Independence of Irrelevant Alternatives

Individual choice behavior usually involves a complex decision-making process, and is often contextdependent reflecting the influence of choice environment and the fact that the individual has limited information processing ability and varying levels of interest in alternatives. However, the existing models in transportation have not represented these behavioral mechanisms satisfactorily, although to avoid the Independence of Irrelevant Alternatives (IIA) property of the widely used multinomial logit (MNL) model, a variety of non-IIA models have been suggested in the literature. This paper will propose another random utility choice model by introducing the concepts of relative utility and relative interest. A revised MNL model and a revised Nested-MNL model will be developed. Both of these models do not have the IIA property. The performance of these new models will be assessed using conjoint-based activity diary data about the choice of destination and stop pattern.

In this paper we introduce a new flexible mixed model for multinomial discrete choice where the key individual-and alternative-specific parameters of interest are allowed to follow an assumptionfree nonparametric density specification while other alternative-specific coefficients are assumed to be drawn from a multivariate normal distribution which eliminates the independence of irrelevant alternatives assumption at the individual level. A hierarchical specification of our model allows us to break down a complex data structure into a set of submodels with the desired features that are naturally assembled in the original system. We estimate the model using a Bayesian Markov Chain Monte Carlo technique with a multivariate Dirichlet Process (DP) prior on the coefficients with nonparametrically estimated density. We employ a "latent class" sampling algorithm which is applicable to a general class of models including non-conjugate DP base priors. The model is applied to supermarket choices of a panel of Houston households whose shopping behavior was observed over a 24-month period in years 2004-2005. We estimate the nonparametric density of two key variables of interest: the price of a basket of goods based on scanner data, and driving distance to the supermarket based on their respective locations. Our semi-parametric approach allows us to identify a complex multi-modal preference distribution which distinguishes between inframarginal consumers and consumers who strongly value either lower prices or shopping convenience.

This paper reconsiders the discussion on ordinal utilities versus preference intensities in voting theory. It is shown by way of an example that arguments concerning observability and riskattitudes that have been presented in favour of Arrow's Independence of Irrelevant Alternatives (IIA), and against utilitarian evaluation, fail due to strategic voting. The failure of these two arguments is then used to justify utilitarian evaluation of outcomes in voting. Given a utilitarian viewpoint, it is then argued that strategy-proofness is not normatively acceptable. Social choice theory is criticised not just by showing that some of its most important conditions are not normatively acceptable, but also by showing that the very idea of imposing condition on social choice function under the assumption of sincere behaviour does not make much sense because satisfying a condition does not quarantee that a voting rule actually has the properties that the condition confers to it under sincere behaviour. IIA, the binary intensity IIA, and monotonicity are used as illustrations of this phenomenon.

Modern-day environmental policies or programs, such as watershed ecosystem restoration, are designed to improve multiple ecosystem services and consist of multiple components or parts. The valuation of such policies or programs should address the multi-dimensionality of the problem. A hybrid of the contingent valuation method (CVM) and attribute-based analysis (Holmes and Adamowicz 2003) is often used. Several related policy options are included in the survey, which

The feasibility of new shopping centers is largely related to their relative location and spending power in the trade area. Commercial developers, retailers, and retail planners need information about the likely impact of new retail developments on consumer choice behavior. Several types of consumer choice models have been applied to assess the effects of retail developments.

We study how to evaluate allocations independently of individual preferences over unavailable commodities. We prove impossibility results suggesting that such evaluations encounter serious difficulties. This is related to the well-known problem of performing international comparisons of standard of living across countries with different consumption goods. We show how possibility results can be retrieved with restrictions on the domain of preferences, on the application of the independence * We thank the Editor, L. Samuelson, and three referees for very helpful comments and suggestions.

