Irrelevant Alternatives Research Articles

A simple solution to the problem of independence of irrelevant alternatives in Choo and Siow marriage market model

This paper proposes a simple solution to the independence of irrelevant alternatives (IIA) problem in Choo and Siow (2006b) model, overcoming what is probably the main limitation of this approach. The solution consists of assuming match-specific rather than choice-specific random preferences. The original marriage matching function gets modified by an adjustment factor that improves its empirical properties.

Negotiations in Competitive 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.

Discrete Choice Data with Unobserved Heterogeneity: A Conditional Binary Quantile Model

In political science, data with heterogeneous units are used in many studies, such as those involving legislative proposals in different policy areas, electoral choices by different types of voters, and government formation in varying party systems. To disentangle decision-making mechanisms by units, traditional discrete choice models focus exclusively on the conditional mean and ignore the heterogeneous effects within a population. This paper proposes a conditional binary quantile model that goes beyond this limitation to analyze discrete response data with varying alternative-specific features. This model offers an in-depth understanding of the relationship between the explanatory and response variables. Compared to conditional mean-based models, the conditional binary quantile model relies on weak distributional assumptions and is more robust to distributional misspecification. The model also relaxes the assumption of the independence of irrelevant alternatives, which is often violated in practice. The method is applied to a range of political studies to show the heterogeneous effects of explanatory variables across the conditional distribution. Substantive interpretations from counterfactual scenarios are used to illustrate how the conditional binary quantile model captures unobserved heterogeneity, which extant models fail to do. The results point to the risk of averaging out the heterogeneous effects across units by conditional mean-based models.

Product line optimisation based on semiparametric choice model

Consumer choice behaviour is important in the product line optimisation problem. The extant literature on product line optimisation is mostly based on traditional consumer choice models, such as the multinomial logit and multinomial probit models. These models either assume that the utility errors are independent from irrelevant alternatives (IIA) or are limited by complex calculation processes or pre-given, specific distributions of measuring errors. The marginal moment model (MMM), which is classified as a semiparametric choice model, does not require specific distributions of errors; thus, it can overcome the IIA shortcoming. This study focuses on the concavity of the profit functions of a product line optimisation model based on MMM. We prove that the profit function based on MMM is concave in market share under a monopoly or oligopoly. Numerical experiments show that the choice probabilities obtained from the MMM, multinomial logit, and multinomial probit models are similar although they are obtained under different assumptions. Experimental results under monopolistic, Cournot, and Bertrand competition based on MMM are compared. Some interesting managerial insights are summarised based on the sensitivity analysis of the various model parameters.

A Simple Solution to the Problem of Independence of Irrelevant Alternatives in Choo and Siow Marriage Market Model

This paper proposes a simple solution to the independence of irrelevant alternatives (IIA) problem in Choo and Siow (2006) model, overcoming what is probably the main limitation of this approach. The solution consists of assuming match-specific rather than choice-specific random preferences. The original marriage matching function gets modified by an adjustment factor that improves its empirical properties. Using the American Community Survey, I show that the new approach yields significantly different results affecting the qualitative conclusions of the analysis. The proposed solution to the IIA problem applies to other settings in which the relative supply'' of choices is observable.

Bounded rationality in C. elegans is explained by circuit-specific normalization in chemosensory pathways

Rational choice theory assumes optimality in decision-making. Violations of a basic axiom of economic rationality known as “Independence of Irrelevant Alternatives” (IIA) have been demonstrated in both humans and animals and could stem from common neuronal constraints. Here we develop tests for IIA in the nematode Caenorhabditis elegans, an animal with only 302 neurons, using olfactory chemotaxis assays. We find that in most cases C. elegans make rational decisions. However, by probing multiple neuronal architectures using various choice sets, we show that violations of rationality arise when the circuit of olfactory sensory neurons is asymmetric. We further show that genetic manipulations of the asymmetry between the AWC neurons can make the worm irrational. Last, a context-dependent normalization-based model of value coding and gain control explains how particular neuronal constraints on information coding give rise to irrationality. Thus, we demonstrate that bounded rationality could arise due to basic neuronal constraints.

