I'm just addicted to this Gendankenexperiment, aren't I?

[packbat]

Newcomb's Paradox again. This time I'm making it as utterly simple as possible.

The Predictor is playing the following game: they examine a subject - you, for instance - they get two boxes - boxes A and B - and they drop the two boxes off with the subject. Then they leave.

The rules are simple. Box A is transparent and contains €1000. Box B is opaque, and contains either nothing or €1 000 000. If the Predictor thinks you'll take Box A, Box B contains nothing. If the Predictor thinks you'll leave Box A just sitting there and walk away from a thousand euros right in front of you, Box B contains the million.

Remember, though - the Predictor is gone. No-one is watching. You can even step right up and open Box B before you decide whether to take Box A. Heck, you could get your good friend down at the bank to come examine all the bills, look up the serial numbers, and verify they're valid if you like. You have full control.

(Why, you could even take Box A and leave Box B on the table unopened. Dunno why you'd do that, but you could - you have the power.)

But: if the Predictor thinks you're not going to leave that thousand on the table, if the Predictor thinks that the next person walking by after you and all your friends are gone won't find the thousand on the table, then the Predictor is going to leave Box B empty. Only if the Predictor is sure you'll abandon Box A's contents will you find the million in Box B.

What would you do?

Edit: If you would act differently given different conditions on the hypothetical (e.g. the presence or absence of the million, the track record of the Predictor to date, the outcome of a coin flip - whatever), please describe how.

Comments

[packbat.livejournal.com]

For the record, I would take Box B, unopened, and leave Box A behind, unopened.

Naughty bad hypothetical!

[the-zaniak.livejournal.com]

From what I understand of the situation you've described, the Predictor doesn't seem to factor you opening Box B into account at all. In addition to that, you've not mentioned the Predictor's accuracy rate.

As such, it seems that the Predictor is relying on you checking Box B and finding it empty - because if you do, then you're definitely going to take the thousand euros and leave. If he put a million euros in Box B, then there's nothing to stop you taking both, and his prediction would be wrong.

I think the Predictor is a bit of a prick!

[packbat.livejournal.com]

A cogent point! What of this variation: the Predictor has done the trick a hundred times, and twenty or fifty people actually picked Box B and left Box A, with nothing stopping them - and those people got the million, where everyone who took the thousand did not. What would you do then?

But putting "supernatural forces" into hypotheticals tends to alter people's reactions...:P

[the-zaniak.livejournal.com]

Take box B and leave box A. As soon as you get a 100% success rate, then to my mind, there's supernatural forces at work, and it's best not to fight against them.

It doesn't *have* to be supernatural ... quite ... ;)

[packbat.livejournal.com]

Fair enough!

On further thought, a clarification:

[packbat.livejournal.com]

I mentioned before that supernatural forces were not required, and it seems to me I should emphasize this - it is possible that the player could precommit themself to only taking Box B (perhaps even without checking the contents), and have sufficient willpower to actually do so when tested. If such a person were examined by the Predictor, the Predictor would be obliged to leave the million in Box B in order to win.

It is not implausible that such a person could exist, and it is not implausible that a Predictor might be skilled enough to identify such a person beforehand.

But I'd want to see his prior track record.

[the-zaniak.livejournal.com]

A person, yes. Hundreds of people with a 100% success rate? Now we're talking supernatural.

If the Predictor did an interview with people beforehand, and if they committed themself to picking box B without checking, and the Predictor was able to accurately predict which of those people were telling the truth (which is plausible) then I would do that, commit myself to box B and then take that without checking.

[packbat.livejournal.com]

That's really the best strategy - people get distracted by the boxes, but it's really a three-move game: you, to convince the Predictor of your choice; the Predictor, to predict your choice; and you, to make your choice.