Social choice theory understands a voting rule as a mapping from preferences over possible outcomes to a specific choice or choices. However, actual election procedures often do not have this structure. Rather, in a typical election, although the outcome is an assembly comprising several people occupying different seats, voters cast their ballots for individual candidates, and these candidates have their votes tallied on a seat-by-seat basis. We prove two theorems: the only efficient seat-by-seat procedure is a dictatorship and the only neutral seat-by-seat procedure is a dictatorship. * We thank Juan Dubra for his many comments.

Researchers and analysts are increasingly using mixed logit models for estimating responses to forecast demand and to determine the factors that affect individual choices. These models are interesting in that they allow for taste variations between individuals and they do not exhibit the independent of irrelevant alternatives property. However the numerical cost associated to their evaluation can be prohibitive, the

OLS becomes inefficient. Determination of wages generally causes a high correlation between the non-observable characteristics affecting wages and those that simultaneously determine the sector in which the individuals are currently /located/ functioning (working).

Data envelopment analysis (DEA) is proposed in this paper to generate local weights of alternatives from pair-wise comparison judgment matrices used in the analytic hierarchy process (AHP). The underlying assumption behind the approach is explained, and some salient features are explored. It is proved that DEA correctly estimates the true weights when applied to a consistent matrix formed using a known set of weights. DEA is further proposed to aggregate the local weights of alternatives in terms of different criteria to compute final weights. It is proved further that the proposed approach, called DEAHP in this paper, does not suffer from rank reversal when an irrelevant alternative(s) is added or removed.

Several recent studies of voter choice in multiparty elections point to the advantages of multinomial probit (MNP) relative to multinomial/conditional logit (MNL). We compare the MNP and MNL models and argue that the simpler logit is often preferable to the more complex probit for the study of voter choice in multi-party elections. Our argument rests on three areas of comparison between MNP and MNL. First, within the limits of typical data-a small sample of revealed voter choices among a few candidates or parties-neither model will clearly appear to have generated the observed data. Second, MNP is susceptible to a number of estimation problems, the most serious of which is that the MNP is often weakly identified in application. Weak identification is difficult to diagnose and may lead to plausible, yet arbitrary or misleading inferences. Finally, the logit model is criticized because it imposes the independence of irrelevant alternatives (IIA) property on voter choice. For most applications the IIA property is neither relevant nor particularly restrictive. We illustrate our arguments using data from recent US and French presidential elections. 

Overcoming the independence of irrelevant alternatives (IIA) property of the basic Multinomial Logit (MNL) model is a major research issue in the field of discrete choice modelling. In recent years, several approaches have been developed to achieve this goal with different degrees of appropriateness.

Arrow's celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and nondictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about indifference hypersurfaces is needed to construct social ordering functions satisfying the weak Pareto principle and anonymity. We show that local information such as marginal rates of substitution or the shapes "within the Edgeworth box" is not enough, and knowledge of substantially non-local information is necessary.

We characterize the Nash bargaining solution replacing the axiom of Independence of Irrelevant Alternatives with three independent axioms: Independence of Non-Individually Rational Alternatives, Twisting, and Disagreement Point Convexity. We give a non-cooperative bargaining interpretation to this last axiom.

Individual choice behavior usually involves a complex decision-making process, and is often contextdependent reflecting the influence of choice environment and the fact that the individual has limited information processing ability and varying levels of interest in alternatives. However, the existing models in transportation have not represented these behavioral mechanisms satisfactorily, although to avoid the Independence of Irrelevant Alternatives (IIA) property of the widely used multinomial logit (MNL) model, a variety of non-IIA models have been suggested in the literature. This paper will propose another random utility choice model by introducing the concepts of relative utility and relative interest. A revised MNL model and a revised Nested-MNL model will be developed. Both of these models do not have the IIA property. The performance of these new models will be assessed using conjoint-based activity diary data about the choice of destination and stop pattern.

