# Dutch Book Arguments

> 【EN】The Dutch Book argument (DBA) for probabilism (namely the view that an agent’s degrees of belief should satisfy the axioms of probability) traces to Ramsey’s work in “Truth and Probability”. He mentioned only in passing that an agent who violates the probability axioms would be vulnerable to having a book made against him and this has led to considerable debate and confusion both about exactly what Ramsey intended to show and about if, and how, a cogent version of the argument can be given. The basic idea behind the argument has also been applied in defense of a variety of principles, some of which place additional constraints on an agent’s current beliefs, with others, such as Conditionalization, purporting to govern how degrees of belief should evolve over time. 【中】该论证可追溯到拉姆齐在《真理与概率》中顺带提到的一句话，正因为它只是一笔带过，围绕拉姆齐究竟想证明什么、以及能否给出一个可靠的版本，引发了长期的争论与混乱。词条给出详细版本、逆荷兰书定理、违反概率公理是否可能理性、去实用化的论证、可数可加性的荷兰书论证，以及涉及条件化与杰弗里条件化的历时版本。

- ID: m13195
- Category: decide
- Domain: 决策科学

## Definition

荷兰书论证是支持概率主义的一种论证：如果一个人的信念度不满足概率公理，就能构造出一组赌局——一本“荷兰书”——使他在每一种可能情形下都必然亏钱，因此违反概率公理在实践上是不融贯的。 脚手架作用：- 信念体检：检查置信度是否满足概率公理，剔除矛盾判断。 - 赔率换算：把模糊把握度换成可接受赔率，使强度可比较。 - 校准修正：发现一组判断必亏时，调低过高的概率赋值。

## How it works

把信念度与愿意接受的赔率对应起来，信念度一旦不满足概率公理，各赌注的价格组合在算术上就不一致：对手可以组合出一组赌局，使你无论结果如何净收益都为负。也就是说，缺陷不在输赢运气，而在你的估价体系本身给了别人套利空间。

## Practice

1) 把你对若干命题的信心转成愿意接受的赔率；2) 检查这些赔率是否满足概率公理；3) 找出不一致的地方，看它是否会导致必输的组合；4) 反过来用概率约束修正信念度，使整套估价融贯。

## Use

- 信念体检：检查置信度是否满足概率公理，剔除矛盾判断。 - 赔率换算：把模糊把握度换成可接受赔率，使强度可比较。 - 校准修正：发现一组判断必亏时，调低过高的概率赋值。

[Read the web page](https://thinkingmodels.site/en/entries/detail/m13195)