Independence Of Irrelevant Alternatives Research Articles

Development of a Physicians’ Choice Model Using Mixed Logit with Random Prices for Drugs Case Study on Diabetes Type II

Abstract Background: this paper presents a first experiment with random generator of drug prices and a first simulation on physicians’ treatment choices (case on pharmacotherapies) for diabetes type II care. It also aims to compare the effects of the price variables according to public versus private health plans on physicians’ choices (Medicare versus commercial Health Plans). Methods: the base line model used is a Mixed Logit model with Random Price variables. A series of experiments with random parameters generations is designed with various sequences and number of draws. The model is tested on a real analytical dataset, extracted from the CDC physician survey (National Ambulatory Care Survey, NAMCS), for patients with diabetes type II without complications, for previous predictive econometrics with ENDEPUS research, Inc. The model uses a first drug choice set with three alternatives: oral agents only, combined therapies, no drug. The choice models introduce qualitative dependent variables and complement the series of cumulative logistic models per disease. The matlab code for the new specification test on the Independence of Irrelevant Alternatives at individual level is modified to fit this type of medical applications.

The Order-Dependent Luce Model

I develop a simple axiomatic model that incorporates the order effect: the ordering of alternatives (e.g., ranking of universities, the location of products in a grocery store, the order of candidates on a ballot) affects choice frequencies. In my model, the probability of choosing an alternative is proportional to the utility of the alternative, similar to the Luce model. However, the utility of the alternative depends on the relative ordering of the alternative in the menu. I characterize this model by two weakenings of Luce’s axiom of independence of irrelevant alternatives. I discuss how to identify the ordering of alternatives from choice data when it is not observed. Finally, I apply my model to an optimal ordering problem and to experimental data on intertemporal choice. This paper was accepted by Manel Baucells, decision analysis.

Odds supermodularity and the Luce rule

We present a characterization of the Luce rule in terms of positivity and a new choice axiom called odds supermodularity that strengthens the regularity axiom. This new characterization illuminates a connection that goes unnoticed, and sheds light on the behavioral underpinnings of the Luce rule and its extensions from a different perspective. We show that odds supermodularity per se characterizes a structured extension of the Luce rule that accommodates zero probability choices. We identify the random choice model characterized via a stochastic counterpart of Plott (1973)'s path independence axiom, which strengthens odds supermodularity.

Testing Classic Theories of Migration in the Lab

We test the predictions of different classic migration theories by using incentivized laboratory experiments to investigate how potential migrants decide between working in different destinations. We test theories of income maximization, migrant skill-selection, and multidestination choice as we vary migration costs, liquidity constraints, risk, social benefits, and incomplete information. We show the standard income maximization model of migration with selection on observed and unobserved skills leads to a much higher migration rate and more negative skill-selection than is obtained when migration decisions take place under more realistic assumptions. Second, we investigate whether the independence of irrelevant alternatives (IIA) assumption holds. We find it holds for most people when decisions just involve wages, costs, and liquidity constraints. However, once we add a risk of unemployment and incomplete information, IIA no longer holds for about 20 percent of our sample.

Smarter Than Humans: Rationality Reflected in Primate Neuronal Reward Signals

Rational choice, in all its definitions by various disciplines, allows agents to maximize utility. Formal axioms and simple choice designs are suitable for assessing rationality in monkeys. Their economic preferences are complete and transitive. In this paper I will describe how neuronal reward signals demonstrate a propensity for rational choice. Dopamine signals follow transitivity and satisfy first-order stochastic dominance that defines the better option. Neurons in orbitofrontal cortex reflect unchanged preferences when a dominated option is removed from the option set, thus satisfying Independence of Irrelevant Alternatives (IIA). While monkeys, with their reward neurons, may not be more rational than humans, the constraints of controlled experiments seem to allow them to behave rationally within their informational, cognitive and temporal bounds.

A zero attraction effect in naturalistic choice.

