Pub Date : 2019-07-29DOI: 10.4324/9781315496290-20
J. Blatt
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Pub Date : 1979-12-01DOI: 10.1080/01603477.1980.11489205
T. Brennan, J. Blatt
1. I thank the editors for permitting me to reply to criticisms of my views (Blatt 1979-80 and 1980). Ulph (1981-82) shows, in his Figure 1, that a von Neumann individual may accept the gamble for small probability p of disaster and reject it for large p; yet this man has an unbounded utility of money. However, Ulph's man exhibits some highly peculiar preferences. Suppose the money gain M becomes very large. In his Figure 1 the point labeled V(Wo + M, 0) moves ever higher on the vertical axis, hence the critical probability p* (below which the gamble is accepted) moves ever closer to unity on the horizontal axis. Thus, by merely promising him enough money M upon success, Ulph's man can be induced to accept the gamble, no matter how poor his chances of escaping the gallows! While some criminals may be so utterly foolhardy, not all rational people act that way; this is all that is needed to refute the objection. 2. Let me make this argument more formal. Define a "greedy but cautious criminal," abbreviated GCC henceforth, by the three properties: (1) His utility of money u(M) is unbounded (Blatt, 1980); (2) There exists a maximum probability Pma Pmax, no matter how big the money sum M; (3) He accepts the gamble for small enough, but nonzero, p. THEOREM: The preference scale of a GCC is inconsistent with expected utility theory. PROOF: Expected utility is E(U) = (1 p) u(M) + pu(G). Let
1. 我感谢编辑们允许我回复对我观点的批评(Blatt 1979- 1980和1980)。Ulph(1981-82)在他的图1中表明，冯·诺伊曼个体可能在发生灾难的概率p较小时接受赌博，而在p较大时拒绝赌博;然而，这个人拥有无限的金钱效用。然而，乌尔夫的男人表现出一些非常特殊的偏好。假设货币收益M变得非常大。在他的图1中，标记为V(Wo + M, 0)的点在垂直轴上移动得越来越高，因此临界概率p*(低于此值可接受赌博)在水平轴上移动得越来越接近统一。因此，只要向他保证在成功后给他足够的钱，就可以诱使他接受这场赌博，不管他逃脱绞刑架的机会有多渺茫!虽然有些罪犯可能是如此蛮干，但并非所有理性的人都是这样做的;这就是反驳反对意见所需要的全部内容。2. 让我让这个论证更正式一些。定义一个“贪婪但谨慎的罪犯”(以下简称GCC)的三个性质:(1)他对金钱的效用u(M)是无限大的(Blatt, 1980);(2)无论金额M多大，都存在一个最大概率Pma Pmax;(3)他接受足够小但不为零的p的赌博。定理:GCC的偏好尺度与期望效用理论不一致。证明:期望效用是E(U) = (1p) U (M) + pu(G)。让
{"title":"The utility of being hanged on the gallows","authors":"T. Brennan, J. Blatt","doi":"10.1080/01603477.1980.11489205","DOIUrl":"https://doi.org/10.1080/01603477.1980.11489205","url":null,"abstract":"1. I thank the editors for permitting me to reply to criticisms of my views (Blatt 1979-80 and 1980). Ulph (1981-82) shows, in his Figure 1, that a von Neumann individual may accept the gamble for small probability p of disaster and reject it for large p; yet this man has an unbounded utility of money. However, Ulph's man exhibits some highly peculiar preferences. Suppose the money gain M becomes very large. In his Figure 1 the point labeled V(Wo + M, 0) moves ever higher on the vertical axis, hence the critical probability p* (below which the gamble is accepted) moves ever closer to unity on the horizontal axis. Thus, by merely promising him enough money M upon success, Ulph's man can be induced to accept the gamble, no matter how poor his chances of escaping the gallows! While some criminals may be so utterly foolhardy, not all rational people act that way; this is all that is needed to refute the objection. 2. Let me make this argument more formal. Define a \"greedy but cautious criminal,\" abbreviated GCC henceforth, by the three properties: (1) His utility of money u(M) is unbounded (Blatt, 1980); (2) There exists a maximum probability Pma Pmax, no matter how big the money sum M; (3) He accepts the gamble for small enough, but nonzero, p. THEOREM: The preference scale of a GCC is inconsistent with expected utility theory. PROOF: Expected utility is E(U) = (1 p) u(M) + pu(G). Let","PeriodicalId":318945,"journal":{"name":"Dynamic Economic Systems","volume":"37 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1979-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117279023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
* Evaluation of future cash flows under conditions of certainty is well known; it leads to the "discounted present value" method. This paper shows that maximization of expected utility is a very restrictive method of expressing one's attitude to risk. Most businessmen would judge it unreasonable once it is explained to them what this method really implies. By using a preference ordering, which is not equivalent to any utility function, and by focusing attention on the possibility of unpredictable "disasters" in the future, we develop a new method of investment evaluation. Qualitatively, the new approach turns out to be very similar to the one used by businessmen, and not at all similar to discounted present value. We give an example of two projects, A and B, where A is preferred to B by the discounted present value method at all values of the discount rate, but A is inferior to B by the new evaluation. The discussion in the body of this paper is literary. All the mathematics is contained in appendices and can be skipped by the non-mathematical reader. Introduction and Notation
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