Can Bayesianism deal with the mail-order prophet scam? If so, how?
This scam uses a segmented mailing list and a large initial population to advertise predictions so that a 'winning' portion of recipients receive an apparently improbable series of correct predictions. Most recipients (the 'losers') receive an incorrect prediction at some point.
For clarity, here is the situation:
A Bayesian with no prior knowledge of the scam receives a letter advertising stock predictions via a new proprietary quantitative model. The letter predicts that by the end of the month, stock XYZ will be up. It also states that the firm will prove their legitimacy by sending 6 more predictions (one per month) that will correctly predict whether XYZ is up or down. Sure enough, the Bayesian receives each letter, and the predictions all end up correct!
Unbeknownst to the Bayesian, 63 other Bayesians also received the first letter, 31 others received the second, 15 the third, 7 the fourth, 3 the fifth, and 1 other received the sixth letter. Our unlucky Bayesian was the only one to receive the seventh.
The question is, assuming no knowledge of the scam or communication with the "losers" (for whom a stock prediction was wrong), should the Bayesian -- strictly adhering to Bayesian Epistemology -- believe that the firm's stock predictions are legit?
I don't know how to approach this from a Bayesian perspective and would appreciate any guidance from someone who's more familiar. My intuition is that the Bayesian should believe that the predictions are legit (which we observers know to be incorrect).
Also I feel I should disclose that I'm not a Bayesian (rather a Critical Fallibilist), and I'm looking for the best Bayesian answers to this problem (links to prior material welcome). It's often quite hard to find the best answers to a problem from a particular school, so please bear with me if I've missed something obvious.
If someone is able to consistently predict the market, they don't need the sort of investors they could get from mass-mailing people. The only conceivable reason they would be sending stuff to random strangers (and not like, hedge funds, banks, or billionaires) is if they're trying to scam you.
Maybe if you looked at just the predictions, and didn't consider the context in which someone would be sending accurate market predictions to you, then you could get tricked. In context though, there's no plausible scenario where someone intelligent (superhuman) enough to make accurate stock picks consistently is marketing their services through the mail. They would have to be both smart enough to succeed, and dumb enough to not have access to better sources of funding, and dumb enough to not realize that their 10% weekly return strategy invalidates the need for investment in the first place. This sort of person is incompatible with the real world -- intelligence is general enough.
It would be like if someone claiming to be Donald Trump starting texting you to tell you about his next Tariff. Even if your Trump got it right 6 times in a row, it's not plausible he would be texting a random citizen his intentions. Maybe it warrants further attention since it is definitely some sort of signal, but it doesn't warrant belief.
Can Bayesianism deal with the mail-order prophet scam? If so, how?
This scam uses a segmented mailing list and a large initial population to advertise predictions so that a 'winning' portion of recipients receive an apparently improbable series of correct predictions. Most recipients (the 'losers') receive an incorrect prediction at some point.
For clarity, here is the situation:
A Bayesian with no prior knowledge of the scam receives a letter advertising stock predictions via a new proprietary quantitative model. The letter predicts that by the end of the month, stock XYZ will be up. It also states that the firm will prove their legitimacy by sending 6 more predictions (one per month) that will correctly predict whether XYZ is up or down. Sure enough, the Bayesian receives each letter, and the predictions all end up correct!
Unbeknownst to the Bayesian, 63 other Bayesians also received the first letter, 31 others received the second, 15 the third, 7 the fourth, 3 the fifth, and 1 other received the sixth letter. Our unlucky Bayesian was the only one to receive the seventh.
The question is, assuming no knowledge of the scam or communication with the "losers" (for whom a stock prediction was wrong), should the Bayesian -- strictly adhering to Bayesian Epistemology -- believe that the firm's stock predictions are legit?
I don't know how to approach this from a Bayesian perspective and would appreciate any guidance from someone who's more familiar. My intuition is that the Bayesian should believe that the predictions are legit (which we observers know to be incorrect).
Also I feel I should disclose that I'm not a Bayesian (rather a Critical Fallibilist), and I'm looking for the best Bayesian answers to this problem (links to prior material welcome). It's often quite hard to find the best answers to a problem from a particular school, so please bear with me if I've missed something obvious.