In the attraction effect, adding a dominated third option to a choice set of two options can reverse the preference for the original two options, and even increase one of the option’s choice share. This constitutes a violation of the axioms of regularity and independence from irrelevant alternatives, which are core properties of any choice model in which the utility of each option is stable across choice sets. Consequently, in the past 20 years, the attraction effect has driven the development of a set of influential models of multiattribute choice. However, Frederick, Lee, and Baskin (2014) have recently claimed that the attraction effect is only limited to options with numerical attributes, and does not hold for choices between naturalistic options (e.g., snacks, movies) — a claim which would severely undermine its theoretical importance. Huber, Payne, and Puto (2014) criticised Frederick et al.’s experiments, laying down a set of criteria that should be met by any experiment wishing to test for the attraction effect in real-world consumer choices. This article presents the first experiment that meets these criteria. The results show a precisely zero attraction effect.

Probability weighting explains Independence Axiom violations of Expected Utility Theory in monkeys

Probability weighting explains Independence Axiom violations of Expected Utility Theory in monkeys

Sharing the cost of cleaning up a polluted river

Consider a group of agents located along a polluted river where every agent must pay a certain cost for cleaning up the polluted river. Following the model of Ni and Wang (2007), we propose the class of alpha-Local Responsibility Sharing methods, which generalizes the Local Responsibility Sharing (LRS) method and the Upstream Equal Sharing (UES) method. We fi rst show that the UES method is characterized by relaxing independence of upstream costs appearing in Ni and Wang (2007). Then we provide two axiomatizations with endogenous responsibility of the alpha-Local Responsibility Sharing method, one using this weak independence axiom (taken from the UES method) and one using a weak version of the no blind cost axiom (taken from the LRS method). Moreover, we also provide an axiomatization with exogenous responsibility by introducing alpha-responsibility balance. Finally, we defi ne a pollution cost-sharing game, and show that, interestingly, the Half Local Responsibility Sharing (HLRS) method coincides with the Shapley value, the nucleolus and the tau-value of the corresponding pollution cost-sharing game. This HLRS method can be seen as some kind of middle compromise of the LRS and UES methods.

APPLICATION OF AXIOMATIC DESIGN THEORY IN THERMOFORMING APPARATUS DESIGN AND FABRICATION

In this article, the authors synthesized and analyzed research papers that utilized axiomatic design theory (ADT), both in scope of applications and pros and cons. After the benefits of ADT for design in particular and scientific research in general were carefully investigated, ADT was studied and translated from the author's original book. Accordingly, the axiomatic design is to consider the design in a scientific way, thereby providing a basic framework to understand design activities. ADT includes some basic concepts - domain and mapping, hierarchy, zigzagging, the independence axiom and the information axiom. Design tasks can be represented as mappings between domains. Designers map from the requirements of what they want to achieve to posible solutions. As the design progresses, broad, high level requirements are decomposed into smaller sub-requirements, which are then fulfilled by sub-solutions. When designers choose solutions, they utilize two design axioms to evaluate the quality of these solutions. Therefore, the axiomatic design provides guidance on how to make good decisions, promising to be a powerful tool for design activities in Vietnam. Finally, to master the theory, ADT is applied to the design of a thermoforming device. However, in this casestudy, only axiom 1, axiom of maintaining the independence of functional requirements was utilized; therefore, the next research will be to optimize the functional structures of the device, using the axiom 2, the axiom of minimizing information content.

Strategy-Proofness, Independence of Irrelevant Alternatives, and Majority Rule

We show that strategy-proofness, the Pareto principle, anonymity, neutrality, independence of irrelevant alternatives, and decisiveness uniquely characterize majority rule on any domain of preferences for which there exists a voting rule satisfying these axioms. In our formulation, strategy-proofness includes manipulations by coalitions. However, we demonstrate that the characterization still holds when coalitions are restricted to arbitrarily small size. We also show that when coalitions can manipulate outside the domain, there is an extension of majority rule that satisfies these axioms on any domain without Condorcet cycles. (JEL D72)

Integrated building design technology based on quality function deployment and axiomatic design methods: A case study

By 2050, the EU aims to become a Union where buildings will no longer emit greenhouse gases. The traditional building design process is becoming ineffective in meeting new sustainability challenges, which calls for a fundamentally different and more advanced design process. The paper presents the newly developed technology of building conceptual design, which integrates the Quality Function Deployment (QFD) and Axiomatic Design (AD) methods. The scope of the proposed design technology is to eliminate the drawbacks of traditional building design to ensure a smooth Integrated Building Design (IBD) among the project participants and a sustainable and customer oriented design solution. The validation of the technology has shown that, compared to the traditional design, it enables to decrease primary energy demand by 10 % with less design iterations to match the initial project requirements. The structured algorithm of the technology facilitated the communication between project groups. Nevertheless, the technology requires an additional team member – a design facilitator, which leads to additional expenses. The validation of the technology also highlighted that some limitations may appear due to the implementation of the Independence Axiom from AD.However, the technology is universal and can be easily adapted for different design areas outside of building design.

