A geometric approach to revealed preference via Hamiltonian cycles

It is shown that a fundamental question of revealed preference theory, namely whether the weak axiom of revealed preference (WARP) implies the strong axiom of revealed preference (SARP), can be reduced to a Hamiltonian cycle problem: A set of bundles allows a preference cycle of irreducible length if and only if the convex monotonic hull of these bundles admits a Hamiltonian cycle. This leads to a new proof to show that preference cycles can be of arbitrary length for more than two but not for two commodities. For this, it is shown that a set of bundles satisfying the given condition exists if and only if the dimension of the commodity space is at least three. Preference cycles can be constructed by embedding a cyclic $(L-1)$ -polytope into a facet of a convex monotonic hull in $L$ -space, because cyclic polytopes always admit Hamiltonian cycles. An immediate corollary is that WARP only implies SARP for two commodities. The proof is intuitively appealing as this gives a geometric interpretation of preference cycles.     

Indecisiveness aversion and preference for commitment

We present an axiomatic model of preferences over menus that is motivated by three assumptions. First, the decision maker is uncertain ex ante (i.e., at the time of choosing a menu) about her ex post (i.e., at the time of choosing an option within her chosen menu) preferences over options, and she anticipates that this subjective uncertainty will not resolve before the ex post stage. Second, she is averse to ex post indecisiveness (i.e., to having to choose between options that she cannot rank with certainty). Third, when evaluating a menu she discards options that are dominated (i.e., inferior to another option whatever her ex post preferences may be) and restricts attention to the undominated ones. Under these assumptions, the decision maker has a preference for commitment in the sense of preferring menus with fewer undominated alternatives. We derive a representation in which the decision maker’s uncertainty about her ex post preferences is captured by means of a subjective state space, which in turn determines which options are undominated in a given menu, and in which the decision maker fears, whenever indecisive, to choose an option that will turn out to be the worst (undominated) one according to the realization of her ex post preferences.     

The conflict between naive and sophisticated choice as a form of the ‘liberal paradox’

Pareto-inefficient perfect equilibria can be represented by the liberal paradox approach of Sen, appropriately reconfigured to model intertemporal decision-making by an individual. We show that the preference profile used by Grout (1982) to construct a case in which naive choice Pareto-dominates sophisticated choice can be so represented, if tastes change and if the individual can make decisions at time t, which restrict or determine opportunities available in period t + 1 and beyond. This ability to make a decision that binds oneself in the future is a form of rights assignment. We also show how two resolutions of the liberal paradox work out in the individual decision framework.     

商品社会使用价值与市场价格规律论

现代经济理论的两大体系 ,都对价格的有关理论做出了说明。有一种说法 ,把马克思主义经济学的劳动价值论与当代西方主流经济学派的供求论综合起来 ,就应当可以得到较为完美的价格理论。但这是不可能的。解决问题的出路 ,只能是按马克思主义经济学的内在逻辑 ,深入研究商品的使用价值 ,通过商品价值和使用价值对商品价格做出完整的说明 ,同时破解在供求与价值决定上的相互循环论证 ,发展以劳动价值为基础的价格理论。商品的使用价值 ,具有自然使用价值和社会使用价值两重属性。商品的社会使用价值深刻地反映着商品交换的经济关系 ,由自然使用价值等一系列因素决定。商品社会使用价值 ,在量上最终表现为某一商品的社会需求量与生产供给量的比率 ,在不同的条件下具有不同的值。商品的市场价格 ,由商品价值或其转化形式与商品社会使用价值共同决定。社会使用价值比价值或其转化形式更复杂、更多样、更易变 ,是市场价格变化的主导因素。社会使用价值为 1的市场价格 ,即是市场均衡价格。所谓市场价格围绕商品价值或其转化形式上下波动 ,实质上应是围绕市场均衡价格上下波动。调节市场供求关系的根本因素 ,表面上看是商品价格 ,而实质上是市场供求的相互作用。     

A revealed preference analysis of solutions to simple allocation problems

We interpret solution rules on a class of simple allocation problems as data on the choices of a policy maker. We analyze conditions under which the policy maker’s choices are (i) rational (ii) transitive-rational, and (iii) representable; that is, they coincide with maximization of a (i) binary relation, (ii) transitive binary relation, and (iii) numerical function on the allocation space. Our main results are as follows: (i) a well-known property, contraction independence (a.k.a. IIA) is equivalent to rationality; (ii) every contraction independent and other-c monotonic rule is transitive-rational; and (iii) every contraction independent and other-c monotonic rule, if additionally continuous, can be represented by a numerical function.     

Strategy-proofness,tops-only,and the uniform rule

In the division problem with single-peaked preferences, an allocation rule is strategy-proof for same tops if no one can gain by reporting a false preference relation having the true peak. This new condition is so weak that it is implied by strategy-proofness and tops-only. We show that the uniform rule is the only rule satisfying this mild property under efficiency and envy-freeness. We then analyze how largely the preference domain can be extended with admitting a rule satisfying the three axioms, and show that the single-plateaued domain is the unique such maximal domain.     

