaching conclusions about one group and then modifying it to get the new group, but the modification is always relevant to Participation.
Let me try to understand which stage exactly it is that you do not agree with. Again let me start with the idea that you believe that the winner of the first election (the one with four voting groups) can only be A, in order to satisfy Condorcet and Participation. Step 0: Assume A must win (everybody agrees nobody else is possible) Case 1: proved that D cannot win (you agree with this) Case 2: proved that B cannot win (you agree with this) Case 3: proved that C cannot win (you agree with this) Case 4: proved that either A or C must win in this election: 3 voters vote A > D > C > B. 3 voters vote A > D > B > C. 5 voters vote D > B > C > A. 4 voters vote B > C > A > D. 4 voters vote C > A > B > D. Do you disagree with that? The new voters are C>A voters so the new winner cannot be anybody worse than A, because we know that A was previously winning. I will wait to continue until you say whether you agree that the winner of that five-faction election must be A or C. Kevin ---- Election-Methods mailing list - see http://electorama.com/em for list info
