In my previous post, I presented the core insight of Frank Ramsey’s “betting paradigm”: probabilities are based on beliefs, and beliefs, in turn, are like bets. I now want to take a “time out” from my extended review of Cheryl Misak’s beautiful biography of Ramsey to explain why this betting paradigm, i.e. Ramsey’s subjective or psychological theory of probability, is so “significant” (pun intended, for my frequentist friends).
- First and foremost, Ramsey’s betting paradigm fills a huge gap left open by standard probability theory (i.e. frequency theory), for as Misak herself correctly notes (p. 266), frequentist methods can neither “provide an account of partial belief, nor an account of how an individual should make one-off decisions.” This blind spot is so enormous and so well-known by now that I won’t belabor it here. Instead, it suffices to say that Ramsey single-handedly delivered a serious blow to frequency theory when he developed his subjective theory of probability.
- In addition, Ramsey’s betting paradigm fills another big blind spot in probability theory. Before Ramsey, the conventional wisdom so to speak was that some probabilities (especially personal probabilities) were not measureable in any rigorous way. After Ramsey, by contrast, we are now fully able to express any person’s partial beliefs, even his subjective ones, using numerical values. How? By converting one’s beliefs into betting odds. (As an added bonus, Ramsey’s intellectual framework even enables us to determine whether our subjective beliefs are rational are or not, via now-standard Dutch book arguments.)
- Thirdly, Ramsey’s betting paradigm also provides the intellectual foundations for modern prediction markets, one of the most promising and exciting “mechanism designs” or market innovations of our time! (Check out this introduction to prediction markets here, via BitEdge.) Perhaps we should rename prediction markets “Ramsey markets” in honor of Frank Ramsey. In any case, I have blogged about prediction markets many times before, so I won’t belabor this third point here.
- And last but not least, Ramsey’s subjective approach to probability can be used to improve collective decision making (via a simple method my friend and colleague Warren Smith calls “range voting”) and to improve legal adjudication as well (via a similar method I like to call “Bayesian verdicts” and “Bayesian judging”). Again, perhaps we should rename these alternative methods of voting “Ramsian voting” or “Ramsey voting” in honor of Frank Ramsey.
To sum up, I can’t overstate enough how important and exciting Ramsey’s subjective approach is. For now, however, I will conclude my review of Misak’s biography of Ramsey in my next post.