Why is it possible to calibrate your subjective probabilities?
Empirically yes, it seems confidence has a positive correlation with correctness. One reference is Bordalo et al. 2018 Beliefs about gender, see Fig.1 for example. The actual probability of a correct answer is different from own or other people's estimate of the probability of a correct answer, but if the estimated probability is higher, then the actual probability is higher. 

As to the axioms or theoretical assumptions - you can just assume that people's estimates of their correctness are increasing in the correctness. Or assume Bayesian updating about own correctness, in which case past correct guesses would increase the guesser's confidence in own correctness. The number of past correct guesses in turn is positively correlated with the guesser's actual correctness (by the Law of large numbers).