decision analysis under states additive ssb preferences we survey fishburn s skew symmetric bilinear ssb theory of risky choice under nonlinear and potentially nontransitive preferences and apply the states additive special case in the context of decision analysis showing that tractable characterizations of optimal choices are obtainable via linear programming once the decision has been expressed in normal i e tabular form if preferences are transitive they are also linear and representable by von neumann morgenstern utility in which case optimal choices may be obtained by the familiar recursion analysis of the extensive i e tree form

preference reversal and the observability of preferences by experimental methods this paper shows that 1 the preference reversal phenomenon can be consistent with transitive preferences if these preferences violate the independence axiom of expected utility theory and 2 for the class of experiments that were used to produce the evidence concerning preference reversal the elicitation of certainty equivalents is possible if and only if the respondent s preferences can be represented by functionals that are linear in the probabilities furthermore a more general class of experiments is not immune to preference reversal if nonexpected utility preferences are admitted copyright 1987 by the econometric society

complete prolongation for infinitesimal automorphisms on almost complex manifolds we study the almost complex manifold and its symmetry algebra the set of germs of infinitesimal automorphisms the main result is that there is a certain condition to a torsion bundle under which the dimension of the symmetry algebra can not exceed 4 in the case of complex dimension 2 we will give an example which attains the maximal dimension 4 and another example without non degeneracy whose symmetry algebra is of infinite dimension

two stage lotteries without the reduction axiom preference relations over two stage lotteries are analyzed empirical evidence indicates that decisionmakers do not always behave in accordance with the reduction of compound lotteries axiom but they seem to satisfy a compound independence axiom although the reduction and the compound independence axioms together with continuity imply expected utility theory each of them by itself is compatible with all possible preference relations over simple lotteries using these axioms the author analyzes three different versions of expected utility for two stage lotteries the author suggests several different compound dominance axioms as possible replacements of the reduction axiom which are strictly weaker than the reduction of compound lotteries axiom copyright 1990 by the econometric society

inductive inference an axiomatic approach a predictor is asked to rank eventualities according to their plausibility based on past cases we assume that she can form a ranking given any memory that consists of finitely many past cases mild consistency requirements on these rankings imply that they have a numerical representation via a matrix assigning numbers to eventuality case pairs as follows given a memory each eventuality is ranked according to the sum of the numbers in its row over cases in memory the number attached to an eventuality case pair can be interpreted as the degree of support that the past case lends to the plausibility of the eventuality special instances of this result may be viewed as axiomatizing kernel methods for estimation of densities and for classification problems interpreting the same result for rankings of theories or hypotheses rather than of specific eventualities it is shown that one may ascribe to the predictor subjective conditional probabilities of cases given theories such that her rankings of theories agree with rankings by the likelihood functions

local embeddability of pseudohermitian manifolds into spheres in this paper we solve the problem of local pseudohermitian embeddability into spheres we state necessary and sufficient conditions for the embeddability as a finite number of equations and rank conditions on the curvature and torsion tensors and their derivatives

on the power of membership queries in agnostic learning we study the properties of the agnostic learning framework of haussler 1992 and kearns schapire and sellie 1994 in particular we address the question is there any situation in which membership queries are useful in agnostic learning our results show that the answer is negative for distribution independent agnostic learning and positive for agnostic learning with respect to a specific marginal distribution namely we give a simple proof that any concept class learnable agnostically by a distribution independent algorithm with access to membership queries is also learnable agnostically without membership queries this resolves an open problem posed by kearns et al 1994 for agnostic learning with respect to the uniform distribution over 0 1 n we show a concept class that is learnable with membership queries but computationally hard to learn from random examples alone assuming that one way functions exist

query strategies for evading convex inducing classifiers classifiers are often used to detect miscreant activities we study how an adversary can systematically query a classifier to elicit information that allows the attacker to evade detection while incurring a near minimal cost of modifying their intended malfeasance we generalize the theory of lowd and meek 2005 to the family of convex inducing classifiers that partition their feature space into two sets one of which is convex we present query algorithms for this family that construct undetected instances of approximately minimal cost using only polynomially many queries in the dimension of the space and in the level of approximation our results demonstrate that nearoptimal evasion can be accomplished for this family without reverse engineering the classifier s decision boundary we also consider general lp costs and show that near optimal evasion on the family of convex inducing classifiers is generally efficient for both positive and negative convexity for all levels of approximation if p 1

