[EM] SODA

[Jameson Quinn]

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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