Given sound theoretical underpinnings, the random utility maximization-based conditional logit model (CLM) serves as the principal method for applied research on industrial location decisions. Studies that implement this methodology, however, confront several problems, notably the disadvantages of the underlying Independence of Irrelevant Alternatives (IIA) assumption. This paper shows that by taking advantage of an equivalent relation between the CLM and Poisson regression likelihood functions one can more effectively control for the potential IIA violation in complex choice scenarios where the decision maker confronts a large number of narrowly defined spatial alternatives. As demonstrated here our approach to the IIA problem is compliant with the random utility (profit) maximization framework.

Single-peaked preferences have played an important role in the literature ever since they were used by Black (1948) to formulate a domain restriction that is sufficient for theexclusion of cycles according to the majority rule. In this paper, we approach single-peakedness from a choice-theoretic perspective. We show that the well-known axiom independence of irrelevant alternatives (a form of contraction consistency)

The article considers the construction of social welfare functions when the set of alternatives is the two-dimensional nonnegative orthant, as would be the case if there are two divisible public goods which can be consumed in any nonnegative quantities. With individual and social preferences required to be linear and strictly monotonic, but otherwise unrestricted, we characterize all of the social welfare functions which satisfy binary independence of irrelevant alternatives and anonymity and which satisfy binary independence of irrelevant alternatives, anonymity, and weak Pareto. These classes of social welfare functions are shown to be formally equivalent to the classes of social choice functions characterized by Moulin in his study of strategy-proof social choice with singlepeaked preferences.

Several recent studies of voter choice in multiparty elections point to the advantages of multinomial probit (MNP) relative to multinomial/conditional logit (MNL). We compare the MNP and MNL models and argue that the simpler logit is often preferable to the more complex probit for the study of voter choice in multi-party elections. Our argument rests on three areas of comparison between MNP and MNL. First, within the limits of typical data-a small sample of revealed voter choices among a few candidates or parties-neither model will clearly appear to have generated the observed data. Second, MNP is susceptible to a number of estimation problems, the most serious of which is that the MNP is often weakly identified in application. Weak identification is difficult to diagnose and may lead to plausible, yet arbitrary or misleading inferences. Finally, the logit model is criticized because it imposes the independence of irrelevant alternatives (IIA) property on voter choice. For most applications the IIA property is neither relevant nor particularly restrictive. We illustrate our arguments using data from recent US and French presidential elections.

Nested logit is increasingly advocated as a tool of recreational demand and benefit estimation. The intent of this short monograph is to lay out, in a simple fashion, the theory behind the nested-logit model of site choice and the nested-logit model of participation and site choice. Rigorous but straightforward derivations of the properties of nested-logit models are provided, including the probability of choosing a particular alternative, likelihood functions, expected maximum utility, and compensating and equivalent variations. Also discussed are the properties of the underlying distribution, estimation, regularity conditions, the interpretation of the scaling parameters, and the relation between those scaling parameters and the Independence of Irrelevant Alternatives ( IIA) assumption(s) embedded in both the nested logit model and its special cases. Examples are used to link the theory to recreational demand and benefit estimation.

Such inter-brand effects may depend on the specific strategy followed by a firm. For example, a firm may target a particular brand to exploit its vulnerability or to avoid direct competition with other brands. Or a firm may design its pricing strategy aimed at reducing cannibalization of its own brands. Previous studies have utilized standard lofftt models to investigate inter-brand effects. However, these models impose constraints on price elasticities as a consequence of independence of irrelevant alternatives (IIA ) assumptions. As a result, estimated own-and cross-elasticities reflect the restrictive assumptions of the model and may not provide an accurate description of the kinds of asymmetric competition among brands noted previously. Though e.~ting market share models at the aggregate level do capture such competitive asymmetries, most disaggregate level log~t choice models do not capture such asymmetries in a satisfactory manner. In this article a generalized log~t (or mother log~t) model is used to estimate unique interbrand response parameters to capture asymmetry. This methodology, drawn from the econometrics literature, overcomes the necessity of making a priori assumptions of competitive patterns and instead can be used to identify competitive patterns as they exist in the market place. In analyang brand choice data from three product classes, IIA is violated in all three cases to varying degrees. The cross-price elasticities are used to draw managerial implications for brand and product line management, j BUSY RES 1995 34.47--56 uccessful planning and implementation of promotional pricing strategies requires detailed knowledge of the impact of price changes on brand choice. This knowledge is available from the own-and cross-price elasticities of a brand. To obtain information on own-and cross-price elasticities, one needs estimates derived from a modeling framework that allows for unique inter-brand effects. These asymmetries or unique inter-brand effects could arise either as a result of premediated brand strategy or simply be a characteristic of market behavior. For example, a firm's marketing strategy might involve targeting specific competitive brands perhaps to avoid retaliation by other major competitors. Similarly, a brand's vulnerability to competitors may depend on the specific competitor. Another example is of a multi-brand firm that would like to prevent cannibalization of its own brands and instead draw disproportionately from competitors. Regardless of the source of the asymmetry, detailed knowledge of the pattern of competition existing in a market is necessary in formulating brand or product strategy.

