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1.
This paper introduces the likelihood method for decision under uncertainty. The method allows the quantitative determination
of subjective beliefs or decision weights without invoking additional separability conditions, and generalizes the Savage–de
Finetti betting method. It is applied to a number of popular models for decision under uncertainty. In each case, preference
foundations result from the requirement that no inconsistencies are to be revealed by the version of the likelihood method
appropriate for the model considered. A unified treatment of subjective decision weights results for most of the decision
models popular today. Savage’s derivation of subjective expected utility can now be generalized and simplified. In addition
to the intuitive and empirical contributions of the likelihood method, we provide a number of technical contributions: We
generalize Savage’s nonatomiticy condition (“P6”) and his assumption of (sigma) algebras of events, while fully maintaining
his flexibility regarding the outcome set. Derivations of Choquet expected utility and probabilistic sophistication are generalized
and simplified similarly. The likelihood method also reveals a common intuition underlying many other conditions for uncertainty,
such as definitions of ambiguity aversion and pessimism. 相似文献
2.
3.
Jörg Stoye 《Theory and Decision》2011,70(2):129-148
This article provides unified axiomatic foundations for the most common optimality criteria in statistical decision theory.
It considers a decision maker who faces a number of possible models of the world (possibly corresponding to true parameter
values). Every model generates objective probabilities, and von Neumann–Morgenstern expected utility applies where these obtain,
but no probabilities of models are given. This is the classic problem captured by Wald’s (Statistical decision functions,
1950) device of risk functions. In an Anscombe–Aumann environment, I characterize Bayesianism (as a backdrop), the statistical
minimax principle, the Hurwicz criterion, minimax regret, and the “Pareto” preference ordering that rationalizes admissibility.
Two interesting findings are that c-independence is not crucial in characterizing the minimax principle and that the axiom
which picks minimax regret over maximin utility is von Neumann–Morgenstern independence. 相似文献
4.
In this article, we model FPTP systems as social preference rules and give two characterizations. We show that a social preference
rule is an FPTP system if, and only if, it satisfies the axioms of subset consistency, district consistency, subset cancellation,
and district cancellation. The second characterization consists of the axioms of subset consistency, subset anonymity, neutrality,
topsonlyness, Pareto optimality, district consistency and district cancellation. The characterizations give us an opportunity
to compare the characteristic properties of FPTP systems to the characteristic properties that we found for list systems of
proportional representation (list PR systems) in Hout et al. (Social Choice and Welfare, 27:459–475, 2006), where we modelled
those systems also as social preference rules. We find that consistency and anonymity distinguish list PR systems from FPTP
systems. On the other hand, it is district cancellation that distinguishes FPTP systems from list PR systems. 相似文献
5.
This article obtains demand functions for risky assets without making a priori assumptions about the form of the utility function. In a simple portfolio model, the envelope theorem is applied to the indirect expected utility function to derive estimating equations. Tests for the existence of constant absolute or constant relative risk aversion are also developed. Empirical estimation of the demand for financial assets held by U.S. households for the period 1946–1985 indicates that aggregate household behavior is consistent with the existence of constant relative risk aversion, with the coefficient of risk aversion having a value of approximately 1.3.The authors gratefully acknowledge helpful comments from the editor and an anonymous referee. 相似文献
6.
This article revisits the standard results of demand theory when the preference relation is a continuous preorder that admits
an equicontinuous multi-utility representation. We study the consumer problem as the constrained maximization of a continuous
vector-valued utility mapping, and show how to rederive those results. In particular, we provide a link between the literature
on vector optimization and the analysis of the consumer problem under incomplete preferences. 相似文献
7.
Utility Functions for Wealth 总被引:1,自引:0,他引:1
We specify all utility functions on wealth implied by four special conditions on preferences between risky prospects in four theories of utility, under the presumption that preference increases in wealth. The theories are von Neumann-Morgenstern expected utility (EU), rank dependent utility (RDU), weighted linear utility (WLU), and skew-symmetric bilinear utility (SSBU). The special conditions are a weak version of risk neutrality, Pfanzagl's consistency axiom, Bell's one-switch condition, and a contextual uncertainty condition. Previous research has identified the functional forms for utility of wealth for all four conditions under EU, and for risk neutrality and Pfanzagl's consistency axiom under WLU and SSBU. The functional forms for the other condition-theory combinations are derived in this paper. 相似文献
8.
Mikhail V. Sokolov 《Theory and Decision》2011,70(3):255-282
Luce and Narens (Journal of Mathematical Psychology, 29:1–72, 1985) showed that rank-dependent utility (RDU) is the most general interval scale utility model for binary lotteries. It can be
easily established that this result cannot be generalized to lotteries with more than two outcomes. This article suggests
several additional conditions to ensure RDU as the only utility model with the desired property of interval scalability in
the general case. The related axiomatizations of some special cases of RDU of independent interest (the quantile utility,
expected utility, and Yaari’s dual expected utility) are also given. 相似文献
9.
