I can't find what you are talking about in the white paper, but I found this stuff Vitalik said and I am so relieved:
Now, there is another kind of counter-coordination that Vlad Zamfir figured out that does work. Essentially, first of all, instead of the naive Schellingcoin mechanism where winners get P and losers get 0, we add the anti-coordination game to at least the extent at which the mechanism always has an equal total revenue, ie. if there are k winners, winners get NP/k and losers get 0. Then, set up the contract C such that:
(i) to join C you need to put down a security deposit
(ii) after you join C, you need to provably vote with a 60% chance of Obama and a 40% chance of McCain (ie. use some common entropy to decide your vote with that probability distribution, eg. vote Obama iff sha3(block hash) % 10 < 6)
(iii) after you join C and get your reward if you vote Obama, you need to equally redistribute the reward that you get, as well as any bribes that you receive, among all participants in C
(iv) if you violate (ii) or (iii) you lose the deposit
The expected collective payoff, assuming everyone joins C, is going to be P * N + (P + ϵ) * N * 0.4 ~= P * N * 1.4. The incentive to join C is that you receive an expected payoff of 1.4 * P instead of P. Once you join, the security deposit bounds you to participate. The key trick here is that the contract allows the participants to provably share the rewards and collect the maximum possible benefit from the entire combined game. The mechanism doesn't inherit the problems of assurance contracts for public goods because you have the ability to exclude non-participants from sharing in the collective gain (namely, the attacker's attempted bribe).
Essentially, this is basically a way of using a version of my decentralized coordination contract from https://www.youtube.com/watch?v=S47iWiKKvLA&feature=youtu.be
(52:27) against Andrew Miller's centralized coordination contract.