Rational choice theory commonly assumes that the presence of unselected choices cannot impact which among the remaining choices is selected-often referred to as independence of irrelevant alternatives. We show that such seemingly irrelevant alternatives influence choice in a school lunch setting. In these lunchrooms, we provide evidence that the presence of specific side dishes -trigger foods -can strongly increase the sales of unhealthy a la carte options, even when the trigger foods are not selected. This behavioral anomaly can be exploited to lead children to healthier choices. We also offer a method that can be used to identify such foods.

This paper concerns voting with logical consequences, which means that anybody voting for an alternative x should vote for the logical consequences of x as well. Similarly, the social choice set is also supposed to be closed under logical consequences. The central result of the paper is that, given a set of fairly natural conditions, the only social choice functions that satisfy social logical closure are oligarchic (where a subset of the voters are decisive for the social choice). The set of conditions needed for the proof include a version of Independence of Irrelevant Alternatives that also plays a central role in Arrow s impossibility theorem.

This paper develops an extension of the classical multinomial logit model which approximates a class of models obtained when there is uncontrolled taste variation across agents and choices in addition to the stochastic noise inherent in the logit model. Unlike semiparametric and parametric alternatives, the extended logit model is easy to estimate even when there are many potential choices. Unlike parametric alternatives, it does not require the specification of a distribution of varying tastes. The extended logit model can give a quick indication of the impact of taste variation on estimates and it generates estimates of the covariances of the taste shifters. It can be used as an exploratory device en route to the construction of a model incorporating a particular form of random taste variation and it can be used to determine whether such effort is required at all. When the amount of taste variation is not excessive the approximate model can be adequate itself. The model nests the conventional logit model which leads to a misspecification diagnostic. A method for estimating the model using conventional logit model software is proposed, asymptotic properties of estimators are derived and an application is presented.

The class of bargaining solutions that are defined on the domain of finite sets of alterna- tives and satisfy Weak Pareto Optimality (WPO), Independence of Irrelevant Alternatives (IIA) and Covariance (COV), is characterized. These solutions select from the set of max- imizers of a nonsymmetric Nash product - i.e., from a nonsymmetric (multi-valued) Nash bargaining solution - according to a specific decomposition of the indifference curves of this Nash product. We use this characterization in two ways. First, we derive consequences on this domain and on larger domains of compact (non-convex) bargaining problems, and show that most results in the literature are special cases and consequences of our central results - in particular by adding continuity or symmetry axioms. Second, since the conti- nuity axiom prevents nontrivial selections from the Nash bargaining solutions, we use the Axiom of Choice to construct for example non-single-valued discontinuous WPO, IIA and COV bargaining s...

