Dutch Bookies and Money Pumps
Dutch Bookies and Money Pumps
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荷兰博彩公司和资金泵
DOI：
10.2307/2026054
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
F. Schick
中科院分区：
文献类型：
--
作者：
F. Schick
哲学中常见的争论是罕见的，所以我们发现任何这样的争论都是我们珍视的。如果它不仅是决定性的，而且是明智的，那就更好了。荷兰书中关于概率论的论点似乎填补了这一空白。它们背后的想法最早是由弗兰克·拉姆塞尔和布鲁诺·德菲内蒂提出的。1955年，它在三份独立的文件中得到了充分的发展。这些论点为我们提供了一些值得拥有的东西；它们为整个理论提供了一个理论基础。它们现在已经成为文学中固定的一部分。我想证明他们都失败了。他们做这项工作似乎只是因为他们都认为理所当然的一个假设，而这个假设往往是错误的。在这个假设被抛弃的地方，论点就不再起作用。在支持一些基本的偏好原则时，也提出了非常类似的论点，但这些论点也失败了，而且是以同样的方式。教训并不是我们的概率理论和偏好理论遇到了什么麻烦，而是它们并不像人们认为的那样容易证明是正确的。一本荷兰书的论点有这样的形式。有几种可能的押注--假设有三种。假设我愿意为第一个支付x，为第二个支付y，为第三个支付z。我愿意支付的这些价格的总和是x-ty-y-tz，但有争议的赌注是这样的：无论发生什么，如果我把所有的赌注都放在这些价格上，我赢的钱会少于这个数字。因此，我可能会被任何把这三笔赌注一起卖给我的博彩公司骗到。让我陷入困境的是我设定的概率，因为正是这些概率(以及赌注)决定了我将支付什么。因此，我的概率是共同不正确的：它们可以说是不连贯的。
C ONCLUSIVE arguments in philosophy are rare, so any such argument we find we prize. If it is not only conclusive but clever, all the better for it. The Dutch book arguments of the theory of probability seem to fill the bill. The idea behind them was first presented by Frank Ramseyl and by Bruno deFinetti.' It was fully developed in three independent papers in 1955.' The arguments offer us something worth having; they offer a rationale for the whole theory. They have now become a settled part of the literature. I want to show that they all fail. They seem to do the job only because of an assumption they all take for granted, an assumption that may often be false. Where this assumption is dropped, the arguments no longer work. Very similar arguments have been offered in support of some basic principles of preference, and these fail too, and in the same way. The moral is not that our theories of probability and of preference are in any trouble, but only that they are not as easy to justify as is believed. I A Dutch book argument has this form. There are several possible bets-say that there are three. Suppose I am willing to pay x for the first, y for the second, and z for the third. The sum of these prices I am willing to pay is x-t y-t z, but the bets at issue are such that, come what may, I will win less than this sum if I place all the bets at these prices. I can therefore be made a sap of by any bookie who sells me the three bets together. What puts me in this fix are the probabilities that I set, for it is these (along with the stakes) that determine what I will pay. My probabilities are thus jointly improper: they can be said to be incoherent.