Necessary/recommended level of theory for developing statistical intuition

[R_cubed]

While your digressions into the history of physics are interesting, I again see you falling into the pattern noted above:

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I take this aversion to probability and decision theory as having the perfect be the enemy of the good, much like the nihilist who argues because there is the possibility of error, no knowledge is possible.

My question: how could betting markets conception of stats and probability be worse than what occurs in large areas of science now? Fisher [1] himself used game theoretic arguments to justify procedures he invented. Betting arguments have been critical for probability theory.

A primary researcher of this topic of information synthesis via betting markets is Robin Hanson from George Mason University. Prior to earning a doctorate in economics, his academic background includes a graduate level (M.S.) degree in physics and philosophy of science.

In discussing the design of information markets, he writes

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Information markets are institutions for accomplishing this task via trading in speculative markets, at least on topics where truth can be determined later. Relative to simple conversation, it is harder to say any one thing by market trading, and there are fewer things one can say. When people do not know whom to believe, however, the fact that a trader must put his money where his mouth is means that the things people do say in information markets can be more easily believed. Those who know little are encouraged to be quiet, and those who think they know more than they do learn this fact by losing.

Getting back to stat intuition – I’ve found nothing clarifies my thought more than considering whether a proposition or procedure is worth betting a day or a weeks pay on.

It is worthwhile for me to figure out how to derive a proof sketch based on betting type arguments among rational traders, regarding why the practices in the following thread are wrong:

Reference Collection to push back against "Common Statistical Myths"

Note: This topic is a wiki, meaning that this main body of the topic can be edited by others. Use the Reply button only to post questions or comments about material contained in the body, or to suggest new statistical myths you’d like to see someone write about. I am not claiming to be the leading authority on any or all of the things listed below, but several of us on Twitter have repeatedly floated the idea of creating a list of references that may be used to argue against some common stati…

Further Reading

1. Senn, S. (1994), Fisher’s game with the devil. Statist. Med., 13: 217-230. https://doi.org/10.1002/sim.4780130305