I'm designing a SODA poll that would use facebook "like", google+ "+1", and/or reddit upvotes, along with automated delegated vote assignment, to give live-updated results. In thinking about this, I've realized that SODA can be nonmonotonic in the following (highly contrived) scenario:
(delegated preferences in parentheses) 35: A(>C) 30: B 25: C 10-n: X n: Y(>B>A) With n=4, A wins. With n=6, Y's votes are enough to make B win, so A approves C to prevent that from happening, and C wins; a worse result from the perspective of the Y voters. The natural fix is to allow A to approve C with only some of their delegated votes. Then, when n=6, A can approve C with 12 votes. Now Y's votes cannot make B win, so Y approves A, and the nonmonotonicity is gone. Of course, in order for this to work like that in a live poll, I have to make the logic for automatically updating assigned approvals much, much more complex. In fact, off the top of my head, I can't even prove that the general problem isn't NP-hard. But in real life, it's very unlikely that the scenario would be even this complex, so I'm not too worried about that. Jameson
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