Stochastic revealed preference and rationalizability

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.     

文化商品的特殊性与文化的经济化趋势

文化商品是指文化产品消费者在交换过程中所得到的文化精神产品的文化娱乐服务的总和.文化商品具有双重属性,同时又具有其特殊性.文化商品的双重属性表现在它具有商品属性和社会意识形态性,文化商品的三个特殊性是指文化商品消费的永恒性、文化商品的复杂性和创新性.文化商品作为一种特殊商品进入文化市场必然要同时发挥其社会效益和经济效益,文化必然要表现经济化趋势.     

Tasting off-flavors: food science,sensory knowledge and the consumer sensorium

Abstract

In food science and technology, understanding off-flavors has a significance with both technical and commercial implications. In the food industry in the United States, it is a widely held truism that consumers will not buy a product if they do not like the way it tastes or if it contains unpleasant flavors. But how can science determine when food is off putting, and how do scientists learn to address bad tastes in their experimental and technical practice? Based on ethnographic work with food scientists in the United States, this paper is a reflexive account of learning to taste off-flavors, a form of sensory learning that utilizes the scientist’s own body as a kind of instrument. The paper argues that a particular understanding of the consumer sensorium emerges through food scientists’ approach to off-flavors. This is an image of the consumer as a chemically receptive sensory system that is highly sensitive to compounds at trace levels. By utilizing the sensitivity of their own senses, food scientists exploit the relationship between distaste, memory and sensory perception as a form of training to produce future aesthetic memories of off-flavors that can be deployed in a technical context.     

Ordering tasting in a restaurant: experiencing,socializing, and processing food

Sometimes there are moments in which German speakers will state that something schmeckt gut [tastes good]. Focusing on a family celebration in a restaurant in Austria, the paper considers how in three schmeckt gut moments, participants variously order “tasting” as a process of experiencing, socializing, and processing. It is argued that while it is possible to analyse how a person simultaneously experiences sensual qualities inherent in a particular dish, socializes with others, and processes food, these aspects are not equally relevant for the people involved in the “tasting”. Different modes of ordering “tasting” can exist next to each other such that a “tasting together in difference” takes place. Following from this, this article calls for further investigation into the practical achievement of “tasting together in difference” and the enabling role of care in this process. By shedding light on how tasting is done in practices of dining out in Western Europe, it contributes to a growing set of ethnomethodologically oriented studies on how tasting and taste are done in practice.     

Ratio-Scale Measurement with Intransitivity or Incompleteness: The Homogeneous Case

In the homogeneous case of one-dimensional objects, we show that any relation that is positive and homothetic can be represented by a ratio-scale and a unique and constant biasing factor. This factor may favor or disfavor the preference for an object over another. In the first case, preferences are complete but not transitive and an object may be preferred even when its value is lower. In the second case, preferences are asymmetric and transitive but not negatively transitive and it may not be sufficient for an object to have a greater value to be preferred. In this manner, the biasing factor reflects the extent to which preferences may depart from a maximization process.     

An axiomatic system for multidimensional preferences

An axiomatic system TP is developed which allows the amalgamation of linear preferences (preferences in respect to different criteria) according to the weights of those criteria. Section 1 deals with linear preferences. In Section 2 an axiomatic system for the ordering of classes of criteria is formulated. Section 3 explains the development of system TP. Two TP-systems are distinguished, based on two different linear preference systems. The preference relation of TP is shown to be nontransitive, while the linear preference relation is transitive. In 3.7 an alternative-system TP′ is given. Section 3.8 deals with formulas concerning the disjunction of alternatives, which are not valid in TP, even though they are valid in a linear preference system. In Section 4 types of preference relations and types of alternatives are distinguished to get the opportunity to express preferences between preferences.     

Complementary relations in the theory of preference

(1) This paper uses the following binary relations: > (is preferred to); ⩽ (is not preferred to); < (is less preferred than); ~ (is indifferent to). (2) Savage used primitive ⩾, postulated to be connected and transitive onA (the set of acts), to define the others: [x ~ y ⇔ (x ⩽ y and y ⩽ x)]; [y < x ⇔ notx ⩽ y]; [x > y ⇔ y < x]. Independently of the axioms, this definition implies that ⩽ and > are complementary relations onA: [x < y ⇔ notx > y]. (3) Pratt, Raiffa and Schlaifer used primitive ⩽, postulated to be transitive onL (the set of lotteries), to define the others with a different expression for <: [x < y ⇔ (x ⩽ y and noty ⩽ x)]. Thus, ⩽ and > are not necessarily complementary onL; since ⩽ is not postulated to be connected onL, but connected ⩽ is necessary and sufficient for such complementarity. Since the restriction of ⩽ to the subsetA ofL is connected, ⩽ and > are complementary onA. (4) Fishburn used primitive < onA to define the others with different expression for ~ and ⩽: [x ~ y ⇔ (notx < y and noty < x)]; [x ⩽ y ⇔ (x < y orx ~ y)]. His version of Savage's theory then assumed that < is asymmetric and negatively transitive onA. Thus, ⩽ and > are complementary, since asymmetric < is necessary and sufficient for such complementarity. (5) This analysis provides a new proof that the same list of elementary properties of binary relations onA applies to all three theories: ⩽ is connected, transitive, weakly connected, reflexive, and negatively transitive; while both < and > are asymmetric, negatively transitive, antisymmetric, irreflexive, and transitive; but only ~ is symmetric.     

