Pierre-Simon Laplace, in my opinion the greatest statistician of all time, wrote eloquently about the cost-benefit principle in his magnus opus:
In other contexts, this paradox is often called "paralysis by analysis." Insofar as it holds true, what exactly would mediate the trade-off between probabilistic thinking and timely, necessary action?
I think it's secular vs sacred. In the real world you need to make assumptions to actually make things happen, but in the world of intellectuals, as Robin Hanson says, "sharp people... distinguish themselves by not assuming more than needed to keep the conversation going."
There's no doubt Laplace caught onto this. For example, when asked by Napolean why he didn't mention religion in his tome on probability, he famously replied that he "had no need of that hypothesis."
Again, not sure how far this example generalizes and I'd like to see some systematic data, but this is something to ponder.
Consequently we ought always in the conduct of life to make the product of the benefit hoped for, by its probability, at least equal to the similar product relative to the loss. But it is necessary, in order to attain this, to appreciate exactly the advantages, the losses, and their respective probabilities. For this a great accuracy of mind, a delicate judgment, and a great experience in affairs is necessary; it is necessary to know how to guard one's self against prejudices, illusions of fear or hope, and erroneous ideas, ideas of fortune and happiness, with which the majority of people feed their selflove.Napolean made Laplace the Minister of the Interior in 1799, which he apparently begged for. But he struggled with it, as Napolean recounts,
Laplace was not long in showing himself a worse than average administrator; since his first actions in office we recognized our mistake. Laplace did not consider any question from the right angle: he sought subtleties everywhere, only conceived problems, and finally carried the spirit of "infinitesimals" into the administration.Let's be careful not to read too much into this one anecdote, as it has an n of one. But still, it's scary that thinking too much is a plausible way for a politician to fail.
In other contexts, this paradox is often called "paralysis by analysis." Insofar as it holds true, what exactly would mediate the trade-off between probabilistic thinking and timely, necessary action?
I think it's secular vs sacred. In the real world you need to make assumptions to actually make things happen, but in the world of intellectuals, as Robin Hanson says, "sharp people... distinguish themselves by not assuming more than needed to keep the conversation going."
There's no doubt Laplace caught onto this. For example, when asked by Napolean why he didn't mention religion in his tome on probability, he famously replied that he "had no need of that hypothesis."
Again, not sure how far this example generalizes and I'd like to see some systematic data, but this is something to ponder.
