Irrelevant Alternatives Research Articles

Stochastic Choice and Attention Capacities: Inferring Preferences from Psychological Biases

This paper shows that frequently observed violations of IIA (Independence of Irrelevant Alternatives), namely the similarity and attraction effect can be compatible with the maximization of rational preferences and the violations themselves can be used to infer the underlying rational preference relation. In order to do this, I introduce a new choice rule that is based on the evidence that decision makers do not pay attention to all items in a menu. Nevertheless they have an underlying rational preference. The Fuzzy Attention Model (FAM) is characterized by an axiom based on revealed stochastic choice akin to the Strong Axiom of Revealed Preference (SARP). The model explains both effects by introducing the idea of an attention capacity that allows for complementarity and substitutability in attention. The similarity effect is related to substitutability while the attraction effect has to do with complementarity. The FAM nests the literature on random consideration sets proposed by Manzini and Mariotti (2014) and the standard rational model, but is not nested in the random utility framework.

Nash bargaining with (almost) no rationality

I axiomatize the n-person asymmetric Nash bargaining solution on the basis of independence of irrelevant alternatives, independence of equivalent utility representations, feasible set continuity, and conflict-freeness—the requirement that the solution selects the ideal point whenever it is feasible to do so.

A Solution to Arrow's General Possibility Theorem: Contracting Through Negotiations

This paper is comprised of the greater part of Chapter 2 of my doctoral thesis at SMC University. It approaches Social Choice Theory as a distinctively different way of examining economic activity, one that more closely corresponds to the way in which economic actors organize activity in the pursuit of their ends. Unlike neo-classical economics, Social Choice Theory assumes from the beginning that human action is driven by a desire to achieve social orderings consistent with each person’s personal subjective preferences. When numerous individuals, all inhabitants of the same societal order, attempt this, the theory states that all cannot achieve their preferred orderings simultaneously. This is the content of Arrow’s (1963) well known General Possibility Theorem. Inevitably, there must be compromise. This paper investigates the condition under which these compromises can be made. A particularly difficult question arises in the handling of Arrow’s assumption of the independence of irrelevant alternatives. These are interpreted as the result of risk and uncertainty in determining their impact on social ordering. Their irrelevance therefore cannot be precisely known. Parties to any transaction will differ as to their expectations. Negotiations over risk and in the context of uncertainty are part of any economic transaction. A particularly generalizing manner of handling this issue is through a process originating in a what Rawls called the veil of ignorance where risk and uncertainty are essentially total. Rawls concludes his analysis by advocating lexical principles of justice and a distribution governed by the difference principle. Modified, and somewhat less absolutizing, versions of this theory are found in Harsanyi’s similarity postulate, and in Buchanan’s analysis of the social role of a constitution.

Context-dependent evaluation of prospective mates in a fish.

Female choice is often assumed to be based on absolute preference, driven by a threshold value of mate attractiveness. However, increasing evidence suggests that females may instead perform a comparative evaluation of prospective mates, possibly incurring in violation of rational decision rules (e.g. independence from irrelevant alternative, IIA). A prototypical case is the ‘asymmetrically dominated decoy’ effect where the preference for a target option over a competitor is altered by the addition of an irrelevant alternative. Here, we test for this effect in the peacock blenny Salaria pavo. Females, in binary test (i.e. focal option dyad differing in body size and extension of a yellow spot), strongly preferred one of the options. The effect of decoys, asymmetrically dominating the focal options for either yellow spot extension or body size, varied according to the initially preferred trait and the decoy type. Indeed, the addition of a decoy caused a shift in preference only when the decoy exhibited the intermediate expression of the trait less preferred initially. By contrast, females did not modify their preference in the presence of the decoy for their preferred trait. Although females’ evaluation was context-dependent, the violation of IIA was clearly observed only with respect to the initially less preferred trait. This does not exclude that females are in any case using comparative decision rules. Indeed, when faced with three alternatives, two of which are proportionally closer to each other than to the third one, they might not be able to discriminate among them, perceiving stimulus absolute magnitude.