Any complete preference structure without circuit admits an interval representation

This article proves that all complete preference structures where the strict preference relation (P) has no circuit admit a representation by intervals of the real line; the rule for deciding whether an interval is indifferent or preferred to another is less straightforward than for interval orders: strict preference is indeed compatible with a certain degree of overlapping of intervals, the allowed degree being specified by means of a so-called tolerance function.     

Sincerity and manipulation under approval voting

Under approval voting, each voter can nominate as many candidates as she wishes and the election winners are those candidates that are nominated most often. A voter is said to have voted sincerely if she prefers all those candidates she nominated to all other candidates. As there can be a set of winning candidates rather than just a single winner, a voter’s incentives to vote sincerely will depend on what assumptions we are willing to make regarding the principles by which voters extend their preferences over individual candidates to preferences over sets of candidates. We formulate two such principles, replacement and deletion, and we show that, under approval voting, a voter who accepts those two principles and who knows how the other voters will vote will never have an incentive to vote insincerely. We then discuss the consequences of this result for a number of standard principles of preference extension in view of sincere voting under approval voting.     

On the stability of a triplet of scoring rules

When choosing a voting rule to make subsequent decisions, the members of a committee may wish this rule to be self-selected when it is the object of a choice among a menu of different possible voting rules. Such concepts have recently been explored in Social Choice theory, and a menu of voting rule is said to be stable if it contains at least one self-selective voting rule at each profile of preferences on voting rules. We consider in this article the menu constituted by the three well-known scoring rules {Borda, Plurality, and Antiplurality}. Under the Impartial Culture assumption, which proposes an a priori model to estimate the likelihood of the profiles, we will derive a probability for the stability of this triplet of voting rules.     

Axiomatizing bounded rationality: the priority heuristic

This paper presents an axiomatic framework for the priority heuristic, a model of bounded rationality in Selten’s (in: Gigerenzer and Selten (eds.) Bounded rationality: the adaptive toolbox, 2001) spirit of using empirical evidence on heuristics. The priority heuristic predicts actual human choices between risky gambles well. It implies violations of expected utility theory such as common consequence effects, common ratio effects, the fourfold pattern of risk taking and the reflection effect. We present an axiomatization of a parameterized version of the heuristic which generalizes the heuristic in order to account for individual differences and inconsistencies. The axiomatization uses semiorders (Luce, Econometrica 24:178–191, 1956), which have an intransitive indifference part and a transitive strict preference component. The axiomatization suggests new testable predictions of the priority heuristic and makes it easier for theorists to study the relation between heuristics and other axiomatic theories such as cumulative prospect theory.     

Testing transitivity in choice under risk

Recently proposed models of risky choice imply systematic violations of transitivity of preference. This study explored whether people show the predicted intransitivity of the two models proposed to account for the certainty effect in Allais paradoxes. In order to distinguish “true” violations from those produced by “error,” a model was fit in which each choice can have a different error rate and each person can have a different pattern of preferences that need not be transitive. Error rate for a choice is estimated from preference reversals between repeated presentations of the same choice. Results showed that few people repeated intransitive patterns. We can retain the hypothesis that all participants were transitive.     

Even-chance lotteries in social choice theory

This paper discusses aspects of the theory of social choice when a nonempty choice set is to be determined for each situation, which consists of a feasible set of alternatives and a preference order for each voter on the set of nonempty subsets of alternatives. The individual preference assumptions include ordering properties and averaging conditions, the latter of which are motivated by the interpretation that subset A is preferred to subset B if and only if the individual prefers an even-chance lottery over the basic alternatives in A to an even-chance lottery over the basic alternatives in B. Corresponding to this interpretation, a choice set with two or more alternatives is resolved by an even-chance lottery over these alternatives. Thus, from the traditional no-lottery social choice theory viewpoint, ties are resolved by even-chance lotteries on the tied alternatives. Compared to the approach which allows all lotteries to compete along with the basic alternatives, the present approach is a contraction which allows only even-chance lotteries.After discussing individual preference axioms, the paper examines Pareto optimality for nonempty subsets of a feasible set in a social choice context with n voters. Aspects of simple-majority comparisons in the even-chance context follow, including an analysis of single-peaked preferences. The paper concludes with an Arrowian type impossibility theorem that is designed for the even-chance setting.