I also think that the variant of the problem featuring an actual mugger is about scam recognition.
Suppose you get an unsolicited email claiming that a Nigerian prince wants to send you a Very Large Reward worth $Y. All you have to do is send him a cash advance of $5 first …
I analyze this as a straightforward two-player game tree via the usual minimax procedure. Player one goes first, and can either pay $5 or not. If player one chooses to pay, then player two goes second, and can either pay Very Large Reward $Y to player one, or he can run away with the cash in hand. Under the usual minimax assumptions, player 2 is obviously not going to pay out! Crucially, this analysis does not depend on the value for Y.
The analysis for Pascal’s mugger is equivalent. A decision procedure that needs to introduce ad hoc corrective factors based on the value of Y seems flawed to me. This type of situation should not require an unusual degree of mathematical sophistication to analyze.
When I list out the most relevant facts about this scenario, they include the following: (1) we received an unsolicited offer (2) from an unknown party from whom we won’t be able to seek redress if anything goes wrong (3) who can take our money and run without giving us anything verifiable in return.
That’s all we need to know. The value of Y doesn’t matter. If the mugger performs a cool and impressive magic trick we may want to tip him for his skillful street performance. We still shouldn’t expect him to payout Y.
I generally learn a lot from the posts here, but in this case I think the reasoning in the post confuses rather than enlightens. When I look back on my own life experiences, there are certainly times when I got scammed. I understand that some in the Less Wrong community may also have fallen victim to scams or fraud in the past. I expect that many of us will likely be subject to disingenuous offers by unFriendly parties in the future. I respectfully suggest that knowing about common scams is a helpful part of a rationalist’s training. It may offer a large benefit relative to other investments.
If my analysis is flawed and/or I’ve missed the point of the exercise, I would appreciate learning why. Thanks!
Friendly neighborhood Matrix Lord checking in!
I’d like to apologize for the behavior of my friend in the hypothetical. He likes to make illusory promises. You should realize that regardless of what he may tell you, his choice of whether to hit the green button is independent of your choice of what to do with your $5. He may hit the green button and save 3↑↑↑3 lives, or he may not, at his whim. Your $5 can not be reliably expected to influence his decision in any way you can predict.
You are no doubt accustomed to thinking about enforceable contracts between parties, since those are a staple of your game theoretic literature as well as your storytelling traditions. Often, your literature omits the requisite preconditions for a binding contract since they are implicit or taken for granted in typical cases. Matrix Lords are highly atypical counterparties, however, and it would be a mistake to carry over those assumptions merely because his statements resemble the syntactic form of an offer between humans.
Did my Matrix Lord friend (who you just met a few minutes ago!) volunteer to have his green save-the-multitudes button and your $5 placed under the control of a mutually trustworthy third party escrow agent who will reliably uphold the stated bargain?
Alternately, if my Matrix Lord friend breaches his contract with you, is someone Even More Powerful standing by to forcibly remedy the non-performance?
Absent either of the above conditions, is my Matrix Lord friend participating in an iterated trading game wherein cheating on today’s deal will subject him to less attractive terms on future deals, such that the net present value of his future earnings would be diminished by more than the amount he can steal from you today?
Since none of these three criteria seem to apply, there is no deal to be made here. The power asymmetry enables him to do whatever he feels like regardless of your actions, and he is just toying with you! Do you really think your $5 means anything to him? He’ll spend it making 3↑↑↑3 paperclips for all you know.
Your $5 will not exert any predictable causal influence on the fate of the hypothetical 3↑↑↑3 Matrix Lord hostages. Decision theory doesn’t even begin to apply.
You should stick to taking boxes from Omega; at least she has an established reputation for paying out as promised.