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Computer City sells plenty of interesting gizmos and gadgets. So one day, Vincent went there and for reasons unknown fell in love with a small laptop, even though he is already the proud owner of four or five of them. As a good and informed consumer, he asked the shop assistant various questions to acquire more information about the product.

Echenique and Yenmez [AER 2015, 105(8): 2679-94] study choice rules for a school that express preferences for a diverse student body. Their Theorem 2 characterizes choice rules that are "generated by reserves for the priority". We show that the "only if part" is not correct. We exhibit a choice rule that is generated by reserves for the priority but violates one of their axioms. A similar issue arises in Theorem D.2., where a priority is allowed to be endogenous. We reformulate the axioms and repair the results.

A crucial problem concerning Tikhonov regularization is the proper choice of the regularization parameter. This paper deals with a generalization of a parameter choice rule due to Reginska (1996) [31] , analyzed and algorithmically realized through a fast fixed-point method in Bazan (2008) [3] , which results in a fixed-point method for multi-parameter Tikhonov regularization called MFP. Like the single-parameter case, the algorithm does not require any information on the noise level. Further, combining projection over the Krylov subspace generated by the Golub–Kahan bidiagonalization (GKB) algorithm and the MFP method at each iteration, we derive a new algorithm for large-scale multi-parameter Tikhonov regularization problems. The performance of MFP when applied to well known discrete ill-posed problems is evaluated and compared with results obtained by the discrepancy principle. The results indicate that MFP is efficient and competitive. The efficiency of the new algorithm on a super-resolution problem is also illustrated.

Kirsch’s factorization method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far-field pattern. We present a Tikhonov parameter choice approach based on a maximum product criterion (MPC) which provides a regularization parameter located in the concave part of the L-curve on a log–log scale. The performance of the method is evaluated by comparing our reconstructions with those obtained via the L-curve, Morozov’s discrepancy principle and the SVD-tail. Numerical results that illustrate the effectiveness of the MPC in reconstruction problems involving both simulated and real data are reported and analyzed.

We investigate the choice of the bandwidth for the regression discontinuity estimator. We focus on estimation by local linear regression, which was shown to have attractive properties (Porter, J. 2003, "Estimation in the Regression Discontinuity Model" (unpublished, Department of Economics, University of Wisconsin, Madison)). We derive the asymptotically optimal bandwidth under squared error loss. This optimal bandwidth depends on unknown functionals of the distribution of the data and we propose simple and consistent estimators for these functionals to obtain a fully data-driven bandwidth algorithm. We show that this bandwidth estimator is optimal according to the criterion of Li (1987, "Asymptotic Optimality for C p , C L , Cross-validation and Generalized Cross-validation: Discrete Index Set", Annals of Statistics, 15, 958--975), although it is not unique in the sense that alternative consistent estimators for the unknown functionals would lead to bandwidth estimators with the same optimality properties. We illustrate the proposed bandwidth, and the sensitivity to the choices made in our algorithm, by applying the methods to a data set previously analysed by Lee (2008, "Randomized Experiments from Non-random Selection in U.S. House Elections", Journal of Econometrics, 142, 675--697) as well as by conducting a small simulation study. Copyright , Oxford University Press.

The evolution of cooperation through partner choice mechanisms is often thought to involve relatively complex cognitive abilities. Using agent-based simulations, I model a simple partner choice rule, the “Walk Away” rule, where individuals stay in groups that provide higher returns (by virtue of having more cooperators), and “Walk Away” from groups providing low returns. Implementing this conditional movement rule in a public goods game leads to a number of interesting findings: (a) cooperators have a selective advantage when thresholds are high, corresponding to low tolerance for defectors, (b) high thresholds lead to high initial rates of movement and low final rates of movement (after selection), and (c) as cooperation is selected, the population undergoes a spatial transition from high migration (and many small and ephemeral groups) to low migration (and large and stable groups). These results suggest that the very simple “Walk Away” rule of leaving uncooperative groups can favor the evolution of cooperation and that cooperation can evolve in populations in which individuals are able to move in response to local social conditions. A diverse array of organisms are able to leave degraded physical or social environments. The ubiquitous nature of conditional movement suggests that “Walk Away” dynamics may play an important role in the evolution of social behavior in both cognitively complex and cognitively simple organisms.

In this paper, we consider an analytic continuation problem on a strip domain with the data given approximately only on the real axis. The Gauss mollification method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, we also propose a new a posteriori parameter choice rule and get a good error estimate. Several numerical examples are provided, which show the method works effectively.