stationary holomorphic discs and finite jet determination problems we construct a family of small analytic discs attached to levi non degenerate hypersurfaces in mathbb c n 1 which is globally biholomorphically invariant we then apply this technique to study unique determination problems along levi non degenerate hypersurfaces that are merely of class mathcal c 4 this method gives 2 jet determination results for germs of biholomorphisms cr diffeomorphisms as well as in the almost complex setting

probabilities as similarity weighted frequencies a decision maker is asked to express her beliefs by assigning probabilities to certain possible states we focus on the relationship between her database and her beliefs we show that if beliefs given a union of two databases are a convex combination of beliefs given each of the databases the belief formation process follows a simple formula beliefs are a similarity weighted average of the beliefs induced by each past case

multivariate bandwidth selection for local linear regression the existence and properties of optimal bandwidths for multivariate local linear regression are established using either a scalar bandwidth for all regressors or a diagonal bandwidth vector that has a different bandwidth for each regressor both involve functionals of the derivatives of the unknown multivariate regression function estimating these functionals is difficult primarily because they contain multivariate derivatives in this paper an estimator of the multivariate second derivative is obtained via local cubic regression with most cross terms left out this estimator has the optimal rate of convergence but is simpler and uses much less computing time than the full local estimator using this as a pilot estimator we obtain plug in formulae for the optimal bandwidth both scalar and diagonal for multivariate local linear regression as a simpler alternative we also provide rule of thumb bandwidth selectors all these bandwidths have satisfactory performance in our simulation study

ellsberg revisited a new look at comparative probability suppose you are given the opportunity of guessing whether it will snow or not in chicago next christmas if you guess correctly you win 1 000 if not you win nothing which event snow or no snow would you bet on it is widely accepted among decision theorists that your answer reveals which of the two events you deem more probable furthermore if your choices over a field of events obey certain postulates of coherency and consistency then there is a probability measure p on the field that reflects your choices you regard a as more probable than b if and only if p a p b numerous experiments have shown that people often violate those postulates so they lack full descriptive validity moreover because of systematic and persistent violations of one of the postulates an independence axiomthe theory has been questioned on its normative adequacy as a guide to wellreasoned judgments and choices the purpose of the present paper is to examine a weaker set of postulates that avoids the independence axiom as well as the usual assumption of fully transitive preferences despite this weakening the assumptions imply that there is a unique normalized functional p on pairs of events that preserves choices in the sense that a is more probable than b if and only if p a b 0 the functional p has several nice mathematical properties including conditional additivity that reflect vestiges of numerical probability and it is related to the conventional measure p by p a b p a p b when the omitted independence axiom is coupled to the other postulates

optimization by direct search new perspectives on some classical and modern methods direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked coherent mathematical analysis nonetheless users remained loyal to these methods most of which were easy to program some of which were reliable in the past fifteen years these methods have seen a revival due in part to the appearance of mathematical analysis as well as to interest in parallel and distributed com puting this review begins by briefly summarizing the history of direct search methods and considering the special properties of problems for which they are well suited our focus then turns to a broad class of methods for which we provide a unifying framework that lends itself to a variety of convergence results the underlying principles allow general ization to handle bound constraints and linear constraints we also discuss extensions to problems with nonlinear constraints

regularity of isometric immersions of positively curved riemannian manifolds and its analogy with cr geometry soit m une variete de riemann a n dimensions et f une immersion isometrique de m dans r n 1 on montre que sous certaines conditions sur le signe des courbures principales de f m f satisfait un systeme surdetermine d equations elliptiques apres l addition de l equation de courbure scalaire

