Lexicographic Preferences Research Articles

Characterizing lexicographic preferences

We characterize lexicographic preferences on product sets of finitely many coordinates. The main new axiom is a robustness property. It roughly requires this: Suppose x is preferred to y; many of its coordinates indicate that the former is better and only a few indicate the opposite. Then the decision maker is allowed a change of mind turning one coordinate in favor of x to an indifference: even if one less argument supports the preference, the fact that we started with many arguments in favor of x suggests that such a small change is not enough to give rise to the opposite preference.

Myopic Law Preferences and Non-coercive Market Equilibria

This paper investigates the economic conditions under which the performance of a Judiciary does not impede noncoercive fair socioeconomic allocations under “Strotz-myopia” regarding the law variable, i.e., under a static view of it in an otherwise dynamic context. The law, here, is the positive factor by which consumption volume is multiplied as a result of law introduction in an otherwise fully private social economy. Lexicographic preferences regarding the law is the keyword in establishing non-coercive equilibria either in the static context of a stone-age economy or in the dynamic context of a jungle economy, given in the latter the presence of farsightedness. Nevertheless, such equilibria are found here to exist even under myopia and regardless the presence of lexicographic preferences. We first detect them within a fully private social economy, and we next qualify them by introducing the Judiciary as state officials. The optimality regarding state finances imposes additional restrictions in establishing myopic non-coercive equilibria. In any case, an equilibrium will be stable if it is not influenced by the homotheticity or not of the preferences, i.e., by income distribution considerations. So, any suboptimal behaviour of the Judiciary should be attributed exclusively to the suboptimality of state finances: Macroeconomics does affect law administration.

Law, Coercion and Socioeconomic Equilibrium

Abstract This paper investigates the economic conditions under which the performance of a Judiciary does not impede non-coercive fair socioeconomic allocations under “Strotz-myopia” regarding the law variable, i.e. under a static view of it in an otherwise dynamic context. The law, here, is the positive factor by which consumption volume is multiplied as a result of law introduction in an otherwise fully private social economy. Lexicographic preferences regarding the law is the keyword in establishing non-coercive equilibria either in the static context of a stone-age economy or in the dynamic context of a jungle economy, given in the latter the presence of farsightedness. Nevertheless, such equilibria are found here to exist even under myopia and regardless the presence of lexicographic preferences. We first detect them within a fully private social economy, and we next qualify them by introducing the Judiciary as state officials. The optimality regarding state finances imposes additional restrictions in establishing myopic noncoercive equilibria. In any case, an equilibrium will be stable if it is not influenced by the homotheticity or not of the preferences, i.e. by income distribution considerations. So, any suboptimal behaviour of the Judiciary should be attributed exclusively to the suboptimality of state finances: Macroeconomics does affect law administration.

An Economic Choice Model for Lexicographic Preferences

Consumer's preference structure varies across product categories. For some durable goods, such as laptops and smartphones, consumers tend to distinguish a product from its competing ones by differences in several features ordered in their importance. Under this preference tructure, so called lexicographic preference, it is not easy to find the optimal marketing mix strategy because of two reasons: First, there is no simple functional form to link the ordinal preferences revealed in choice observations to measurable utility that allows us to conduct policy experiments for marketing mix variables. Second, the latent process of ordering attributes according to their importance cannot be easily calibrated in the conventional manners such as MLE, GMM, and Bayesian methods. In this paper, we propose an economic choice model with a recursive utility specification to measure lexicographic preferences, and introduce a data augmentation technique to estimate the latent ordering process. The proposed model is applied into a conjoint analysis for laptop choice, where we find that the recursive utility specification leads to a better model fit and a different pricing strategy compared to the conventional linear utility specification.

Random assignment: Redefining the serial rule

We provide a new, welfarist, interpretation of the well-known Serial rule in the random assignment problem, strikingly different from previous attempts to define or axiomatically characterize this rule.For each agent i we define ti(k) to be the total share of objects from her first k indifference classes this agent i gets. Serial assignment is shown to be the unique one which leximin maximizes the vector of all such shares (ti(k)).This result is very general; it applies to non-strict preferences, and/or non-integer quantities of objects, as well.In addition, we characterize Serial rule as the unique one sd-efficient, sd-envy-free, and strategy-proof on the lexicographic preferences extension to lotteries.

Multi-Objective MDPs with Conditional Lexicographic Reward Preferences

Sequential decision problems that involve multiple objectives are prevalent. Consider for example a driver of a semi-autonomous car who may want to optimize competing objectives such as travel time and the effort associated with manual driving. We introduce a rich model called Lexicographic MDP (LMDP) and a corresponding planning algorithm called LVI that generalize previous work by allowing for conditional lexicographic preferences with slack. We analyze the convergence characteristics of LVI and establish its game theoretic properties. The performance of LVI in practice is tested within a realistic benchmark problem in the domain of semi-autonomous driving. Finally, we demonstrate how GPU-based optimization can improve the scalability of LVI and other value iteration algorithms for MDPs.

