This might lead to a contradiction: since Bob's action depends on Alice's action, and Alice is not always capable of predicting her own action, especially while deciding what it should be, it might be impossible for Alice to predict Bob's action, even if the dependence of Bob's action on Alice's action is simple, i.e. if Alice understands Bob's algorithm very well.
The scenarios which result in a contradiction are not compatible with the verbal description of the problem. As such we must conclude that the scenario is one of the ones which contains instances of the pair "Alice and Bob" for which it is possible for Alice to predict the moves of Bob.
If there was a problem that specified "Alice can predict Bob" and there are possible instances of those two where prediction is possible and an answer happened to conclude "it is impossible for Alice to predict Bob's action" then the person giving the answer would just be wrong because they are responding to a problem incompatible with the specified problem.
The first draft of the 2012 Less Wrong Census/Survey is complete (see 2011 here). I will link it below if you promise not to try to take the survey because it's not done yet and this is just an example!
2012 Less Wrong Census/Survey Draft
I want three things from you.
First, please critique this draft. Tell me if any questions are unclear, misleading, offensive, confusing, or stupid. Tell me if the survey is so unbearably long that you would never possibly take it. Tell me if anything needs to be rephrased.
Second, I am willing to include any question you want in the Super Extra Bonus Questions section, as long as it is not offensive, super-long-and-involved, or really dumb. Please post any questions you want there. Please be specific - not "Ask something about abortion" but give the exact question you want me to ask as well as all answer choices.
Try not to add more than five or so questions per person, unless you're sure yours are really interesting. Please also don't add any questions that aren't very easily sort-able by a computer program like SPSS unless you can commit to sorting the answers yourself.
Third, please suggest a decent, quick, and at least somewhat accurate Internet IQ test I can stick in a new section, Unreasonably Long Bonus Questions.
I will probably post the survey to Main and officially open it for responses sometime early next week.