We use reference-dependent expected utility theory to develop a model of status quo effects in consumer choice. We hypothesise
that, when making their decisions, individuals are uncertain about the utility that will be yielded by their consumption experiences
in different ‘taste states’ of the world. If individuals have asymmetric attitudes to gains and losses of utility, the model
entails acyclic reference-dependent preferences over consumption bundles. The model explains why status quo effects may vary
substantially from one decision context to another and why some such effects may decay as individuals gain market experience. 相似文献
10.
What are the minimal requirements of rational choice? Arguments from the sequential-decision setting
Katie Siobhan Steele 《Theory and Decision》2010,68(4):463-487
There are at least two plausible generalisations of subjective expected utility (SEU) theory: cumulative prospect theory (which
relaxes the independence axiom) and Levi’s decision theory (which relaxes at least ordering). These theories call for a re-assessment
of the minimal requirements of rational choice. Here, I consider how an analysis of sequential decision making contributes
to this assessment. I criticise Hammond’s (Economica 44(176):337–350, 1977; Econ Philos 4:292–297, 1988a; Risk, decision and
rationality, 1988b; Theory Decis 25:25–78, 1988c) ‘consequentialist’ argument for the SEU preference axioms, but go on to
formulate a related diachronic-Dutch-book-style’ argument that better achieves Hammond’s aims. Some deny the importance of
Dutch-book sure losses, however, in which case, Seidenfeld’s (Econ Philos 4:267–290, 1988a) argument that distinguishes between
theories that relax independence and those that relax ordering is relevant. I unravel Seidenfeld’s argument in light of the
various criticisms of it and show that the crux of the argument is somewhat different and much more persuasive than what others
have taken it to be; the critical issue is the modelling of future choices between ‘indifferent’ decision-tree branches in
the sequential setting. Finally, I consider how Seidenfeld’s conclusions might nonetheless be resisted. 相似文献
11.
It is increasingly recognized that decision making under uncertainty depends not only on probabilities, but also on psychological
factors such as ambiguity and familiarity. Using 325 Beijing subjects, we conduct a neurogenetic study of ambiguity aversion
and familiarity bias in an incentivized laboratory setting. For ambiguity aversion, 49.4% of the subjects choose to bet on
the 50–50 deck despite the unknown deck paying 20% more. For familiarity bias, 39.6% choose the bet on Beijing’s temperature
rather than the corresponding bet with Tokyo even though the latter pays 20% more. We genotype subjects for anxiety-related
candidate genes and find a serotonin transporter polymorphism being associated with familiarity bias, but not ambiguity aversion,
while the dopamine D5 receptor gene and estrogen receptor beta gene are associated with ambiguity aversion only among female
subjects. Our findings contribute to understanding of decision making under uncertainty beyond revealed preference. 相似文献
12.
13.
Ilia Tsetlin 《Theory and Decision》2006,61(1):51-62
Designing a mechanism that provides a direct incentive for an individual to report her utility function over several alternatives
is a difficult task. A framework for such mechanism design is the following: an individual (a decision maker) is faced with
an optimization problem (e.g., maximization of expected utility), and a mechanism designer observes the decision maker’s action.
The mechanism does reveal the individual’s utility truthfully if the mechanism designer, having observed the decision maker’s
action, infers the decision maker’s utilities over several alternatives. This paper studies an example of such a mechanism
and discusses its application to the problem of optimal social choice. Under certain simplifying assumptions about individuals’
utility functions and about how voters choose their voting strategies, this mechanism selects the alternative that maximizes
Harsanyi’s social utility function and is Pareto-efficient. 相似文献
14.
Alexander Zimper 《Theory and Decision》2007,63(1):53-78
This paper examines the existence of strategic solutions to finite normal form games under the assumption that strategy choices
can be described as choices among lotteries where players have security- and potential level preferences over lotteries (e.g., Cohen, Theory and Decision, 33, 101–104, 1992, Gilboa, Journal of Mathematical Psychology, 32, 405–420,
1988, Jaffray, Theory and Decision, 24, 169–200, 1988). Since security- and potential level preferences require discontinuous
utility representations, standard existence results for Nash equilibria in mixed strategies (Nash, Proceedings of the National Academy of Sciences, 36, 48–49, 1950a, Non-Cooperative Games, Ph.D. Dissertation, Princeton
University Press, 1950b) or for equilibria in beliefs (Crawford, Journal of Economic Theory, 50, 127–154, 1990) do not apply. As a key insight this paper proves that non-existence
of equilibria in beliefs, and therefore non-existence of Nash equilibria in mixed strategies, is possible in finite games
with security- and potential level players. But, as this paper also shows, rationalizable strategies (Bernheim, Econometrica, 52, 1007–1028, 1984, Moulin, Mathematical Social Sciences, 7, 83–102, 1984, Pearce, Econometrica,
52, 1029–1050, 1984) exist for such games. Rationalizability rather than equilibrium in beliefs therefore appears to be a
more favorable solution concept for games with security- and potential level players.