Competitive location modeling deals with a strategic spatial decision which seeks to identify optimal locations for new facilities among existing competing facilities. The capture of customers by a new facility essentially depends on customer-choice behaviors. In this paper, we introduce a competitive location model incorporating a rank proportional choice rule. Also, we explore how the competitive location model with a ranking system differs from other models with two more-typical choice rules—deterministic and probabilistic choices. To do so, we present a numerical example and an illustrative application in the broadband market context, focusing on customer-capture patterns. Our analytical findings reveal that the different choice rules in modeling significantly influence customer-capture and market-share estimates. In particular, a competitive location model with a rank proportional allocation captures fewer customers than other models with different allocation rules, given a fixed number of few facilities.

An original method for studying cognitive abilities in largely wild passerine birds was developed. Studies of five crossbills (Loxia curvirostra) showed that this approach could be used to assess their ability to form concepts. All five crossbills learned selection rules for the "larger number" feature over the range "1-10." The birds successfully transferred this to stimuli significantly different from those used in training, which were not comparable in terms of all quantitative properties, but only some (only area or number). Only one bird was able to transfer the learned choice rule to multiples in a new range ("10-20"). Thus, the ability of representative small forest passerine birds to form the "larger than" concept was demonstrated.

A new estimate of the hazard rate function is proposed, based on nonparametric transformations of the data and motivated by the bias expression of conventional kernel hazard estimates. The squared error of this estimate is considered, and it is shown to be considerably smaller than that of ordinary kernel estimates. With the use of a practical bandwidth choice rule, the estimate is illustrated graphically on distributional and real-world data.

If we assume that the preferences of a set of political actors are not cyclic, we would like to know if their collective choices are rationalizable. Given a fuzzy choice rule, do they collectively choose an alternative from the set of undominated alternatives? We consider necessary and sufficient conditions for a partially acyclic fuzzy choice function to be rationalizable. We find that certain fuzzy choice functions that satisfy conditions α and β are rationalizable. Furthermore, any fuzzy choice function that satisfies these two conditions also satisfies Arrow and Warp.

In a recent article, the authors (Miller & Shettleworth, 2007) showed how the apparently exceptional features of behavior in geometry learning ("reorientation") experiments can be modeled by assuming that geometric and other features at given locations in an arena are learned competitively as in the Rescorla-Wagner model and that the probability of visiting a location is proportional to the total associative strength of cues at that location relative to that of all relevant locations. Reinforced or unreinforced visits to locations drive changes in associative strengths. Dawson, Kelly, Spetch, and Dupuis (2008) have correctly pointed out that at parameter values outside the ranges the authors used to simulate a body of real experiments, our equation for choice probabilities can give impossible and/or wildly fluctuating results. Here, the authors show that a simple modification of the choice rule eliminates this problem while retaining the transparent way in which the model relates spatial choice to competitive associative learning of cue values.

We introduce three spectral regularization methods for solving a backward heat conduction problem (BHCP). For the three spectral regularization methods, we give the stability error estimates with optimal order under an a-priori and an a-posteriori regularization parameter choice rule. Numerical results show that our theoretical results are effective.

A two-stage sequential choice model is studied, the first stage being defined by q-Pareto multicriterial choice rule, and the second stage being defined by scalar extremization model. In this model, at the first stage the q-Pareto rule choses alternatives which are not only undominated in terms of Pareto comparison, but also includes into choice the alternatives which are dominated by no more than q alternatives. Since the choice set of the first-stage usually contains too many elements, obtained set is used as a presentation for the second stage constructed by a scalar extremization model. The properties of the model are studied as well as its representability to one-stage scalar extremization model.

Erickson and Kruschke (2002b) have shown that human subjects generalize category knowledge in a rule-like fashion when exposed to a rule-plus-exception categorization task. This resulth as remained a challenge to exemplar models of category learning. We show that these models can account for such performance, if they are augmented with exemplar-specific specificity or exemplar-specific attention. This result, however, is only achieved if the choice rule that converts evidence for competing categories into probabilities is sensitive to small differences between evidence values close to 0. Exemplar-specific attention provided the best overall approximation of the data. Exemplar-specific specificity provided a slightly worse approximation, but it predicted better the rule-like generalization pattern observed.

