Dear Jay, Dear Serena, Dear colleagues,
On 2/19/21 12:35 PM, Serena Doria wrote:
[…] we assign 1/2 head and 1/2 cross in the toss of a fair coin. […] in the subjectivist approach such assignment can be interpreted as that of a person betting on the given event in a coherent bet. […]
On vrijdag 19 februari 2021 19:06:09 CET, Jay Kadane wrote:
I think that our assignment of probabilities to the outcome offlipping a fair coin stem from the definition of "fair", and hence are neither subjective or frequentistic.
Fair to whom?
The notion of ‘fairness’ of a coin seems to me to have its origins in a betting context. And as Serena mentions, the betting setup is central in the subjectivist approach. The core elicitation question in that approach could be formulated as follows: “Which of these bets are acceptable to you?”. (In this question, I see ‘you’ as the ‘subject’ in ‘subjective’.)
I would call a coin fair to the subject if any exchange of a bet and its counterpart with heads and tails switched is acceptable [*]. So I think that the notion of ‘fairness’ itself can be defined as a subjective assessment property.
N.B.: To arrive at (subjective) probability ½, on top of fairness, the subject would need to avoid sure loss. (Cf. coherence mentioned by Serena.)
Best,
Erik
[*] Cf. ‘model of symmetry’ in De Cooman & Miranda's “Symmetry of models versus models of symmetry”