stochastically more risk averse a contextual theory of stochastic discrete choice under risk abstract microeconometric treatments of discrete choice under risk are typically homoscedastic latent variable models specifically choice probabilities are given by preference functional differences given by expected utility rank dependent utility etc embedded in cumulative distribution functions this approach has a problem estimated utility function parameters meant to represent agents degree of risk aversion in the sense of pratt 1964 do not imply a suggested stochastically more risk averse relation within such models a new heteroscedastic model called contextual utility remedies this and estimates in one data set suggest it explains and especially predicts as well as or better than other stochastic models

imprecise data sets as a source of ambiguity a model and experimental evidence in many circumstances evaluations are based on empirical data however some observations may be imprecise meaning that it is not entirely clear what occurred in them we address the question of how beliefs are formed in these situations the individual in our model is essentially a frequentist he first makes a subjective judgment about the occurrence of the event for each imprecise observation this may be any number between zero and one he then evaluates the event by its subjective frequency of occurrence our model connects the method of processing imprecise observations with the individual s attitude toward ambiguity an individual who in imprecise observations puts low high weight on the possibility that an event occurred is ambiguity averse loving an experiment supports the main assertions of the model with precise data subjects behave as if there were no ambiguity whereas with imprecise data subjects turn out to be ambiguity averse this paper was accepted by brad barber teck ho and terrance odean special issue editors

average utility maximization a preference foundation this paper provides necessary and sufficient preference conditions for average utility maximization over sequences of variable length we obtain full generality by using a new algebraic technique that exploits the richness structure naturally provided by the variable length of the sequences thus we generalize many preceding results in the literature for example continuity in outcomes a condition needed in other approaches now is an option rather than a requirement applications to expected utility decisions under ambiguity welfare evaluations for variable population size discounted utility and quasilinear means in functional analysis are presented

local embeddability of cr manifolds into spheres in this paper we solve local cr embeddability problem of smooth cr manifolds into spheres under a certain nondegeneracy condition on the chern moser s curvature tensor we state necessary and sufficient conditions for the existence of cr embeddings as finite number of equations and rank conditions on the chern moser s curvature tensors and their derivatives we also discuss the rigidity of those embeddings

preference structures and their numerical representations abstract this paper presents a selective survey of numerical representations of preference structures from the perspective of the representational theory of measurement it reviews historical contributions to ordinal additive and expected utility theories then describes recent contributions in these areas

temporal resolution of uncertainty and recursive non expected utility models if an agent weakly prefers early resolution of uncertainty then the recursive forms of both the most commonly used non expected utility models betweenness and rank dependence almost reduce to kreps porteus s 1978 recursive expected utility

solving convex programs by random walks minimizing a convex function over a convex set in n dimensional space is a basic general problem with many interesting special cases here we present a simple new algorithm for convex optimization based on sampling by a random walk it extends naturally to minimizing quasi convex functions and to other generalizations

are people bayesian uncovering behavioral strategies abstract economists and psychologists have recently been developing new theories of decision making under uncertainty that can accommodate the observed violations of standard statistical decision theoretic axioms by experimental subjects we propose a procedure that finds a collection of decision rules that best explain the behavior of experimental subjects the procedure is a combination of maximum likelihood estimation of the rules together with an implicit classification of subjects to the various rules and a penalty for having too many rules we apply our procedure to data on probabilistic updating by subjects in four different universities we get remarkably robust results showing that the most important rules used by the subjects in order of importance are bayes s rule a representativeness rule ignoring the prior and to a lesser extent conservatism overweighting the prior

investigating generalisations of expected utility theory using experimental data a number of generalizations of the expected utility preference functional are estimated using experimentally generated data involving 100 pairwise choice questions repeated on two separate occasions likelihood ratio tests are conducted to investigate the statistical superiority of the various generalizations and the akaike information criterion is used to distinguish between them the economic superiority of the various generalizations is also explored and the paper concludes that for many subjects the superiority of several of the generalizations is not established copyright 1994 by the econometric society

