Monotonicity Axiom Research Articles

Generalization of weighted-egalitarian Shapley values

In this study, we provide a new class of solutions that generalize the weighted-egalitarian Shapley values by permitting heterogeneity of players in both the Shapley value and equal division value. To derive the proposed value, we present axioms of weak monotonicity, weak differential null player out, efficiency, null game, ratio invariance for null players, and weak superweak differential marginality.

Aczel–Alsina T-norm based group decision-making technique for the evaluation of electric cars using generalized orthopair fuzzy aggregation information with unknown weights

Data management and finding precise outcomes from large amounts of information are among the biggest challenges for scientists. The technique of multi-attribute group decision-making (MAGDM) is a valuable tool for investigating fuzzy data precisely. The key objective of the paper is to redefine the q-rung orthopair (q-RO) fuzzy set (FS) (q-ROFS) in the term of interval-valued and proposed new aggregation operators (AOs) based on the Aczel-Alsina (AA) t-norm (TN) and t-conorm (TCN) operations. The AA operational laws are a generalized form of existing TNs and TCNs and give more reliable results because they can fluctuate in their parametric values. The concept of interval-valued enlarges the space of membership degree (MD) and non-membership degree (NMD) for decision-makers. By taking qth power, the interval-valued q-ROFS (IV-q-ROFS) structure. The IV-q-ROFS can handle the uncertainty and vagueness in data, then interval-valued intuitionistic FS (IV-IFS) and interval-valued Pythagorean FS (PyFS) (IV-PyFS) and provide accurate results. The thought of power AOs (PAOs) makes the relationship between weight vectors and reduces the chances of uncertainty in aggregated results. By taking advantage of PAOs, this article is devoted to introducing the interval-valued q-ROF Aczel-Alsina power-weighted averaging (IV-q-ROFAAPWA) and interval-valued q-ROF Aczel-Alsina power-weighted geometric (IV-q-ROFAAPWG) operators. The fundamental axioms of AOs, idempotency, boundedness, and monotonicity, are also discussed. To illustrate the importance of suggested AOs, the real-life problem of electric car selection was solved by applying the MAGDM method using the proposed IV-q-ROFAAPWA and IV-q-ROFAAPWG operators. The comparison of proposed AOs with currently present AOs is also part of the article. We finally constructed solid conclusions.

Risk concentration and the mean‐expected shortfall criterion

AbstractExpected shortfall (ES, also known as CVaR) is the most important coherent risk measure in finance, insurance, risk management, and engineering. Recently, Wang and Zitikis (2021) put forward four economic axioms for portfolio risk assessment and provide the first economic axiomatic foundation for the family of . In particular, the axiom of no reward for concentration (NRC) is arguably quite strong, which imposes an additive form of the risk measure on portfolios with a certain dependence structure. We move away from the axiom of NRC by introducing the notion of concentration aversion, which does not impose any specific form of the risk measure. It turns out that risk measures with concentration aversion are functions of ES and the expectation. Together with the other three standard axioms of monotonicity, translation invariance and lower semicontinuity, concentration aversion uniquely characterizes the family of ES. In addition, we establish an axiomatic foundation for the problem of mean‐ES portfolio selection and new explicit formulas for convex and consistent risk measures. Finally, we provide an economic justification for concentration aversion via a few axioms on the attitude of a regulator towards dependence structures.

A planner-optimal matching mechanism and its incentive compatibility in a restricted domain

In many random assignment problems, the central planner pursues their own policy objective, such as matching size and minimum quota fulfillment. Several practically important policy objectives do not align with agents' preferences and are known to be incompatible with strategy-proofness. This paper demonstrates that such policy objectives can be attained using mechanisms that satisfy Bayesian incentive compatibility within a restricted domain of von Neumann Morgenstern utilities. We establish that a mechanism satisfies Bayesian incentive compatibility in an inverse-bounded-indifference domain if and only if the mechanism satisfies the three axioms of swap monotonicity, lower invariance, and interior upper variance. We apply this axiomatic characterization to analyze the incentive property of the constrained random serial dictatorship mechanism (CRSD). CRSD is designed to generate an individually rational assignment that optimizes the central planner's policy objective function. Since CRSD satisfies these axioms, it is Bayesian incentive compatible within an IBI domain.