IIA, rationality, and the individuation of options

The independence of irrelevant alternatives (IIA) is a popular and important axiom of decision theory. It states, roughly, that one’s choice from a set of options should not be influenced by the addition or removal of further, unchosen options. In recent debates, a number of authors have given putative counterexamples to it, involving intuitively rational agents who violate IIA. Generally speaking, however, these counterexamples do not tend to move IIA’s proponents. Their strategy tends to be to individuate the options that the agent faces differently, so that the case no longer counts as a violation of IIA. In this paper, we examine whether this strategy succeeds. We argue that the ways of individuating options required to save IIA from the most problematic counterexamples—in particular, cases where agents violate IIA due to nonconsequentialist moral beliefs—do so only at the expense of severely compromising its central function within decision theory.

A nested recursive logit model for route choice analysis

We propose a route choice model that relaxes the independence from irrelevant alternatives property of the logit model by allowing scale parameters to be link specific. Similar to the recursive logit (RL) model proposed by Fosgerau et al. (2013), the choice of path is modeled as a sequence of link choices and the model does not require any sampling of choice sets. Furthermore, the model can be consistently estimated and efficiently used for prediction.A key challenge lies in the computation of the value functions, i.e. the expected maximum utility from any position in the network to a destination. The value functions are the solution to a system of non-linear equations. We propose an iterative method with dynamic accuracy that allows to efficiently solve these systems.We report estimation results and a cross-validation study for a real network. The results show that the NRL model yields sensible parameter estimates and the fit is significantly better than the RL model. Moreover, the NRL model outperforms the RL model in terms of prediction.

Axiomatizing core extensions on NTU games

We study solution concepts for NTU games, where the cooperation (or negotiation) of the players can be obtained by means of non-trivial families of coalitions (e.g. balanced families). We give an axiomatization of the aspiration core on the domain of all NTU games as the only solution that satisfies non-emptiness, individual rationality, a generalized version of consistency and independence of individual irrelevant alternatives. If we consider solutions supported by partitions, our axioms characterize the c-core [Guesnerie and Oddou in, Econ Lett 3(4):301–306, 1979; Sun et al. in, J Math Econ 44(7–8):853–860, 2008], and if we consider solutions supported only by the grand coalition, our axioms also characterize the classical core, on appropriate subdomains. The main result of this paper generalizes Peleg’s core axiomatization [J Math Econ 14(2):203–214, 1985] to non-empty solutions that are supported by non-trivial families of coalitions.

Mean-median compromise method as an innovating voting rule in social choice theory

This paper aims at presenting a new voting function which is obtained in Balinski-Laraki's framework and benefits mean and median advantages. The so-called Mean-Median Comprise Method (MMCM) has fulfilled criteria such as unanimity, neutrality, anonymity, monotonicity, and Arrow's independence of irrelevant alternatives. It also generalizes approval voting system.

A characterization of the asymmetric Nash solution

The asymmetric Nash bargaining solution is characterized on the basis of independence of irrelevant alternatives, independence of equivalent utility representations, and a new axiom—moderate collective rationality. The latter is logically weaker than Roth’s (Math Oper Res 2:64–65, 1977) strong individual rationality and logically stronger than Anbarci and Sun’s (Soc Choice Welf 37:425–429, 2011) weakest collective rationality.

Studying Rules Changes in the U.S. House: Evidence from an Alternative Empirical Model

Binder (1996) and Schickler (2000) define the current debate as to why the U.S. House has changed its standing rules regarding the majority rule and the minority rights. I revisit their empirical models—binary logit and ordered logit—and theoretically and statistically test the appropriateness of these models. I find that both of them are actually choosing inappropriate models. Their theoretical claims cannot be properly examined by utilizing their choices of models. In addition, the data do not satisfy the “parallel regression” assumption but do satisfy the “independence of irrelevant alternatives” assumption, which supports using an alternative multinomial logit model. I further extend the model, and find the dynamic nature of rules changes in the U.S. House. It appears there is no symmetry between the rules changes that promote the majority rule and the rules changes that enhance the minority rights.

