Dear Richard, you wrote (1 July 2021): > I am not understanding what you are suggesting. > > It sounds like you want to sub-divide the fourth category > into these two sub-categories: > > * A wins before cloning, A(1) wins after cloning, and > A(1) wins if only the clones participate. > > * A wins before cloning, A(1) wins after cloning, but > A(1) does not win if only the clones participate. > > Do we need to distinguish between these two cases? Yes, that's what I am suggesting. It should make no difference whether we (1) apply the election method to all candidates at once or (2) shrink all candidates A(1),...,A(n) of a set of clones to a single candidate A, apply the election method to this reduced set of candidates and then -- when candidate A is elected -- unshrink candidate A and apply the election method to the candidates A(1),...,A(n) only. Markus Schulze