Why are we told that Kim has been saying how much he hates Hillary if the probability of the US being nuked is the same whether Hillary or Jeb is elected (conditional on Kim being in power)? And why would the probability of Hillary being elected go up if Kim is still in power, in this situation? Even if the actual probability of Kim nuking is the same whether Hillary or Jeb is in office, his statements should lead us to believe otherwise. (I realize the latter has no effect on the analysis—if we switch the probabilities of jeb and hillary being elected in the ‘overthrow’ case, the conclusion remains essentially the same—but I feel it bears pointing out).
Perhaps the reason this example is so counter intuitive is because the quantitative probabilities given do not match the qualitative set-up. The example just seems rather contrived, though I’m having trouble putting my finger on why (other than the above apparent contradiction). For now, the best I can come up with is “the demon has done what the prediction market is supposed to do (that is, evaluate the probabilities of Kim being overthrown or not, and of each candidate winning in each case) and everyone is ignoring it for no particular reason, except that some outside observers are using that information to evaluate [the market’s choice in absence of that information].” But perhaps I’m misunderstanding something?
sorry if this post seems somewhat scattered—I just sort of wrote what I thought of as I thought of it.
Is there a summary of the timeline in this example? In particular, when do we know if Kim is overthrown? In order for it to be the confounder you describe, we must know before the election—but then simply conditioning on the election result gives the same chance of being nuked in either case (1/2 if kim is still in power and 0 otherwise).
Maybe I’m not following, but the example is not intuitive to me, and seems contrived.