naturalplastic wrote:
Try:
"Fool me once, shame on you. Fool me twice, shame on me."
The underlying concept expressed in probabilities seems to include the idea of making predictions in the face of deception. Game theory demonstrates the Best Response Functions for these kinds of situations in simpler terms.
To boil it down, if you get information from another party to inform your decision, you have to consider the alignment of your goals and the other party's goals. If you both benefit from the same outcome, the BRF of the other party is to give you accurate information, and your BRF is to trust them. If you benefit from completely different outcomes, then they have no incentive to give you accurate information and you have no reason to make your decision based on the information they give you.
The cases in between, where there is some overlap between goals, where both you and your informer both benefit to some degree from the same outcomes, give you a BRF that uses the similarity between your goals to decide how much to utilize the information.
The saying, "fool me once, shame on you; fool me twice, shame on me," oversimplifies this dynamic by reducing the choices to two, eliminating the in-between cases. The first instance of making a detrimental or at least non-beneficial decision proves that you benefit from different outcomes, in this conception. The saying seems like an expression of Black & White thinking.
I don't think it has mathematical validity, so it's a really interesting case. Let's say that I'm the decider trying to choose a number as close as possible to some unknown target, and I benefit in direct proportion to how close the number is to that target up to a range of eight units. My informant also benefits from my choice in the same way, but they have a different target number that is four lower than my target. They know my target number, but they can tell me whatever they want about what that number is. From there, you can specify the benefits in equations, and actually find the best number for the informant to tell the decider (lower than the decider's target, but not too much lower), and the best number for the decider to choose (higher than what they're told by some specific amount). However, in the simplified mathematical conception, the mathematician knows all of the underlying functions exactly, and that's not often the case in reality; we have to wing it on our best-informed best guesses.
The saying indicates that the decider and the informer are playing a repeated game. In the standard Game Theory conception, the decider uses the outcomes to figure out those underlying functions, and can make better decisions as they play more rounds of the same game. In the conception given by the saying, one bad decision or bad guess by the decider about the motivations of the informer indicates that the decider and informer don't have any overlapping areas of interest, and that the decider should stop playing that game altogether.
If you consider the Cognitive Miser hypothesis as valid, and take into account all the costs of figuring out the motivations of an unreliable informant, and the likely availability of other informants and other games to play, the heuristic makes some sense. It may be more beneficial to only take information from people with whom you have completely shared interests. I'm skeptical, though.
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"I find that the best way [to increase self-confidence] is to lie to yourself about who you are, what you've done, and where you're going." - Richard Ayoade