Random utility models with ordered types and domains

Random utility models in which heterogeneity of preferences is modeled by means of an ordered collection of utilities, or types, provide a powerful framework for understanding a variety of economic behaviors. This paper studies the micro-foundations of ordered random utility models with the objective of meeting empirical requirements. This is done by working with arbitrary collections of ordered menus of alternatives, and by making no parametric assumptions about the type distribution. The model is characterized by a simple monotonicity axiom. Goodness-of-fit measures are proposed, with proof provided of the strong consistency of extremum estimators defined upon them. A statistical test for the model is also provided.

Choice with Affirmative Action

A choice rule with affirmative action decides on the recipients of a limited number of identical objects by reconciling two objectives: respecting a priority ordering over the applicants and supporting a minority group. We extend the standard formulation of a choice problem by incorporating a type function and a priority ordering and introduce monotonicity axioms on how a choice rule should respond to variations in these parameters. We show that monotonic and substitutable affirmative action rules are the ones that admit a bounded reserve representation. As a prominent class of choice rules that satisfy the monotonicity axioms, we characterize lexicographic affirmative action rules that are prevalent both in the literature and in practice. Our axiomatic approach provides a novel way to think about reserve systems and uncovers choice rules that go beyond lexicographic affirmative action rules. This paper was accepted by Yan Chen, behavioral economics and decision analysis. Funding: B. Doğan gratefully acknowledges financial support from the British Academy/Leverhulme Trust [Grant SRG1819\190133].

On the General Deviation Measure and the Gini coefficient

AbstractThe General Deviation Measure introduces a progressive definition for financial risk measurement, which presents an alternative to the Coherent Risk Measure. This definition replaces the Translation Invariance and Monotonicity axioms with the Shift Invariance and Nonnegativity axioms, and it includes the Mean Absolute Deviation measure and other variations of the Value‐at‐Risk measurements. This research shows that Coherent Risk Measure holds an intrinsic contradiction regarding riskless assets, and it proves that the Gini coefficient is also a General Deviation Measure. These contributions improve the efficiency of risk measurement and asset pricing in the financial markets.

Pro-poor Growth: Concepts and Measurement with Country Case Studies (Distinguished Lecture)

This paper looks into the interrelation between economic growth, inequality, and poverty. Using the notion of pro-poor growth, we examine the extent to which the poor benefit from economic growth. First, various approaches to defining and measuring propoor growth are scrutinised using a variety of criteria. It is argued that the satisfaction of a monotonicity axiom is a key criterion for measuring pro-poor growth. The monotonicity axiom sets out a condition that the proportional reduction in poverty is a monotonically increasing function of the pro-poor growth measure. The paper proposes a pro-poor growth measure that satisfies the monotonicity criterion. This measure is called a ‘poverty equivalent growth rate’, which takes into account both the magnitude of growth and how the benefits of growth are distributed to the poor and the non-poor. As the new measure satisfies the criterion of monotonicity, it is indicative that to achieve rapid poverty reduction, the poverty equivalent growth rate—rather than the actual growth rate—ought to be maximised. The methodology developed in the paper is then applied to three Asian countries, namely, the Republic of Korea, Thailand, and Vietnam.

New constructions of decision evaluation functions in three-way decision spaces based on uninorms.

In 2014, Hu introduced the concept of three-way decision spaces and axiomatic definition of decision evaluation functions. In three-way decision spaces, decision evaluation function satisfies minimum element axiom, monotonicity axiom and complement axiom. Since then, the research on construction method of decision evaluation functions from commonly used binary aggregation functions becomes a research hotspot. Meanwhile, uninorms, as one class of binary aggregation functions, have been successfully applied in various application problems, such as in decision making, image processing, data mining, etc. This paper continues to consider this research topic and mainly explores the new construction methods of decision evaluation functions based on uninorms. Firstly, we show two novel transformation methods from semi-decision evaluation functions to decision evaluation functions based on uninorms. Secondly, using known semi-decision evaluation functions, we give some new construction methods of semi-decision evaluation functions. Thirdly, we give some novel construction methods of decision evaluation functions and semi-decision evaluation functions related to fuzzy sets, interval-valued fuzzy sets, fuzzy relations and hesitant fuzzy sets. Based on them, decision maker can obtain more useful decision evaluation functions, thereby more choices can be used for realistic decision-making problems. Finally, we consider two real evaluation problems to illustrate the results obtained in this paper. The three-way decisions results of evaluation problem show that the construction method proposed in this paper is superior to some existing construction methodsunder some conditions.