This chapter studies one particular property of voting rules in applications in which the choice set is one-dimensional: whether the median alternative is chosen. Our results suggest that with three or more alternatives, it is difficult to rule out non-median outcomes, even if all voters have linear Euclidean preferences.

Algorithm selection techniques are known to improve the performance of systems for several knowledge representation and reasoning frameworks.This holds also in the case of Answer Set Programming (ASP), which is a rule-based programming paradigm with roots in logic programming and non-monotonic reasoning. Indeed, the multi-engine approach to ASP solving implemented in me-asp was particularly effective on the instances of the third ASP competition. In this paper we report about the advances we made on me-asp in order to deal with the new standard language ASPCore 2.0, which substantially extends the previous version of the standard language.An experimental analysis conducted on the Fifth ASP Competition benchmarks and solvers confirms the effectiveness of our approach also in comparison to rival systems.

A decision maker (DM) makes choices from different sets of alternatives. The DM is initially fully ignorant of the payoff associated to each alternative, and learns these payoffs only after a large number of choices have been made. We show that, in the presence of an outside option once payoffs are learned, the optimal choice rule from sets of alternatives is one that is as if the DM had strict preferences over all alternatives. Under this model, the DM has preferences for preferences while being ignorant of what preferences are "right".

This paper summarizes some results for the leader–follower location model on networks in several scenarios. Discretization results are considered and differences derived from the inelastic and elastic demand assumptions, as well as from the customer’s choice rule, are emphasized. Finally, some issues for future lines of investigation are suggested.

Feeding animals often prefer small, quickly delivered rewards over larger, more delayed rewards. Students of feeding behaviour typically explain this behaviour by saying that animals discount delayed benefits. Temporal discounting implies that delayed benefits are worth less than immediate benefits. This paper presents a new explanation of short–sighted decision–making called the discrimination advantage model that does not rely on discounting. A new model that includes several possible causes of discounting is developed. This model has many interesting features, but it cannot account for two empirical results: the strength of the ‘discounting‘ effect and the fact that the time between choice presentations (the intertrial interval or ITI) has no effect. This leads to the conclusion that although discounting may be important it is probably not a complete explanation of the experimental facts. In the discrimination advantage model the observation that the ITI does not affect choice is seen as a strategy to make a cleaner discrimination between delayed alternatives in a noisy world. A simple example shows that when discrimination is imperfect a short–sighted choice rule can, in some situations, lead to a higher long–term rate than a rule that actually compares long–term rates. This idea is developed and extended in several ways.

One central issue tackled in epistemic game theory is whether for a general class of strategic games the solution generated by iterated application of a choice rule gives exactly the strategy profiles that might be realized by players who follow this choice rule and commonly believe they follow this rule. For example, Brandenburger and Dekel (1987) and Tan and Werlang (1988) have established that this coincidence holds for the choice rule of strict undominance in mixtures in the class of finite strategic games, and Mariotti (2003) has established that this coincidence holds for Bernheim's (1984) choice rule of point rationality in the class of strategic games in which the strategy sets are compact Hausdorff and the payoff functions are continuous. In this paper, we aim at studying this coincidence in a general way. We seek to figure out general conditions of the choice rules ensuring it for a general class of strategic games. We state four substantial assumptions on choice rules. If the players' choices rules satisfy - besides the technical assumption of regularity - the properties of reflexivity, monotonicity, Aizerman's property, and the independence of payoff equivalent conditions, then this coincidence applies. This result proves to be strict in the following sense. None of the four substantial properties can be omitted without eliminating the coincidence.

We conduct an experimental study on the decision biases in a scenario where two newsvendors compete a common market, in which if stockout happens at a newsvendor, the unsatisfied demand is reallocated to his/her competitor. Following the existing theory, an experiment of competing game with high and low profit settings is designed, with equivalent ordering benchmarks as single newsvendor scenarios. The results show that the competing environment can induce participants to significantly increase the ordering level in the high profit group and increase the ordering oscillation in the low profit group. In addition, we propose a behavioral model by combining the logit choice rule and mental accounting. The model fits the experimental data satisfactorily, and the estimations of the parameters indicate that the participants in the high profit group like to ignore the distractions from competitors, while the participants in the low profit group are highly influenced by their competitors. The observations from this study suggest that managers should carefully pay attention to different profit-margin products in competing practice.

This paper provides an ethical intepretation of the Nash choice rule. In a setting in which (cardinal) utilities are interpersonally comparable, this procedure is characterised by an impartiality requirement and by the assumption that choices are not responsive to the agents' relative ability to convert resources into utility.