Learning Partial Lexicographic Preference Trees over Combinatorial Domains

We introduce partial lexicographic preference trees (PLPtrees) as a formalism for compact representations of preferences over combinatorial domains. Our main results concern the problem of passive learning of PLP-trees. Specifically, forseveral classes of PLP-trees, we study how to learn (i) a PLP-tree consistent with a dataset of examples, possibly subject to requirements on the size of the tree, and (ii) a PLP-tree correctly ordering as many of the examples as possible in case the dataset of examples is inconsistent. We establish complexity of these problems and, in all cases where the problem is in the class P, propose polynomial time algorithms.

A Complexity Approach for Core-Selecting Exchange with Multiple Indivisible Goods under Lexicographic Preferences

Core-selection is a crucial property of social choice functions, or rules, in social choice literature. It is also desirable to address the incentive of agents to cheat by misreporting their preferences. This paper investigates an exchange problem where each agent may have multiple indivisible goods, agents' preferences over sets of goods are assumed to be lexicographic, and side payments are not allowed. We propose an exchange rule called augmented top-trading-cycles (ATTC) procedure based on the original TTC procedure. We first show that the ATTC procedure is core-selecting. We then show that finding a beneficial misreport under the ATTC procedure is NP-hard. Under the ATTC procedure, we finally clarify the relationship between preference misreport and splitting, which is a different type of manipulation.

A Modified Nature Publishing Index via Shannon Entropy

This paper develops a Shannon Entropy approach based only on the number of papers published to propose scientific institution rankings. A simple and efficient approach with weight restrictions is employed to derive the score under specific preferences. The importance degrees for each preference are determined using the concept of Shannon Entropy. Finally, a weighted linear combination of different lexicographic preferences with subjective perceptions between the corrected count and the number of articles criteria is proposed. An application to Asia-Pacific ranking of the Nature Publishing Index is to illustrate the effectiveness of our proposed method.

Citizens' preferences for the conservation of agricultural genetic resources.

Evaluation of conservation policies for agricultural genetic resources (AgGR) requires information on the use and non-use values of plant varieties and animal breeds, as well as on the preferences for in situ and ex situ conservation. We conducted a choice experiment to estimate citizens' willingness to pay (WTP) for AgGR conservation programmes in Finland, and used a latent class model to identify heterogeneity in preferences among respondent groups. The findings indicate that citizens have a high interest in the conservation of native breeds and varieties, but also reveal the presence of preference heterogeneity. Five respondent groups could be identified based on latent class modeling: one implying lexicographic preferences, two with reasoned choices, one indicating uncertain support and one with a preference for the current status of conservation. The results emphasize the importance of in situ conservation of native cattle breeds and plant varieties in developing conservation policies.

Latent Ordering Conjoint Model Under Lexicographic Preferences

Consumer's preference structure varies over product categories. For some durable goods, such as laptops and smartphones, consumers tend to distinguish a product from its competing ones by differences in several features ordered in their importance. This preference structure, so called lexicographic preference, does not allow us to simply find the optimal marketing mix strategy because of two reasons: First, there is no simple utility function that captures the cardinal link with a continuous price variable as well as the ordinal preference structure. Secondly, the latent process of ordering attributes according to their importance cannot be easily calibrated in the conventional manners, such as MLE, GMM, and Bayesian methods. In this paper, we propose an economic framework that takes into account the ordinal lexicographic preference, the cardinal link with prices, and the latent ordering process by introducing a recursive utility specification and a data augmentation technique that employs multinomial-Dirichlet conjugacy.

Stable lexicographic rules for shortest path games

For the class of shortest path games, we propose a family of new cost sharing rules satisfying core selection. These rules allocate shares according to some lexicographic preference relation. A computational procedure is provided. Our results relate to those of Tijs et al. (2011).

Strategyproof Exchange with Multiple Private Endowments

We study a mechanism design problem for exchange economies where each agent is initially endowed with a set of indivisible goods and side payments are not allowed. We assume each agent can withhold some endowments, as well as misreport her preference. Under this assumption, strategyproofness requires that for each agent, reporting her true preference with revealing all her endowments is a dominant strategy, and thus implies individual rationality. Our objective in this paper is to analyze the effect of such private ownership in exchange economies with multiple endowments. As fundamental results, we first show that the revelation principle holds under a natural assumption and that strategyproofness and Pareto efficiency are incompatible even under the lexicographic preference domain. We then propose a class of exchange rules, each of which has a corresponding directed graph to prescribe possible trades, and provide necessary and sufficient conditions on the graph structure so that they satisfy strategyproofness.

