[EM] SODA: polls via "like/+1/reddit"; resulting nonmonotonicity; natural fix

Jameson Quinn jameson.quinn at gmail.com
Tue Jan 10 09:59:05 PST 2012

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.

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