Notes and Communications “A DECISION THEORY EXAMPLE IN FOOTBALL”: A COMMENT*

Janssen and Daniel analyzed the choice between a one- or a two-point conversion for a particular game situation in college football. Their decision criteria was maximum expected utility based on a von Neumann-Morgenstern utility function defined over the games outcomes. An alternative approach based on a stochastic dominance criterion is presented that does not rely on knowledge of the relative importance of tying vs. winning; rather, it relies on a notion of consistency in the sequential problem.     

A DECISION THEORY EXAMPLE IN FOOTBALL

In the 1967 Harvard-Cornell football game, Harvard was ahead 14–0 late in the game when Cornell scored two touchdowns. On both occasions, Cornell tried and failed on the two-point conversion attempt and lost the game 14–12. Postgame arguments were divided on the merits of Cornell's strategy. For this frequently occurring scenario in college football, we derive a maximum expected utility decision rule for the decision of kicking versus running/passing based on the relative utility of a win, a tie, or a loss and the probabilities of success with a kick as opposed to a run/pass.     

Reconciliation with the Utility of Chance by Elaborated Outcomes Destroys the Axiomatic Basis of Expected Utility Theory

Expected utility theory does not directly deal with the utility of chance. It has been suggested in the literature (Samuelson, 1952, Markowitz, 1959) that this can be remedied by an approach which explicitly models the emotional consequences which give rise to the utility of chance. We refer to this as the elaborated outcomes approach. It is argued that the elaborated outcomes approach destroys the possibility of deriving a representation theorem based on the usual axioms of expected utility theory. This is shown with the help of an example due to Markowitz. It turns out that the space of conceivable lotteries over elaborated outcomes is too narrow to permit the application of the axioms. Moreover it is shown that a representation theorem does not hold for the example.     

Testing Prospect Theory in a Deterministic Multiple Criteria Decision-Making Environment*

Prospect theory by Kahneman and Tversky [7] is tested in a deterministic multiple criteria decision-making context. In two experiments conducted in classroom settings subjects made pairwise preference comparisons of condominiums for sale. The results of the experiments indicate that the traditional value model did not explain the subjects' revealed preferences as well as the prospect model. We conclude that prospect theory is a reasonable model of choice for many individuals in such a context.     

Using relative utility curves to evaluate risk prediction

Summary.  Because many medical decisions are based on risk prediction models that are constructed from medical history and results of tests, the evaluation of these prediction models is important. This paper makes five contributions to this evaluation: the relative utility curve which gauges the potential for better prediction in terms of utilities, without the need for a reference level for one utility, while providing a sensitivity analysis for misspecification of utilities, the relevant region, which is the set of values of prediction performance that are consistent with the recommended treatment status in the absence of prediction, the test threshold, which is the minimum number of tests that would be traded for a true positive prediction in order for the expected utility to be non-negative, the evaluation of two-stage predictions that reduce test costs and connections between various measures of performance of prediction. An application involving the risk of cardiovascular disease is discussed.     

旅游目的地社会经济承载力的经济学分析

旅游目的地可持续发展的核心是其旅游承载力。社会经济承载力则是构成旅游承载力的重要因素。社会经济承载力决定了目的地在有关各方利益得到基本满足的前提下所能够接待外来游客的最大数量。本文运用经济学理论和数学模型,模拟了构成社会经济承载力的各要素之间达到均衡的过程。     

Modeling collecting behavior: The role of set completion

Collecting is a complex behavior that has been studied from a variety of different perspectives. Art objects, stamps, coins, and other established collectibles markets, have been shown over the years to provide some degree of return to the collector in the economics literature. Wonderment over the success of certain collectibles such as Swatch watches and Beanie Babies has received much attention in the popular press. But how does one rationally explain the collecting of matchbook covers, Cracker Jacks toys, belt buckles, salt cellars, Aunt Jemima, etc.? Collecting in the absence of financial gain has received little attention in the economics literature. In the social psychology literature, many individuals are understood to have a natural desire to collect things for various reasons. Financial gain is only one of those reasons. Set completion is another. The reasons for collecting are not always mutually exclusive. For example, a complete set may be worth more in the secondary market, if one exists, than the sum of the individual pieces. This reflects the value of the rarest pieces and the opportunity costs of obtaining them. The model presented in this study explains how set completion motivates collecting behavior, which sheds light on collecting for both financial and nonfinancial reasons. The model accommodates both collectors and noncollectors and illustrates how consumption behavior may vary accordingly. Insight into how manufacturers of collectibles can use this behavior for commercial exploitation is explored.     

Disappointment without prior expectation: a unifying perspective on decision under risk

The central idea of Disappointment theory is that an individual forms an expectation about a risky alternative, and may experience disappointment if the outcome eventually obtained falls short of the expectation. We abandon the hypothesis of a well-defined prior expectation: disappointment feelings may arise from comparing the outcome received with anyof the gamble’s outcomes that the individual failed to get. This leads to a new, general form of Disappointment model. It encompasses Rank Dependent Utility with an explicit one-parameter probability transformation, and Risk-Value models with a generic risk measure including Variance, providing a unifying behavioral foundation for these models. JEL Classification D80 . D81     

Semicontinuous Representability of Homothetic Interval Orders by Means of Two Homogeneous Functionals

It is well known that interval orders are particularly interesting in decision theory, since they are reflexive, complete and nontransitive binary relations which may be fully represented by means of two real-valued functions. In this paper, we discuss the existence of a pair of nonnegative, positively homogeneous and semicontinuous real-valued functionals representing an interval order on a real cone in a topological vector space. We recover as a particular case a result concerning the existence of a nonnegative, positively homogeneous and continuous utility functional for a complete preorder on a real cone in a topological vector space.     

On the Cycle-Transitivity of the Dice Model

We introduce the notion of a dice model as a framework for describing a class of probabilistic relations. We investigate the transitivity of the probabilistic relation generated by a dice model and prove that it is a special type of cycle-transitivity that is situated between moderate stochastic transitivity or product-transitivity on the one side, and ukasiewicz-transitivity on the other side. Finally, it is shown that any probabilistic relation with rational elements on a three-dimensional space of alternatives which possesses this particular type of cycle-transitivity, can be represented by a dice model. The same does not hold in higher dimensions.