A feasible mechanism is constructed which weakly Nash-implements the weak Pareto choice rule over a certain class of indecomposable pure-exchange environments, where there may be no private goods whose consumption has no external effects.

Many real-world design problems such as product configuration require a flexible number of components and thus rely on tuple generating dependencies in order to express relations between entities. Often, such problems are subject to optimization, preferring models which include a minimal number of constants substituted in existentially quantified formulas. In this paper we propose an approach based on automated program rewriting which avoids such substitutions of existentially quantified variables that would lead to a contradiction. While preserving all solutions, the method significantly reduces runtime and solves instances of a class of real-world configuration problems which could not be efficiently solved by current techniques.

We characterize single-crossing preference profiles in terms of two forbidden substructures, one of which contains three voters and six (not necessarily distinct) alternatives, and one of which contains four voters and four (not necessarily distinct) alternatives. We also provide an efficient way to decide whether a preference profile is single-crossing.

In answer-set programming ASP, there is a lack of debugging tools that are capable of handling programs with variables. Hence, we implemented a tool, called Ouroboros , for debugging non-ground answer-set programs. The system builds on a previous approach based on ASP meta-programming that has been recently extended to cover weight constraints and choice rules. The main debugging question addressed is "given a program P and an interpretation I, why is I not an answer set of P". Our tool gives answers in terms of two categories of explanations: unsatisfied rules and unfounded loops. Ouroboros is a plugin of the SeaLion integrated development environment for ASP that is built on Eclipse. Thereby, Ouroboros complements and profits from SeaLion 's Stepping plugin, that implements a different debugging approach for ASP.

In two experiments rats were trained to find one of two submerged platforms that were located in diagonally opposite corners-the correct corners-of a rectangular pool. Additional training was given to endow two different landmarks with excitatory and inhibitory properties, by using them to indicate where a platform was or was not located in either a rectangular (Experiment 1) or a square pool (Experiment 2). Subsequent test trials, with the platforms removed from the pool, revealed that placing the excitatory landmark in each of the four corners of the rectangle resulted in more time being spent in the correct corners than when the four corners contained inhibitory landmarks. This result is contrary to predictions derived from a choice rule for spatial behavior proposed by Miller and Shettleworth (2007).

This paper studies the impact of new telecom services tariff on the customers inside (customers who have ever chosen the original telecom service packages) and the revenue variation from the perspective of utility and customer choice behavior. On the basis of the quantification of telecom services tariff, a measurement model is built through multi-nominal logit (MNL) choice rule to predict the impact. Important indicators such as utility of service packages, transfer probability of the customers inside and expected change of revenue are obtained, which are useful for market orientation, revenue prediction and optimization management of the new telecom services tariff.

Are there general algebraic laws which describe how consumers make choices from sets of alternatives? In this paper we review the verdict of research which has sought to answer this question. We focus on the functional forms which have been found to best characterize three component processes of consumer choice: those of attribute valuation, attribute integration, and choice. Our central conclusion is that there exists support for three major generalizations about the form of consumer decision processes: (1) subjective attribute valuations are a nonlinear, reference-point dependent, function of the corresponding objective measure of product attributes; (2) the integration rule which best describes how these attribute valuations are integrated to form overall valuations is multiplicative-multilinear, characterizing an overweighting of negative attribute information; and (3) the choice rule which links overall valuations of an option to the likelihood that it is chosen from a set is a member of a family of functions which recognize the attributewise proximity of a considered alternative to others in the set. The evidence supporting these generalizations is reviewed, as well as their implications for future theoretical and applied work in consumer choice modeling.

The issue of the order-dependence of iterative deletion processes is well-known in the game theory community, and meanwhile conditions on the dominance concept underlying these processes have been detected which ensure order-independence (see e.g. the criteria of Gilboa et al., 1990 and Apt, 2011). While this kind of research deals with the technical issue, whether certain iterative deletion processes are order-independent, or not, our focus is on the normative issue, whether there are good reasons for employing order-independent iterative deletion processes on strategic games. We tackle this question from an epistemic perspective and attempt to figure out, whether order-independence contains some specific epistemic meaning. It turns out that, under fairly general preconditions on the choice rules underlying the iterative deletion processes, the order-independence of these deletion processes coincides with the epistemic characterization of their solutions by the common belief of choice-rule following behavior. The presumably most challenging precondition of this coincidence is the property of the independence of irrelevant acts. We also examine the consequences of two weakenings of this property on our epistemic motivation for order-independence. Although the coincidence mentioned above breaks down for both weakenings, still there exist interesting links between the order-independence of iterative deletion processes and the common belief of following the choice rules, on which these processes are based.