Modeling Absolute and Relative Cost Differences in Stochastic User Equilibrium Problem

This paper aims to develop a hybrid closed-form route choice model and the corresponding stochastic user equilibrium (SUE) to alleviate the drawbacks of both Logit and Weibit models by simultaneously considering absolute cost difference and relative cost difference in travelers’ route choice decisions. The model development is based on an observation that the issues of absolute and relative cost differences are analogous to the negative exponential and power impedance functions of the trip distribution gravity model. Some theoretical properties of the hybrid model are also examined, such as the probability relationship among the three models, independence from irrelevant alternatives, and direct and indirect elasticities. To consider the congestion effect, we provide a unified modeling framework to formulate the Logit, Weibit and hybrid SUE models with the same entropy maximization objective but with different total cost constraint specifications representing the modelers’ knowledge of the system. With this, there are two ways to interpret the dual variable associated with the cost constraint: shadow price representing the marginal change in the entropy level to a marginal change in the total cost, and dispersion/shape parameter representing the travelers’ perceptions of travel costs. To further consider the route overlapping effect, a path-size factor is incorporated into the hybrid SUE model. Numerical examples are also provided to illustrate the capability of the hybrid model in handling both absolute and relative cost differences as well as the route overlapping problem in travelers’ route choice decisions.

Contest Success Functions: The Common-Pool Perspective

The axiomatic route to the foundation of contest success functions (CSF) has proved to be both useful and prolific. The standard approach in the literature is based on the decision-theoretic notion that choice probabilities should be independent of irrelevant alternatives (Skaperdas, Economic Theory 1996). The present paper develops an alternative approach that suggests itself once the contest is re-interpreted as a common-pool resource problem. Proceeding along these lines, new axiomatizations are obtained for a variety of popular classes of CSFs, including the logit, Tullock, and difference-form CSFs. The axiomatizations provided are particularly parsimonious in the important special case of two contestants.

Weak Independence and Social Semi-Orders

This paper provides variants of Arrow’s impossibility theorem, which states that there exists no non-dictatorial aggregation rule satisfying weak Pareto, independence of irrelevant alternatives and collective rationality. In this paper, independence of irrelevant alternatives and collective rationality are simultaneously relaxed. Weak independence is imposed instead of independence of irrelevant alternatives. Social preferences are assumed to satisfy the semi-order properties of semi-transitivity and the interval-order property. We prove that there exists a vetoer when the number of alternatives is greater than or equal to six.

A critique of benchmark theory

Benchmark theory (BT), introduced by Ralph Wedgwood, departs from decision theories of pure expectation maximization like evidential decision theory (EDT) and causal decision theory (CDT) and instead ranks actions according to the desirability of an outcome they produce in some state of affairs compared to a standard—a benchmark—for that state of affairs. Wedgwood motivates BT through what he terms Gandalf’s principle, that the merits of an action in a given state should be evaluated relative only to the performances of other actions in that state, and not to their performances in other states. Although BT succeeds in selecting intuitively rational actions in a number of cases—including some in which EDT or CDT seem to go wrong—it places constraints on rational decision-making that either lack motivation or are untenable. Specifically, I argue that as it stands BT is committed both to endorsing and rejecting the independence of irrelevant alternatives. Furthermore its requirement that weakly dominated actions be excluded from consideration of rational action lacks motivation and threatens to collide with traditional game theory. In the final section of the paper, I construct a counterexample to BT.

A quest for fundamental theorems of social choice

We explore the frontier between possibility and impossibility results by analyzing different combinations of "pro-socialness" and "consistency" conditions. This exercise delivers stronger versions of four classical impossibility theorems, and offers a thorough understanding of connections among them. We also characterize social choice functions that are "independent of irrelevant alternatives," which makes evident that the fundamental difficulty of social choice lies in "pairwise" consistency requirements. We also introduce a concise pedagogical approach to classical impossibility theorems.

