 It need not be irrational for Sophia to be willing to bet you $5.5 to $4.5 that tomorrow it will be sunny in Vienna, but not be willing to bet you $550 to $450 that this proposition is true. She may even refuse a bet of $200 to $999. That is because there are other factors affecting her betting quotients than her degrees of belief. Sophia may be risk-averse, e.g. if she cannot risk blowing a $200 dollar hole in her monthly budget. Others may be risk-prone. For example, gamblers in the casino are risk prone: they pay more for playing roulette than the fair monetary value according to reasonable subjective probabilities. That may be perfectly rational if the thrill of gambling is itself a compensation. Note that it does not help to say that Sophia’s fair betting ratio for \(A\) is that number \(r = b/(a + b)\) such that she considers the following bet to be fair: $\(1 - r = a/(a + b)\) if \(A\), and \(\$ -r = -b/(a + b)\) otherwise \((a, b \ge 0\) with inequality for at least one). Just as stakes of $200 may be too high for the measurement to work, stakes of $1 may be too low.