Optimal policy for multi-alternative decisions.

Everyday decisions frequently require choosing among multiple alternatives. Yet the optimal policy for such decisions is unknown. Here we derive the normative policy for general multi-alternative decisions. This strategy requires evidence accumulation to nonlinear, time-dependent bounds that trigger choices. A geometric symmetry in those boundaries allows the optimal strategy to be implemented by a simple neural circuit involving normalization with fixed decision bounds and an urgency signal. The model captures several key features of the response of decision-making neurons as well as the increase in reaction time as a function of the number of alternatives, known as Hick's law. In addition, we show that in the presence of divisive normalization and internal variability, our model can account for several so-called 'irrational' behaviors, such as the similarity effect as well as the violation of both the independence of irrelevant alternatives principle and the regularity principle.

Cache Me if You Can: Capacitated Selfish Replication Games in Networks

In Peer-to-Peer (P2P) network systems, content (object) delivery between nodes is often required. One way to study such a distributed system is by defining games, which involve selfish nodes that make strategic choices on replicating content in their local limited memory (cache) or accessing content from other nodes for a cost. These Selfish Replication games have been introduced in Chun et al. (2004) for nodes that do not have any capacity limits, leaving the capacitated problem, i.e. Capacitated Selfish Replication (CSR) games, open. In this work, we first form the model of the CSR games, for which we perform a Nash equilibria analysis. In particular, we focus on hierarchical networks, given their extensive use to model communication costs of content delivery in P2P systems. We present an exact polynomial-time algorithm for any hierarchical network, under two constraints on the utility functions: 1) “Nearer is better”, i.e. the closest the content is to the node the less its access cost is, and 2) “Independence of irrelevant alternatives”, i.e. aggregation of individual node preferences. This generalization represents a vast class of utilities and more interestingly allows each of the nodes to have simultaneously completely different functional forms of utility functions. In this general framework, we present CSR games results on arbitrary networks and outline the boundary between intractability and effective computability in terms of the network structure, object preferences, and the total number of objects. Moreover, we prove that the problem of equilibria existence becomes NP-hard for general CSR games. By adding some constraints in the number of objects and their preferences, we show that the equilibrium can be found in polynomial time. Finally, we introduce the fractional version of CSR games (F-CSR) to represent content distribution. We prove that equilibrium exists for every F-CSR game, but it is PPAD-complete.

Irrational behavior in C. elegans arises from asymmetric modulatory effects within single sensory neurons

C. elegans worms exhibit a natural chemotaxis towards food cues. This provides a potential platform to study the interactions between stimulus valence and innate behavioral preferences. Here we perform a comprehensive set of choice assays to measure worms’ relative preference towards various attractants. Surprisingly, we find that when facing a combination of choices, worms’ preferences do not always follow value-based hierarchy. In fact, the innate chemotaxis behavior in worms robustly violates key rationality paradigms of transitivity, independence of irrelevant alternatives and regularity. These violations arise due to asymmetric modulatory effects between the presented options. Functional analysis of the entire chemosensory system at a single-neuron resolution, coupled with analyses of mutants, defective in individual neurons, reveals that these asymmetric effects originate in specific sensory neurons.

Choice on the simplex domain

One unit of a good has to be divided among a group of agents who each are entitled to a minimal share, and these shares sum up to less than one. The associated set of choice problems consists of the unit simplex and all its full-dimensional subsimplices with the same orientation. We characterize all choice rules that are independent of irrelevant alternatives, continuous, and monotonic; the last condition means that if an agent receives its minimal share and that share increases, then no other agent benefits. In line with Kıbrıs (2012) we show that these rules are rationalizable and representable by a real-valued function. On the issue of rationalizability, we also consider weakenings of our conditions. In particular, we show that in general, excluding cycles of any fixed length does not imply the strong axiom of revealed preference, that is, the exclusion of cycles of any length. For continuous three-agent choice rules, however, excluding cycles of length three implies the strong axiom of revealed preference.