An alternative proof of Fishburn’s axiomatization of lexicographic preferences

We present an alternative proof of Fishburn’s (1975) axiomatization of lexicographic preferences. The essence of our proof lies in identifying “an extremely pivotal factor”. Our proof reconfirms the strong interconnections between Arrow’s and Gibbard–Satterthwaite’s theorems with Fishburn’s axiomatization.

CITIZENS' PREFERENCES FOR POLICIES TO CONSERVE AGRICULTURAL GENETIC RESOURCES

To evaluate conservation policies of agricultural genetic resources (AgGR), information on the use and non-use values of plant varieties and animal breeds, as well as on the preferences for in situ and ex situ conservation are needed. Here we present the results of a choice experiment of AgGR conservation programs in Finland. The findings indicate that citizens’ have high interest in the conservation of native breeds and varieties, but also that there is heterogeneity in preferences between citizens. Five groups can be identified: one implying lexicographic preferences, two with reasoned choices, one indicating ambivalence and one with status quo preferences.

Lexicographic preferences representable by real-branching trees with countable height: A dichotomy result

The linear ordering Rlex<ω is the lexicographic linearization of the tree of R-valued functions defined on a finite initial segment of ω and ordered by extension. We identify suitable notions of smallness and largeness for linear orderings that embed into Rlex<ω by using tree representations of chains. Specifically, small linear orderings are representable by inversely well-founded trees, and large linear orderings are representable by fully uncountably branching trees. We prove the rather surprising result that all linear orderings embeddable into Rlex<ω are either small or large. This fact sheds some light on the complicated structure of the linear ordering Rlex<ω, and can be useful in applications to utility theory and preference modeling.

Two-dimensional model of lexicographic preferences

This paper characterizes lexicographic utility based on the consumer preferences on the available sets of commodities by focusing in the Islamic approach. It begins with the introduction of several general preference axioms in the conventional sense that only restricted to the worldly commodity which is one-dimensional utility model. Next, the paper explores the preference ordering grounded by the notion of Islamic teachings that includes worldly and ukhrawi commodity in which a rational consumer should apply in making any economic decision. The preference herein illustrates the connectivity between both of the commodities which generate two-dimensional utility model that is crucial to be hold in the lexicographic manner. 5354 Hassilah Salleh, Rusmi Rasul and Shaharir Mohamad Zain

Platform Markets and Matching with Contracts

A matching problem exists when two sets of agents want to find each other. Platform markets can provide a solution to this problem. However, existing models of platform markets restrict agent heterogeneity and thus the matching problem is trivial. We introduce agent heterogeneity by modeling platform markets as a matching problem. This raises three important questions. The first question is how to model matching in platform markets. We propose a model in which platforms are objects of choice, with agents matching directly with each other. Second, we adopt stability as our equilibrium concept since it eliminates the possibility of an individual or group of agents switching in equilibrium. Third, we consider properties of equilibrium. In particular, we show that opposition of interests at stable matchings implies a form of the “seesaw principle:” in equilibrium, one side gets more favorable terms at the expense of the other side. Moreover, we provide conditions under which the market may tip toward a dominant platform in equilibrium. Finally, we show that coordination failure occurs if agents from the same side are required to join a platform under the same terms. In this environment, we obtain stability if agents have lexicographic preferences. Our matching model provides a new approach to studying platform markets.

Using a discrete choice experiment to elicit the demand for a nutritious food: Willingness-to-pay for orange maize in rural Zambia

Using a discrete choice experiment, this paper estimates the willingness to pay for biofortified orange maize in rural Zambia. The study design has five treatment arms, which enable an analysis of the impact of nutrition information, comparing the use of simulated radio versus community leaders in transmitting the nutrition message, on willingness to pay, and to account for possible novelty effects in the magnitude of premiums or discounts. The estimation strategy also takes into account lexicographic preferences of a subset of our respondents. The results suggest that (a) orange maize is not confused with yellow maize, and has the potential to compete with white maize in the absence of a nutrition campaign, (b) there is a premium for orange maize with nutrition information, and (c) different modes of nutritional message dissemination have the same impact on consumer acceptance.

Preferences, rational choices and economic valuation: Some empirical tests

This study focuses on the respondent rationality hypothesis, usually assumed to be true in Discrete Choice Experiments. We examine lexicographic preferences, the influence of consistency, and the role of task complexity in the individual choice process. To this end, we carry out rationality tests in a survey on forest recreation. Results show that choice set orderings do not impact on choice probability. If a violation of continuity or consistency axioms does impact on choice probability, the Willingness-To-Pay estimators calculated using the total sample and the sub-samples of “irrational” respondents are not significantly different. This serves as a basis for discussing the traditional concept of rationality.