Cahier de recherche du groupe HEC; International audience; Indeterminate preferences have long been a tricky subject for choice theory. One reason for which preferences may be less than fully determinate is the lack of confidence in one's preferences. In this paper, a representation of confidence in preferences is proposed. It is used to develop an account of the role which confidence which rests on the following intuition: the more important the decision to be taken, the more confidence is required in the preferences needed to take it. An axiomatisation of this choice rule is proposed. This theory provides a natural account of when an agent should defer a decision; namely, when the importance of the decision exceeds his confidence in the relevant preferences. Possible applications of the notion of confidence in preferences to social choice are briefly explored.

The numerical solution of inverse problems using Tikhonov’s regularization methods requires a huge amount of computations in iterative processes. It can employ extrapolation techniques to accelerate the convergence process or to improve accuracy of the regularized solution. This chapter aims to introduce some main extrapolation methods that have been studied for solving linear inverse problems in detail. Our emphasis is to discuss related technical problems, to propose a new extrapolation algorithm based on the Hermitian interpolation and to present results of numerical experiments for showing the merits of extrapolated regularization methods.

A total variation (TV) model with an L 1 -fidelity term and a spatially adapted regularization parameter is presented in order to reconstruct images contaminated by impulse noise. This model intends to preserve small details while homogeneous features still remain smooth. The regularization parameter is locally adapted according to a local expected absolute value estimator depending on the statistical characteristics of the noise. The numerical solution of the L 1 -TV minimization problem with a spatially adapted parameter is obtained by a superlinearly convergent algorithm based on Fenchel-duality and inexact semismooth Newton techniques, which is stable with respect to noise in the data. Numerical results justifying the advantage of such a regularization parameter choice rule are presented.

This paper reports the results of two experiments to investigate the effects of payoff alterations in two-person symmetric games. The initial experiment involved 60 subjects, each of whom could earn from £0 to £15, depending on the interaction of their decisions and the unknown decisions of one other person. All decisions were made without feedback to isolate the impact on subjects' behaviour of the game's parameters. A primary aim was to see if the games had strategically distinct structures, or whether uncertainty over the choice rule of others would influence choice behaviour and lessen this independence. An alternative model of rational choice, making allowance for uncertainty in the decision environment, was proposed to capture subjects' behaviour. The results indicated that the frontiers of most of the games had no impact on choice behaviour other than through the magnitude of the change in payoffs. The model received strong support across an identifiable set of ‘frontierless’ games. However, the variety of games was not sufficient to provide a comprehensive test. A second experiment was recently held to close these gaps. Fifty subjects took part, each of whom earned from A$0 to A$24, averaging A$17. The findings provided broad additional support for the theory.

In this paper, we present a Newton-type method with double regularization parameters for nonlinear ill-pose problems. The key step in the process that a reasonable choice rule to determine these two regularization parameters is presented. And the convergence and the stability of the method are discussed. Numerical experiment shows the effectiveness of the method.

This paper uses a particular choice rule over sets of alternatives under the Pareto rule. Starting from the sincere situation every strategic misrevelation of preference is shown to be an improvement for all voters. The existence of an equilibrium under successive misrepresentations by sincere voters is demonstrated.

Publisher Summary This chapter presents the contribution of Robert G. Jeroslow to mathematics. Bob started his graduate work in Operations Research (at Columbia first, then at Cornell), but soon switched to Mathematics and wrote his dissertation in Logic, under Anil Nerode. Egon Balas, the author, describes his experience of working with Bob. Eden describes how he first met him and how they continued their contacts through telephone and correspondence, and the upshot of their interaction was the paper “On the Structure of the Hypercube.” While at CMU, Bob also made some interesting contributions to complexity theory. In one of his paper (Discrete Mathematics, 4, 1973) he extended the Klee-Minty result about the simplex method requiring exponentially many steps on certain problem classes, to a non-standard variant of the simplex method that uses the pivot column choice rule of maximizing the improvement of the objective function value. Besides being an outstanding mathematician, Bob had exceptional pedagogical skills: his students used to rave about him. He was a very earnest person, scrupulously conscientious about his commitments and obligations, generous with his time for students and colleagues alike.