So... I wrote this. Maybe I can clarify a little what I meant by the statement "Since Silver’s forecasts begin with probability models, it’s safe to assume they obey all the rules, including Bayes’, and would be arbitrage-free.", since this seems to be confusing some people: What I'm addressing here is Taleb's claim that Silver's probabilities would allow for arbitrage (i.e., riskless profit, not just profit on avera…
t=0: P(heads) = 0.75, P(tails) = 0.25
t=1: P(heads) = 0.60, P(tails) = 0.40
These are consistent (or behave as probabilities or what have you) at each time (separately), so de Finetti's argument covers each (separately). Does this alone somehow protect from arbitrage over time? Or is the martingale stuff in the next paragraph, though postured as only a technical rephrasing, essential? Unsure since that part's over my head.The above's enough to pose the question, but continuing for concreteness: if a buyer can determine any "significant" pattern in my assessments over time--for instance maybe my past assessments have been routinely seen to tend to a uniform distribution over time--aren't I still vulnerable to arbitrage, or else what's protecting me?