Twofold multiprior preferences and failures of contingent reasoning

We propose a model of incomplete twofold multiprior preferences, in which an act f is ranked above an act g only when f provides higher utility in a worst-case scenario than what g provides in a best-case scenario. The model explains failures of contingent reasoning, captured through a weakening of the state-by-state monotonicity (or dominance) axiom. Our model gives rise to rich comparative statics results, as well as extension exercises, and connections to choice theory. We present an application to second-price auctions.

Negotiations in Competing Supply Chains: The Kalai-Smorodinsky Bargaining Solution

Supply chain contract negotiation has gained increasing attention in recent years, and the studies involving negotiations in the operations literature almost exclusively apply the concept of the Nash bargaining (NB) solution. The NB solution, however, is derived based on the axiom of independence of irrelevant alternatives (IIA), an unrealistic assumption in many contexts. Indeed, our analysis suggests that the NB solution can lead to unreasonable negotiation outcomes in supply chains with horizontal competition. As an alternative, the Kalai-Smorodinsky (KS) solution has been applied in many fields but has not been introduced to the supply chain contexts. The KS solution is derived under the axiom of individual monotonicity in replacement of the IIA axiom. We perform a comprehensive comparison of contract negotiations under the KS and NB solutions in horizontally competing supply chains. Although the KS solution does not possess the flexibility of explicitly specifying the relative bargaining power as the NB solution does, the KS solution can appropriately capture the negotiation power shift induced by the decision ownership, the negotiation sequence, the vertical relationship, the competition intensity, the trade contingency, and the contract type. Our study sheds lights on the appropriate selection of solution concepts in studying negotiations in competing supply chains.This paper was accepted by David Simchi-Levi, operations management.

Axiomatic foundations of the core for games in effectiveness form

We provide an axiomatic characterization of the core of games in effectiveness form. We point out that the core, whenever it applies to appropriate classes of these games, coincides with a wide variety of prominent stability concepts in social choice and game theory, such as the Condorcet winner, the Nash equilibrium, pairwise stability, and stable matchings, among others. Our characterization of the core invokes the axioms of weak nonemptiness, coalitional unanimity, and Maskin monotonicity together with a principle of independence of irrelevant states, and uses in its proof a holdover property echoing the conventional ancestor property. Taking special cases of this general characterization of the core, we derive new characterizations of the previously mentioned stability concepts.

Axiomatizations of the proportional division value

We present axiomatic characterizations of the proportional division value for TU-games, which distributes the worth of the grand coalition in proportion to the stand-alone worths of the players. First, a new proportionality principle, called proportional-balanced treatment, is introduced by strengthening Shapley’s symmetry axiom, which states that if two players make the same contribution to any nonempty coalition, then they receive the amounts in proportion to their stand-alone worths. We characterize the family of values satisfying efficiency, weak linearity, and proportional-balanced treatment. We also show that this family is incompatible with the dummy player property. However, we show that the proportional division value is the unique value in this family that satisfies the dummifying player property. Second, we propose appropriate monotonicity axioms, and obtain axiomatizations of the proportional division value without both weak linearity and the dummifying player property. Third, from the perspective of a variable player set, we show that the proportional division value is the only one that satisfies proportional standardness and projection consistency. Finally, we provide a characterization of proportional standardness.

Axiomatizations of the $$\beta $$ and the score measures in networks

Monotonicity is an appealing principle of relational power measures in social networks. It states that as the influence of an individual changes, the relational power measure should change in the same direction. We axiomatically characterize the $$\beta $$ - and score-measures on directed networks using three axioms: two different monotonicity axioms, the same symmetry axiom and two different efficiency axioms, respectively. For every individual, the $$\beta $$ -measure refers to a weighted sum over all dominated individuals by itself, in which for each dominated individual the weight is given by the reciprocal of the number of its dominators, while the score-measure refers simply to the number of dominated individuals by itself. We also extend the result for the score-measure to undirected networks.

A note on stochastic complementarity for the applied researcher

In their discussion of stochastic complementarity, Manzini et al. (2018) show that the intuitively appealing correlation criterion does not—in general—satisfy the axiom of monotonicity: products classified as complements can turn into substitutes following an increase in their joint purchases. In this note, we show that, however, by restricting attention to mixed logit models along the lines of Gentzkow (2007)’s, one can prevent such violations.