相似文献
15.
Jan Heufer 《Theory and Decision》2011,71(4):575-592
This article explores rationalizability issues for finite sets of observations of stochastic choice in the framework introduced
by Bandyopadhyay et al. (Journal of Economic Theory, 84(1), 95–110, 1999). It is argued that a useful approach is to consider indirect preferences on budgets instead of direct preferences on commodity
bundles. A new rationalizability condition for stochastic choices, “rationalizable in terms of stochastic orderings on the
normalized price space” (rsop), is defined. rsop is satisfied if and only if there exists a solution to a linear feasibility problem. The existence of a solution also implies
rationalizability in terms of stochastic orderings on the commodity space. Furthermore it is shown that the problem of finding
sufficiency conditions for binary choice probabilities to be rationalizable bears similarities to the problem considered here. 相似文献
16.
Patrick Roger 《Theory and Decision》2011,70(1):27-44
In a recent article entitled “Putting Risk in its Proper Place,” Eeckhoudt and Schlesinger (2006) established a theorem linking
the sign of the n-th derivative of an agent’s utility function to her preferences among pairs of simple lotteries. We characterize these lotteries
and show that, in a given pair, they only differ by their moments of order greater than or equal to n. When the n-th derivative of the utility function is positive (negative) and n is odd (even), the agent prefers a lottery with higher (lower) n + 2p-th moments for p belonging to the set of positive integers. This result links the preference for disaggregation of risks across states of
nature to the complete structure of moments preferred by mixed risk averse agents. It can be viewed as a generalization of
a proposition appearing in Ekern (1980) which focused only on the differences in the n-th moments. 相似文献
17.
Greg B. Davies 《Theory and Decision》2006,61(2):159-190
There exists no completely satisfactory theory of risk attitude in current normative decision theories. Existing notions confound
attitudes to pure risk with unrelated psychological factors such as strength of preference for certain outcomes, and probability
weighting. In addition traditional measures of risk attitude frequently cannot be applied to non-numerical consequences, and
are not psychologically intuitive. I develop Pure Risk theory which resolves these problems – it is consistent with existing
normative theories, and both internalises and generalises the intuitive notion of risk being related to the probability of
not achieving one’s aspirations. Existing models which ignore pure risk attitudes may be misspecified, and effects hitherto
modelled as loss aversion or utility curvature may be due instead to Pure Risk attitudes. 相似文献
18.
Hagen Lindstädt 《Theory and Decision》2007,62(4):335-353
Sometimes we believe that others receive harmful information. However, Marschak’s value of information framework always assigns
non-negative value under expected utility: it starts from the decision maker’s beliefs – and one can never anticipate information’s
harmfulness for oneself. The impact of decision makers’ capabilities to process information and of their expectations remains
hidden behind the individual and subjective perspective Marschak’s framework assumes. By introducing a second decision maker
as a point of reference, this paper introduces a way for evaluating others’ information from a cross-individual, imperfect
expectations perspective for agents maximising expected utility. We define the cross-value of information that can become negative – then the information is “harmful” from a cross-individual perspective – and we define (mutual) cost of limited information processing capabilities and imperfect expectations as an opportunity cost from this same point of reference. The simple relationship between these two expected utility-based
concepts and Marschak’s framework is shown, and we discuss evaluating short-term reactions of stock market prices to new information
as an important domain of valuing others’ information.
相似文献
19.
An extensive literature overlapping economics, statistical decision theory and finance, contrasts expected utility [EU] with
the more recent framework of mean–variance (MV). A basic proposition is that MV follows from EU under the assumption of quadratic
utility. A less recognized proposition, first raised by Markowitz, is that MV is fully justified under EU, if and only if
utility is quadratic. The existing proof of this proposition relies on an assumption from EU, described here as “Buridan’s
axiom” after the French philosopher’s fable of the ass that starved out of indifference between two bales of hay. To satisfy
this axiom, MV must represent not only “pure” strategies, but also their probability mixtures, as points in the (σ, μ) plane. Markowitz and others have argued that probability mixtures are represented sufficiently by (σ, μ) only under quadratic utility, and hence that MV, interpreted as a mathematical re-expression of EU, implies quadratic utility.
We prove a stronger form of this theorem, not involving or contradicting Buridan’s axiom, nor any more fundamental axiom of
utility theory. 相似文献
20.
Stephen A. Clark 《Theory and Decision》1993,34(1):21-45
We study a Linear Axiom of Revealed Preference (LARP) that characterizes the consistency of a choice function with respect to a preference order satisfying the independence axiom. In addition, LARP characterizes lexicographic linear utility rationality when the choice space is a convex subset of a finite-dimensional real vector space, and LARP characterizes linear utility rationality when the choice space corresponds to a finite choice experiment. 相似文献