On $$\mathcal {S}$$ S -independence and Hansson’s external independence

This paper provides a generalized characterization of the family of independence conditions which are equivalent to independence of irrelevant alternatives by proposing a pair-based refinement of \(\mathcal {S}\)-independence. Equipped with the new result, the relation between external independence conditions and independence of irrelevant alternatives is explored.

Modeling and Sensitivity Analysis for Railway Passengers’ Public Transit Mode Choice

Comprehensive terminal integrates different modes of transport and sharing rates of different traffic modes influence its planning greatly. To determine the sharing rates, it’s necessary to study mode choice probability of passengers. Based on the theory of disaggregate choice, with the survey of mode choices of passengers arriving by rail in Nanjing south railway station, this paper establishes multinomial logit (MNL) model and nest logit (NL) model, considering three types of modes of transport including the subway, regular bus, and taxi. Models are calibrated with SPSS and validated through statistical indicators. Therefore, important factors influencing choice are obtained. The accuracy test results of two kinds of models show that NL model has higher prediction accuracy, and can overcome the shortcomings of traditional logit model’s independent and irrelevant alternatives (IIA). Finally, this paper develops the sensitivity analysis using the NL upper model as an example, and gives the sensitivity physical meaning, namely the development level of taxi.

Public preference for the attributes of the marina port in Korea: a choice experiment study

As of late, the Korean government needs quantitative information on economic feasibility analysis for marina port development projects. This study applies a choice experiment to measure public preference for the attributes of marina port in Korea. We consider the trade-offs between price and four attributes of marina port (capacity, access, waterfront, and program) for selecting a preferred alternative and elicit the marginal willingness to pay (MWTP) estimates for each attribute. We also test whether irrelevant alternatives property for the estimation model holds and compare the estimation results of the multinomial logit (MNL) and the nested logit (NL) models. The results show that the NL model outperforms the MNL model. In the NL model, MWTPs for increasing the level of a waterfront from promenade to both promenade and rest area and for the provision of marine leisure experience program are KRW13 384 (USD11.8) and KRW17 937 (USD15.8), respectively. This study is expected to provide policymakers with quantitative information for evaluating marina port construction projects in Korea.

Collective rationality and monotone path division rules

We impose the axiom Independence of Irrelevant Alternatives on division rules for the conflicting claims problem. With the addition of Consistency and Resource Monotonicity, this characterizes a family of rules which can be described in three different but intuitive ways. First, a rule is identified with a fixed monotone path in the space of awards, and for a given claims vector, the path of awards for that claims vector is simply the monotone path truncated by the claims vector. Second, a rule is identified with a set of parametric functions indexed by the claimants, and for a given claims problem, each claimant receives the value of his parametric function at a common parameter value, but truncated by his claim. Third, a rule is identified with an additively separable, strictly concave social welfare function, and for a given claims problem, the amount awarded is the maximizer of the social welfare function subject to the constraint of choosing a feasible award.

Identifying local determinants of destination choices of international immigrants to the Madrid metropolitan area

AbstractWe examine the local determinants of destination choices of foreign immigrants to the Madrid metro area using data for 2005 and 2009 from the Spanish annual municipal‐level registers of inhabitants. Taking advantage of the equivalence relation between conditional logit and Poisson, we estimate a location‐choice model using the Poisson fixed‐effects estimator. Origin‐destination fixed effects are incorporated to account for the persistent spatial structure of the immigrants' settlement patterns and to control for potential violations of the independence of irrelevant alternatives (IIA) assumption. The Poisson regression model is estimated for seven different groups of immigrants according to world regions or countries of origin. Our modelling strategy has important empirical implications, with magnitudes and/or signs of the estimated coefficients changing in the expected directions. It is found that newly arriving immigrants tend to settle in low‐to‐middle‐income locations in the suburban reaches of the Madrid metro area. Moreover, the effects of the size of local communities of established immigrants are found to be insignificant and even negative in several instances, reflecting hetero‐local settlement preferences and/or the saturation of local networks causing in‐group job rivalry, respectively.