In spatial environments, we consider social welfare functions satisfying Arrow's requirements. i.e., weak Pareto and independence of irrelevant alternatives. When the policy space os a one-dimensional continuum, such a welfare function is determined by a collection of 2n strictly quasi-concave preferences and a tie-breaking rule. As a corrollary, we obtain that when the number of voters is odd, simple majority

This paper introduces two-player bargaining problems allowing for asymmetric subjective uncertainty about factors that determine whether agreement is achieved, focusing on surprising events, i.e. events believed possible by only one player. A 'subjective Nash' solution is proposed, in which a bargaining outcome is defined as immune to all possible appeals given the subjective uncertainty of disagreement. In addition to Pareto optimality and independence of irrelevant alternatives, the main axiom in the solution characterization is 'subjective symmetry'. The solution is shown to be equivalent to a specific, non-symmetric, Nash solution, with preference dependent weights that equal the subjective probability players assign to the intersection of their belief supports.

This paper develops an extension of the classical multinomial logit model which approximates a class of models obtained when there is uncontrolled taste variation across agents and choices in addition to the stochastic noise inherent in the logit model. Unlike semiparametric and parametric alternatives, the extended logit model is easy to estimate even when there are many potential choices. Unlike parametric alternatives, it does not require the specification of a distribution of varying tastes. The extended logit model can give a quick indication of the impact of taste variation on estimates and it generates estimates of the covariances of the taste shifters. It can be used as an exploratory device en route to the construction of a model incorporating a particular form of random taste variation and it can be used to determine whether such effort is required at all. When the amount of taste variation is not excessive the approximate model can be adequate itself. The model nests the conventional logit model which leads to a misspecification diagnostic. A method for estimating the model using conventional logit model software is proposed, asymptotic properties of estimators are derived and an application is presented.

This article summarizes the cumulative progress of a cognitive-dynamical approach to decision making and preferential choice called decision field theory. This review includes applications to (a) binary decisions among risky and uncertain actions, (b) multi-attribute preferential choice, (c) multi-alternative preferential choice, and (d) certainty equivalents such as prices. The theory provides natural explanations for violations of choice principles including strong stochastic transitivity, independence of irrelevant alternatives, and regularity. The theory also accounts for the relation between choice and decision time, preference reversals between choice and certainty equivalents, and preference reversals under time pressure. Comparisons with other dynamic models of decision-making and other random utility models of preference are discussed.

In the Desert Uplands region of Central Queensland, many pastoralists are clearing vegetation in order to improve cattle grazing production. A choice modelling study was undertaken to provide estimates of the bene¢ts of retaining remnant vegetation that are appropriate for inclusion in a cost bene¢t analysis of tighter clearing restrictions. Attributes included in the choice model were reductions in the population size of non-threatened species, the number of endangered species lost to the region, and changes in regional income and employment. A nested logit model was used to model the data in order to avoid violations of the independence of irrelevant alternatives condition. The estimated bene¢ts are reported for several tree clearing policy regimes that are more stringent than those currently applied.

This paper questions the alleged superiority of superlative prices indices (like the Fisher index) over more standard base year indices (like the Laspeyre index) as measures of changes in the "cost of living" (COL). The primary basis of our challenge is the "subjective" concept of welfare favoured by neo-classical economists. As shown by our results, a subjective welfare approach is relatively disadvantageous to those exhibiting more flexible preferences. Given that flexible behaviour could be a characteristic of the more income constrained and the not unreasonable possibility that preferences are income determined, the neo-classical COL approach is problematic in its axiomatic foundations, in its informational requirements and from an equity perspective. By contrast, with base year indices we objectively know what it is we are measuring. This is consistent with the defence by Sen (1985) and others of objective measures of welfare, which are also more conducive to progressive social policy than are subjective utility measures.

