The bitter fights of information theorists, adding some spice to the morning.
Very related: Shannon and Wiener explicitly wrote that we should use probability because we need to evaluate information systems on their average behavior. The convex analysis comes in because we insist on this mechanical average-case assessment.
I probably should have mentioned that in this post... oh well, next time.
> This mindset assumes that people reason only to wager
Can you name a better reason to reason coherently? Every decision-making-under-uncertainty problem, like it or not, is a question of how to wager.
Of course we also reason for other reasons: sometimes for fun, and sometimes (usually?) for social reasons (e.g., to show off, to convince people to do what we want, or to justify ourselves—cf. Mercier and Sperber's IMO excellent "The Enigma of Reason"). But generally the reasoning you get in those settings isn't particularly coherent, because it doesn't need to be.
> and that gambling is somehow the purpose of life...that world sucks.
Look, I hate it here too man, but I think you've got more work to do if you want to connect the historical dots from Dutch-book arguments to memecoins.
"This mindset" only assumes that one's objectives are known (i.e., non-rational or, if you like, suprarational), and that achieving those objectives may involve risk. Reasoning about what choices (wagers) to make is a means to an end, not an end in itself.
To be clear, I do think there are plenty of critiques to be made of this rationalist paradigm, both practical (e.g., what if we need to include the cost of computation in our objective?) and philosophical (e.g., people's expressed preferences are often themselves incoherent)! I just don't find the argument "gambling is gross" very compelling—the world is full of gross stuff, and ignoring it doesn't make it go away.
It is interesting to note that Frank Ramsey's work, which predates that of Bruno de Finetti in laying out foundational axioms for subjective probability, is very much rooted in pragmatist philosophy. Ramsey's focus on defining probability through betting and decision-making aligns perfectly with the pragmatist philosophy, by focusing on practical consequences of probability judgments.
Regarding coherence in the sense of De Finetti, take a look at this footnote to my old post about probabilities, and in particular at the thesis of Peter Jones mentioned there: https://realizable.substack.com/p/probabilities-coherence-correspondence#footnote-2-141765512. The link to the paper of Mitter et al. on coherence and Kolmogorov consistency in the footnote is dead, but here is the fresh one: https://mitter.lids.mit.edu/publications/102_ondefinetti_elsev.pdf. Ultimately they say it's all about convex analysis.
The Predd et al. paper is from 2009, yet no reference there to the 2004 paper of Mitter et al., even though they are closely related.
The bitter fights of information theorists, adding some spice to the morning.
Very related: Shannon and Wiener explicitly wrote that we should use probability because we need to evaluate information systems on their average behavior. The convex analysis comes in because we insist on this mechanical average-case assessment.
I probably should have mentioned that in this post... oh well, next time.
Two of the authors on the Predd et al. paper are mathematical physicists (Seiringer and Lieb).
> This mindset assumes that people reason only to wager
Can you name a better reason to reason coherently? Every decision-making-under-uncertainty problem, like it or not, is a question of how to wager.
Of course we also reason for other reasons: sometimes for fun, and sometimes (usually?) for social reasons (e.g., to show off, to convince people to do what we want, or to justify ourselves—cf. Mercier and Sperber's IMO excellent "The Enigma of Reason"). But generally the reasoning you get in those settings isn't particularly coherent, because it doesn't need to be.
> and that gambling is somehow the purpose of life...that world sucks.
Look, I hate it here too man, but I think you've got more work to do if you want to connect the historical dots from Dutch-book arguments to memecoins.
"This mindset" only assumes that one's objectives are known (i.e., non-rational or, if you like, suprarational), and that achieving those objectives may involve risk. Reasoning about what choices (wagers) to make is a means to an end, not an end in itself.
To be clear, I do think there are plenty of critiques to be made of this rationalist paradigm, both practical (e.g., what if we need to include the cost of computation in our objective?) and philosophical (e.g., people's expressed preferences are often themselves incoherent)! I just don't find the argument "gambling is gross" very compelling—the world is full of gross stuff, and ignoring it doesn't make it go away.
It is interesting to note that Frank Ramsey's work, which predates that of Bruno de Finetti in laying out foundational axioms for subjective probability, is very much rooted in pragmatist philosophy. Ramsey's focus on defining probability through betting and decision-making aligns perfectly with the pragmatist philosophy, by focusing on practical consequences of probability judgments.
I think Savage's reformulation is closer to pragmatism in this sense.