Preference aggregation and atoms in measures

This paper examines the aggregation of preferences with a finitely additive measure space of agents. We consider three types of non-dictatorship axioms: non-dictatorship, coalitional non-dictatorship, and atomic non-dictatorship. First, we show that the existence of an atom is a necessary and sufficient condition for the existence of a social welfare function that satisfies weak Pareto, independence of irrelevant alternatives, and coalitional non-dictatorship. Second, we simultaneously impose non-dictatorship and coalitional non-dictatorship, and specify a necessary and sufficient condition for the finitely additive measure that guarantees the compatibility among the axioms. Third, we impose all non-dictatorship axioms and show that the corresponding measure is extremely restricted.

New Hybrid AD Methodology for Minimizing the Total Amount of Information Content: A Case Study of Rehabilitation Robot Design

Converting customer needs into specific forms and providing consumers with services are crucial in product design. Currently, conversion is no longer difficult due to the development of modern technology, and various measures can be applied for product realization, thus increasing the complexity of analysis and evaluation in the design process. The focus of the design process has thus shifted from problem solving to minimizing the total amount of information content. This paper presents a New Hybrid Axiomatic Design (AD) Methodology based on iteratively matching and merging design parameters that meet the independence axiom and attribute constraints by applying trimming technology, the ideal final results, and technology evolution theory. The proposed method minimizes the total amount of information content and improves the design quality. Finally, a case study of a rehabilitation robot design for hemiplegic patients is presented. The results indicate that the iterative matching and merging of related attributes can minimize the total amount of information content, reduce the cost, and improve design efficiency. Additionally, evolutionary technology prediction can ensure product novelty and improve market competitiveness. The methodology provides an excellent way to design a new (or improved) product.

The ABC mechanism: an incentive compatible payoff mechanism for elicitation of outcome and probability transformations

When it comes to experiments with multiple-round decisions under risk, the current payoff mechanisms are incentive compatible with either outcome weighting theories or probability weighting theories, but not both. In this paper, I introduce a new payoff mechanism, the Accumulative Best Choice (“ABC”) mechanism that is incentive compatible for all rational risk preferences. I also identify three necessary and sufficient conditions for a payoff mechanism to be incentive compatible for all models of decision under risk with complete and transitive preferences. I show that ABC is the unique incentive compatible mechanism for rational risk preferences in a multiple-task setting. In addition, I test empirical validity of the ABC mechanism in the lab. The results from both a choice pattern experiment and a preference (structural) estimation experiment show that individual choices under the ABC mechanism are statistically not different from those observed with the one-round task experimental design. The ABC mechanism supports unbiased elicitation of both outcome and probability transformations as well as testing alternative decision models that do or do not include the independence axiom.

A model of discrete choice based on reinforcement learning under short-term memory

A family of models of individual discrete choice are constructed by means of statistical averaging of choices made by a subject in a reinforcement learning process, where the subject has a short, k-term memory span. The choice probabilities in these models combine in a non-trivial, non-linear way the initial learning bias and the experience gained through learning. The properties of such models are discussed and, in particular, it is shown that probabilities deviate from Luce’s Choice Axiom. Moreover, it is shown that the latter property is recovered as the memory span increases.Two different applications in utility theory are considered. In the first, we use the discrete choice model to generate a binary preference (weak stochastic order) relation on simple lotteries. We show that the relation violate the transitivity and independence axioms of expected utility theory. Furthermore, we establish the dependence of the preferences on frames, with risk aversion for gains, and risk seeking for losses. Based on these findings, we consider a parametric model of choice based on the probability maximization principle, as a model for deviations from the expected utility principle. To illustrate the approach, we apply this model to the classical problem of demand for insurance.