This study provides a Bayesian investigation of rank-ordered multinominal logit models employing conjugate priors for standard multinomial logit models as well as other priors. Also considered is a specification test of the independence of irrelevant alternatives assumption. The proposed techniques are demonstrated in an empirical investigation of Ontario voter preferences before the 1988 Canadian Federal Election. Rank-ordered choice models are of particular interest in survey research because of their cost effectiveness: they enable more information to be collected per observation (i.e. the ranking of some or all of the alternatives rather than just the most preferred alternative). Thus, sampling costs are reduced. In the case of the multinominal logit model, Luce and Suppes (1965, pp. 354-6) derive the probability associated with a particular ranking of alternatives. The substantial computational advantages of the multinominal logit model in the rank-ordered case has made it popular in empirical work in a variety of areas (e.g. see Beggs et a f . 1981; . This article extends our earlier Bayesian analysis (Koop and Pokier, 1993) of multinominal logit models to the rank-ordered case. We apply our analysis to investigate voter preferences immediately before the 1988 Canadian Federal Election. Given that a choice situation admits a multinominal logit specification, rank-ordered choice data can be easily accommodated. The reason is simple: the independence of irrelevant alternatives (IIA ) property that characterizes the multinominal logit model implies that the conditional distribution of the utility of each choice is independent of the ranking of other choices. This implies that the probability assigned to a specific ranking of choices is the product of standard logit probabilities. Specifically, consider an experiment consisting of N trials (indexed n = 1,2, ..., N ) . On trial n there are R, 2 0 replications (indexed r = 1,2, ..., R,,). (While in most micro-economic data sets, replication is not available, i.e. R, = 1 (n = 1,2, ..., N ) , we introduce the general notation here because it proves valuable in later discussion of priors.) On each replication of trial n there are J,, discrete alternatives (indexed j = 1,2, ..., Jn). The D most preferred aIternatives dn,i

This paper analyzes implementable social choice functions (in dominant strategies) over restricted domains of preferences, the leading example being combinatorial auctions. Our work generalizes the characterization of who showed that truthful mechanisms over unrestricted domains with at least 3 possible outcomes must be "affine maximizers". We show that truthful mechanisms for combinatorial auctions (and related restricted domains) must be "almost affine maximizers" if they also satisfy an additional requirement of "independence of irrelevant alternatives". This requirement is without loss of generality for unrestricted domains as well as for auctions between two players where all goods must be allocated. This implies unconditional results for these cases, including a new proof of Roberts' theorem. The computational implications of this characterization are severe, as reasonable "almost affine maximizers" are shown to be as computationally hard as exact optimization.

This paper analyzes implementable social choice functions (in dominant strategies) over restricted domains of preferences, the leading example being combinatorial auctions. Our work generalizes the characterization of who showed that truthful mechanisms over unrestricted domains with at least 3 possible outcomes must be "affine maximizers". We show that truthful mechanisms for combinatorial auctions (and related restricted domains) must be "almost affine maximizers" if they also satisfy an additional requirement of "independence of irrelevant alternatives". This requirement is without loss of generality for unrestricted domains as well as for auctions between two players where all goods must be allocated. This implies unconditional results for these cases, including a new proof of Roberts' theorem. The computational implications of this characterization are severe, as reasonable "almost affine maximizers" are shown to be as computationally hard as exact optimization.

In one-dimensional environments with single-peaked preferences we consider social welfare functions satisfying Arrow's requirements, i.e. weak Pareto and independence of irrelevant alternatives. When the policy space is a onedimensional continuum such a welfare function is determined by a collection of 2 N strictly quasi-concave preferences and a tie-breaking rule. As a corollary we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave.

En este artículo se examinan las preferencias declaradas de los consumidores hacia las nueces, mediante un experimento de elección, con un doble objetivo: primero, identificar los atributos más relevantes para el consumidor a la hora de adquirir este fruto y, segundo, estimar las posibilidades de introducción de la variedad Pecán. De ello se pueden obtener guías sobre la manera de incentivar el consumo y recomendaciones a las empresas comercializadoras. Los datos se analizaron mediante la estimación de un modelo logit mixto o con parámetros aleatorios, que permite relajar la propiedad de IIA (independencia de alternativas irrelevantes) presente en los modelos logit con parámetros fijos, al permitir que el coeficiente de cada atributo/nivel varíe aleatoriamente entre consumidores, reflejando así la heterogeneidad de las preferencias de los individuos. Asimismo, permite estimar eficientemente los parámetros cuando cada individuo elige varias veces, como en la presente investigación.