De Finetti characterizes the violation of coherence as an “intrinsic contradiction.” Neither the Dutch Book argument in the betting context nor its counterpart in the theory of proper scoring rules shows this except by analogy. They show that violating the laws of probability leads to objectively non-optimal decisions. My contribution aims to illustrate better de Finetti’s view that coherence is the probabilistic counterpart of logical consistency. In the context of betting, this paper will show how violating the laws of probability leads to a truly alethically impossible state. I will introduce the notion of an “indirect bet”. An indirect bet on an event E is a simultaneous finite set of bets whose payoff “simulates” a bet on E. An indirect bet is such that its payoffs are the same as a bet on E. If we define subjective probability in terms of indirect bets, it is logically impossible to violate the laws of finite probability. On the other hand, if we define subjective probability in the traditional terms of “direct” bets, the dispositions contained in a finite probability set of events that violate the laws of probability can always be “contradicted,” since they are dispositions that indirectly express a different bet quotient for at least one event. Conversely, direct and indirect bets always yield the same payoff if the bets satisfy the laws of probability.

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Coherence as Logical Consistency

  • Alberto Mura

摘要

De Finetti characterizes the violation of coherence as an “intrinsic contradiction.” Neither the Dutch Book argument in the betting context nor its counterpart in the theory of proper scoring rules shows this except by analogy. They show that violating the laws of probability leads to objectively non-optimal decisions. My contribution aims to illustrate better de Finetti’s view that coherence is the probabilistic counterpart of logical consistency. In the context of betting, this paper will show how violating the laws of probability leads to a truly alethically impossible state. I will introduce the notion of an “indirect bet”. An indirect bet on an event E is a simultaneous finite set of bets whose payoff “simulates” a bet on E. An indirect bet is such that its payoffs are the same as a bet on E. If we define subjective probability in terms of indirect bets, it is logically impossible to violate the laws of finite probability. On the other hand, if we define subjective probability in the traditional terms of “direct” bets, the dispositions contained in a finite probability set of events that violate the laws of probability can always be “contradicted,” since they are dispositions that indirectly express a different bet quotient for at least one event. Conversely, direct and indirect bets always yield the same payoff if the bets satisfy the laws of probability.