О некоторых моделях альтруистического поведения

The paper surveys several recent approaches to studying, modeling, and interpreting altruistic behavior. In the first section we describe a modification of the system of axioms of classical rational choice theory taking into consideration moral reference points. We study the moral monotonicity axiom, compare the predictions of the standard and the modified system of axioms, and describe series of experiments contradicting the standard system, but agreeing with the modified one. In the second section we discuss the approach of J. Roemer who suggested to consider Kantian optimization in place of the standard Nash one. It is well known that Nash equilibria are not necessarily optimal. It happens, as, for example, in the tragedy of the commons, that all the participants would benefit from choosing a different, non-Nash equilibrium, and in this section we consider mechanisms allowing to realize an optimal choice. In the third section we consider a model in which different parenting styles (based on altruism and paternalism) emerge as equilibrium outcomes and are affected by both parental preferences and the socioeconomic environment. We discuss statistical and experimental data showing historical development of parental styles and allowing to check various predictions of the model.

On the monotonicity of the eigenvector method

Pairwise comparisons are used in a wide variety of decision situations where the importance of alternatives should be measured on a numerical scale. One popular method to derive the priorities is based on the right eigenvector of a multiplicative pairwise comparison matrix. We consider two monotonicity axioms in this setting. First, increasing an arbitrary entry of a pairwise comparison matrix is not allowed to result in a counter-intuitive rank reversal, that is, the favoured alternative in the corresponding row cannot be ranked lower than any other alternative if this was not the case before the change (rank monotonicity). Second, the same modification should not decrease the normalised weight of the favoured alternative (weight monotonicity). Both properties are satisfied by the geometric mean method but violated by the eigenvector method. The axioms do not uniquely determine the geometric mean. The relationship between the two monotonicity properties and the Saaty inconsistency index are investigated for the eigenvector method via simulations. Even though their violation turns out not to be a usual problem even for heavily inconsistent matrices, all decision-makers should be informed about the possible occurrence of such unexpected consequences of increasing a matrix entry.

A Path-Based Partial Information Decomposition.

Based on the conceptual basis of information theory, we propose a novel mutual information measure—‘path-based mutual information’. This information measure results from the representation of a set of random variables as a probabilistic graphical model. The edges in this graph are modeled as discrete memoryless communication channels, that is, the underlying data is ergodic, stationary, and the Markov condition is assumed to be applicable. The associated multilinear stochastic maps, tensors, transform source probability mass functions into destination probability mass functions. This allows for an exact expression of the resulting tensor of a cascade of discrete memoryless communication channels in terms of the tensors of the constituting communication channels in the paths. The resulting path-based information measure gives rise to intuitive, non-negative, and additive path-based information components—redundant, unique, and synergistic information—as proposed by Williams and Beer. The path-based redundancy satisfies the axioms postulated by Williams and Beer, the identity axiom postulated by Harder, and the left monotonicity axiom postulated Bertschinger. The ordering relations between redundancies of different joint collections of sources, as captured in the redundancy lattices of Williams and Beer, follow from the data processing inequality. Although negative information components can arise, we speculate that these either result from unobserved variables, or from adding additional sources that are statistically independent from all other sources to a system containing only non-negative information components. This path-based approach illustrates that information theory provides the concepts and measures for a partial information decomposition.

A general theory of subjective mixtures

We provide, and characterize behaviorally, a framework for constructing subjective mixtures which requires neither the Certainty Independence nor the Monotonicity axiom, replacing them with much weaker “local” properties. As we also show by means of examples, this framework provides a purely subjective foundation to most of the recent preference models which employ the Anscombe-Aumann setting. It also allows a subjective formulation of a preference for ambiguity hedging, and as a consequence allows the distinction of the notions of ambiguity aversion and preference for randomization.

Estimating stochastic production frontiers: A one-stage multivariate semiparametric Bayesian concave regression method

This paper describes a nonparametric Bayesian estimator for production frontiers that satisfies the axioms of monotonicity and concavity. An inefficiency term that allows for a departure from the homoscedastic prior distributional assumption is jointly estimated in a single stage with cross-sectional data. Our Monte Carlo simulation experiments demonstrate that the frontier and efficiency estimations are computationally competitive, align well with economic theory, and allow for the analysis of larger data sets than existing nonparametric methods. We use the proposed method to investigate Japan’s concrete industry, an important component of the nation’s construction sector, from 2007 to 2010. Our finding of a significant size-weighted inefficiency supports the argument that economic stimuli given to Japan’s concrete industry may result in large losses due to inefficiency.