On expected utility theorems on mixture sets

This note discusses expected utility theorems on mixture sets by Herstein and Milnor (1953) and Fishburn (1970). We show that the Archimedean axiom in Fishburn’s expected utility theorem can be weakened to a one-sided Archimedean axiom. We also show that the mixture continuity and transitivity axioms in Herstein–Milnor expected utility theorem can be further weakened under the strong independence axiom.

Heterogenous Trip Distance-Based Route Choice Behavior Analysis Using Real-World Large-Scale Taxi Trajectory Data

Most early research on route choice behavior analysis relied on the data collected from the stated preference survey or through small-scale experiments. This manuscript focused on the understanding of commuters’ route choice behavior based on the massive amount of trajectory data collected from occupied taxicabs. The underlying assumption was that travel behavior of occupied taxi drivers can be considered as no different than the well-experienced commuters. To this end, the DBSCAN algorithm and Akaike information criterion (AIC) were first used to classify trips into different categories based on the trip length. Next, a total of 9 explanatory variables were defined to describe the route choice behavior, and and the path size (PS) logit model was then built, which avoided the invalid assumption of independence of irrelevant alternatives (IIA) in the commonly seen multinomial logit (MNL) model. The taxi trajectory data from over 11,000 taxicabs in Xi’an, China, with 40 million trajectory records each day were used in the case study. The results confirmed that commuters’ route choice behavior are heterogenous for trips with varying distances and that considering such heterogeneity in the modeling process would better explain commuters’ route choice behaviors, when compared with the traditional MNL model.

Estimation of porosity of rocks based upon axiomatic local linear model tree (a lolimot model) approach

Shear and Compressional Wave Velocities along with other Petrophysical Logs, are considered as upmost important data for Hydrocarbon reservoirs characterization. In this study, porosity of the extracted rocks form concerned wells is interest as it can indicate the oil capacity of the wells of interest. In this study, we employ the principles of Axiomatic Design theory, specially the first (independence) axiom, to more simplify the measurement system. Also, to clarify the strength of Axiomatic Design theory in reducing the complexity of the system and optimizing the measurement system, we utilize the The Lolimot model (LOcal LInear MOdel Tree) as a model from the neural network family and apply it before and after implementing the basic logic of Axiomatic Design (AD) theory. In addition, in order to illustrate strength of the proposed method emphasizing the effectiveness of a method which benefit from both AD theory and Lolimot model together, the existing system used to measure the rock porosity is addressed and actual data related to one of wells located in southern Iran is utilized. The results of the study show that integrating the Axiomatic Design principles with the LOLIMOT method leads to the least complex and most accurate results.

Stochastic expected utility for binary choice: a ‘modular’ axiomatic foundation

We present new axiomatisations for various models of binary stochastic choice that may be characterised as “expected utility maximisation with noise”. These include axiomatisations of simple scalability (Tversky and Russo in J Math Psychol 6:1–12, 1969) with respect to a scale having the expected utility (EU) form, and strong utility (Debreu in Econometrica 26(3):440–444, 1958) of the EU form. The latter model features Fechnerian “noise”: choice probabilities depend on EU differences. Our axiomatisations complement the important contributions of Blavatskyy (J Math Econ 44:1049–1056, 2008) and Dagsvik (Math Soc Sci 55:341–370, 2008). Our representation theorems set all models on a common axiomatic foundation, with additional axioms added in modular fashion to characterise successively more restrictive models. The key is a decomposition of Blavatskyy’s (2008) common consequence independence axiom into two parts: one (which we call weak independence) that underwrites the EU form of utility and another (stochastic symmetry) than underwrites the Fechnerian structure of noise. We also show that in many cases of interest (which we call preference-bounded domains) stochastic symmetry can be replaced with weak transparent dominance (WTD). For choice between lotteries, WTD only restricts behaviour when choosing between probability mixtures of a “best” and a “worst” possible outcome.

Orthomodular lattices as L-algebras

We first prove that the axioms system of orthomodular L-algebra (O-L-algebras for short) as given in [Rump: Forum Mathematicum, 30(4), 2018: 973–995] are not independent by giving an independent axiom one. Then, two conditions for KL-algebras to be Boolean are provided. Furthermore, some theorems of Holland are reproved using the self-similar closure of OM-L-algebras. In particular, the monoid operation of the self-similar closure is shown to be commutative.