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There is a good chance I am missing something here, but from an economic perspective this seems trivial:
P(Om) is the probability the person assigns Omega of being able to accurately predict their decision ahead of time.
A. P(Om) x $1m is the expected return from opening one box.
B. (1 - P(Om))x$1m + $1000 is the expected return of opening both boxes (the probability that Omega was wrong times the million plus the thousand.)
Since P(Om) is dependent on people's individual belief about Omega's ability to predict their actions it is not surprising different people make different decisions and think they are being rational - they are!
If A > B they choose one box, if B > A they choose both boxes.
This also shows why people will change their views if the amount in the visible box is changed (to $990,000 or $10).
Basically, in this instance, if you think the probability of Omega being able to determine your future action is greater than 0.5005 then you select a single box, if less than that you select both boxes. At P(Om)=0.5005 the expected return of both strategies is $500,500.
EDIT. I think I oversimplified B, but the point still stands. nhamann - I didn't see your post before writing mine. I think the only difference between them is that I state that it is a personal view of the probability of Omega being able to predict choices and you seem to want to use the actual probability that he can.
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Couldn't the alien argue that slippery slopes slip both ways? If we start allowing Holocaust denial, soon it will be legal to yell "fire!" in a theater.
Any theatre offering access to the public should be able to evacuate all patrons safely in the event of a real fire, thus someone falsely yelling "fire!" simply inconveniences people and should be banned by the owner. There is no need to get the police involved and have this ridiculous example as legitimisation on limits on free speech in a public arena.
There are limits that should be upheld, but not necessarily by police (e.g. someone being slandered could sue rather than have the slanderer arrested.) Incitement to violence may be banned as a pragmatic measure, but that would be my Schelling point (and even then I'm not 100% sure...)