Here's the scenario you used to first show your tree method of determining delegation order.
16 A1>A2>B 12 A2>A1>B 24 B>A1=A2 48 C What if some candidate outside the A1 A2 faction had an A2>A1 preference? I mean either: Scenario S 16 A1>A2>B 12 A2>A1>B 24 B>A2>A1 48 C Or: Scenario T 16 A1>A2>B 12 A2>A1>B 24 B>A1=A2 43 C 5 C>A2 Or even: Scenario U 16 A1>A2>B 12 A2>A1>B 24 B>A1=A2 43 C 5 A2>C I believe that A2 should go first in all of the above scenarios. Thus, you'd use the worst relevant pairwise WV totals over the whole electorate to determine order within a coalition. For two-member coalitions, that's just the pairwise WV between them; for a three-member, cycled coalition, it's minimax WV; and for a coalition of two multi-member subcoalitions, it's the worst WV of a member of subcoalition X over a member of subcoalition Y and vice versa. That is, in all cases, lower-bounded by the coalition size, but it can go higher, as it does in the three scenarios I gave above. .... I like this coalition tree method as a theoretical way of making a cloneproof SODA. However, for SODA as a practical proposal, it's too much complication for too little benefit. SODA is already proof against simple pairs of clones, and I don't think that larger clouds of clones without one stand-out winner will ever be a factor in a real election. Certainly I can't think of any historical election where this would have mattered, even including serious 4-way elections like US 1860 or Romania 2009. JQ
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