The possibility of Paretian anonymous decision-making with an infinite population

This paper considers the trade-off between unanimity and anonymity in collective decision-making with an infinite population. This efficiency-equity trade-off is afundamental difficulty in making a normative judgment in a conflict betweengenerations. In particular, it is known that this trade-off is quite sensitive in the formulation of unanimity axioms. In this study, we consider the trade-off in a preference-aggregation framework instead of the standard utility-aggregationframework. We show that there exists a social welfare function that satisfies I-strong Pareto, independence of irrelevant alternatives, and finite anonymity. This contrasts with an impossibility result in the standard utility-aggregation framework, and this means that the trade-off is also sensitive for background frameworks of aggregations.

Consumer Choice with Consideration Set: Threshold Luce Model

This paper investigates the threshold Luce model, a recently proposed choice model with a threshold for the consideration-set formation. Under the threshold Luce model, consumers first form their consideration set: If an alternative with significantly low utility is dominated by another one, it will not be included in the consideration set. The threshold Luce model can alleviate the independence of irrelevant alternatives (IIA) property and allow more flexible substitution patterns. We characterize the optimal strategy and develop efficient solutions for price and assortment optimization problems. Under the threshold Luce model, the price competition may have zero, one, two, or infinite Nash equilibria, depending on the magnitude of the threshold effect. Moreover, we also develop an efficient estimation method to calibrate the threshold Luce model. Our numerical study on synthetic and real data sets shows that the new model can improve the goodness of fit and prediction accuracy of consumer choice behavior, which suggests the threshold effect should be taken into account in decision making.

POSITIVELY RESPONSIVE COLLECTIVE CHOICE RULES AND MAJORITY RULE: A GENERALIZATION OF MAY'S THEOREM TO MANY ALTERNATIVES

AbstractMay's theorem shows that if the set of alternatives contains two members, an anonymous and neutral collective choice rule is positively responsive if and only if it is majority rule. We show that if the set of alternatives contains three or more alternatives only the rule that assigns to every problem its strict Condorcet winner satisfies the three conditions plus Nash's version of “independence of irrelevant alternatives” for the domain of problems that have strict Condorcet winners. We show also that no rule satisfies the four conditions for domains that are more than slightly larger.

Cross-Category Retailing Management: Substitution and Complementarity

This paper studies pricing and assortment management for cross-category products, a common practice in brick-and-mortar retailing and e-tailing. We investigate the complementarity effects between the main products and the secondary products, in addition to the substitution effects for products in the same category. In this paper, we develop a multi-stage sequential choice model, under which a consumer first chooses a main product and then selects a secondary product. The new model can alleviate the restriction of the independence of irrelevant alternatives (IIA) property, and allows more flexible substitution patterns and also takes into account complementarity effects. We characterize the impact of the magnitude of complementarity effects on pricing and assortment management. For the problems that are hard to solve optimally, we propose simple heuristics and establish performance guarantee. In addition, we develop easy-to-implement estimation algorithms to calibrate the proposed sequential choice model by using sales data. We show that ignoring or mis-specifying complementarity effects may lead to substantial losses. The methodologies on modeling, optimization and estimation have potential to make impact on cross-category retailing management.

The limitations of the Arrovian consistency of domains with a fixed preference

In this paper I investigate the properties of social welfare functions defined on domains where the preferences of one agent remain fixed. Such a domain is a degenerate case of those investigated, and proved Arrow consistent, by Sakai and Shimoji (Soc Choice Welf 26(3):435–445, 2006). Thus, they admit functions from them to a social preference that satisfy Arrow’s conditions of Weak Pareto, Independence of Irrelevant Alternatives, and Non-dictatorship. However, I prove that according to any function that satisfies these conditions on such a domain, for any triple of alternatives, if the agent with the fixed preferences does not determine the social preference on any pair of them, then some other agent determines the social preference on the entire triple.

Product optimization with the improved marginal moment model

ABSTRACT The probabilistic choice model is an important theory foundation for investigating consumer choice behavior in product optimization. In most studies, probabilistic choice behavior is simulated by the multinomial logit (MNL) model and a product always obtains some market share even though the utility a consumer obtains from buying the product is negative. However, the MNL model has a very restrictive substitution pattern – the independence of irrelevant alternatives (IIA). This paper investigates a product optimization problem based on the marginal moment model (MMM). Residual utility is involved in the MMM and negative utility is considered as well. The optimization model of product line design, based on the improved MMM, is established to maximize total profit through three types of problems. The established model fits reality better because the MMM does not have the IIA problem and has good statistical performance. Numerical experiments are carried out to evaluate the feasibility of the proposed model. Meanwhile, the relationships are explored between the optimal solutions and several factors, including the competitive products’ prices, utility variance, rate of cost reduction, and utility of competitive products.

Multi-agent soft constraint aggregation via sequential voting: theoretical and experimental results

We consider scenarios where several agents must aggregate their preferences over a large set of candidates with a combinatorial structure. That is, each candidate is an element of the Cartesian product of the domains of some variables (i.e., features). These scenarios are very common when candidates are described by feature vectors, such as cars, or houses, or any complex product. We assume agents to compactly express their preferences over the candidates via soft constraints. This is a compact way to model preferences which naturally models variables domains, and relationship among variables. To aggregate the preferences of the agents, we consider a sequential procedure that asks the agents to vote on one variable at a time. At each step, all agents express their preferences over the domain of a variable; based on such preferences, a voting rule is used to select one value for that variable. When all variables have been considered, the selected values constitute the returned variable assignment, that is, the elected candidate. We study several properties of this procedure (such as Condorcet consistency, anonymity, neutrality, monotonicity, consistency, efficiency, participation, independence of irrelevant alternatives, non dictatorship, and strategy-proofness), by relating them to corresponding properties of the adopted voting rules used for each variable. Moreover, we perform an experimental study on a special kind of soft constraints, namely fuzzy constraints. The experimental study shows that the proposed sequential procedure yields a considerable saving in time with respect to a non-sequential approach, while the winners satisfy the agents just as well, independently of the variable ordering, and of the presence of coalitions of agents.

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.

Product Line Pricing under Marginal Moment Model with Network Effect

The complex network effect of the product exhibits has a significant impact on the product line optimization design. The multinomial logit (MNL) model which is used to simulate consumer choice behavior is applied in most of product line optimization problems. However, its assumptions, independence of irrelevant alternatives (IIA) and the same Gumbel distribution of random error terms, are usually difficult to be met in practice. The marginal moment model (MMM) can be used when the mean and variance of consumer’s utility error are known. The MMM not only has weak assumption conditions but also overcomes the IIA problem of MNL model. In this paper, we study the product pricing problem based on MMM with endogenous negative network effect. Firstly, we construct a variant of MMM considering network effect in product line optimization design. Secondly, we prove that the revenue function is concave in market share. We propose the solving methods of the model to obtain the optimal price, the corresponding market share, and the revenue under three different scenarios, i.e., developing single product, homogeneous products, and heterogeneous products. Finally, numerical experiments show that the proposed model can better simulate consumer choice behavior and potentially increase revenue.

Behavioral Foundations of Nested Stochastic Choice and Nested Logit

We provide the first behavioral characterization of nested logit, a foundational and widely applied model in discrete choice. We take a revealed preference approach to identify the underlying notion of similarity and use it to characterize a non-parametric version of nested logit we call Nested Stochastic Choice(NSC). We characterize NSC with a single axiom that weakens Independence of Irrelevant Alternatives(IIA) based on revealed similarity to allow for the similarity effect. Nested logit is then characterized by one additional axiom that imposes a weak form of menu-independence. We show that a widely applied generalization, cross-nested logit, lacks testable implications.