complete differential system for the mappings of cr manifolds of nondegenerate levi forms letm andn be real analytic c cr manifolds of hypersurface type of dimensions 2m 1 and 2n 1 m n respectively in this paper we show under generic assumptions that a cr mapping f m n satisfies a certain pfaffian system in the jet space which implies the analyticity and rigidity of cr mappings we use a method of prolongation for the tangential cauchy riemann equations the technique is roughly speaking separating the holomorphic derivatives of cr functions from their complex conjugates and applying the tangential cauchy riemann operators and then counting the order of the missing directional derivatives in the holomorphic part the argument of this paper is purely local thus for instance a manifold should be understood as a germ of a manifold at a reference point and mappings are supposed to preserve the reference point first we recall some basic definitions for other definitions and proofs of the facts that we do not present here the readers are refered to jac let m be a differentiable manifold of dimension 2m 1 a cr structure on m is a subbundle v of the complexified tangent bundle tcm having the following properties i each fiber is of complex dimension m ii v v 0 iii v v v integrability given a cr structure v we have levi form

on the existence of subjective upper and lower probabilities consistency between preference under uncertainty modeled by choquet expected utility theory and preference under imprecise risk a particular situation of uncertainty characterized by the existence of objective upper and lower probabilities modeled by linear utility theory is shown to imply that the choquet capacity must coincide on the imprecisely probabilized events with a fixed linear combination of their upper and lower probabilities this result is used to derive conditions for the existence of subjective upper and lower probabilities on all the events

mixture symmetry and quadratic utility the independence axiom of expected utility theory has recently been weakened to the betweenness axiom in this paper an even weaker axiom called mixture symmetry is presented the corresponding functional structure is such that utility is a betweenness functional on part of its domain and quadratic in probabilities elsewhere the experimental evidence against betweenness provides one motivation for the more general theory presented here another advantage of the mixture symmetric class of utility functions is that it is sufficiently flexible to permit the disentangling of attitudes towards risk and towards randomization

calibration results for non expected utility theories rabin 2000 proved that a low level of risk aversion with respect to small gambles leads to a high and absurd level of risk aversion with respect to large gambles rabin s arguments strongly depend on expected utility theory but we show that similar arguments apply to general non expected utility theories

a similarity based approach to prediction abstract assume we are asked to predict a real valued variable y t based on certain characteristics x t x t 1 x t d and on a database consisting of x i 1 x i d y i for i 1 n analogical reasoning suggests to combine past observations of x and y with the current values of x to generate an assessment of y by similarity weighted averaging specifically the predicted value of y y t s is the weighted average of all previously observed values y i where the weight of y i for every i 1 n is the similarity between the vector x t 1 x t d associated with y t and the previously observed vector x i 1 x i d the empirical similarity approach suggests estimation of the similarity function from past data we discuss this approach as a statistical method of prediction study its relationship to the statistical literature and extend it to the estimation of probabilities and of density functions

does rolling back decision trees really require the independence axiom in a recent article lavalle and wapman argue that the recursion analysis of decision trees in extensive form requires the herstein milnor independence axiom i claim that most extensive form analyses are perfectly proper in the absence of independence but that the transformation from extensive to normal form is impermissible

extending proper holomorphic mappings of positive codimension in this paper we obtain results on holomorphic continuation of proper holomorphic mappings between pseudoconvex domains with real analytic boundaries in complex spaces of different dimensions equivalently we obtain results concerning the analyticity of cauchy riemann mappings between real analytic pseudoconvex hypersurfaces in complex spaces of different dimensions to begin with we recall the corresponding results for mappings of equidimensional domains let d and d be bounded pseudoconvex domains with smooth boundaries in c if the boundaries of d and d are strictly pseudoconvex or more generally of finite type in the sense of d angelo 15 then every proper holomorphic map of d onto d extends smoothly t o according to the results of bell and catlin 7 8 and diederich and forn ess 19 for mappings between strictly pseudoconvex domains this was proved by fefferman 26 and nirenberg webster and yang 37 if the boundaries of the pseudoconvex domains d d c c are real analytic then every proper holomorphic mapping of d onto d extends holomorphically to a neighborhood of 3 according to baouendi and rothschild 2 and diederich and forn ess 21 this reflection principle was first discovered by lewy 34 and pin6uk 38 for mappings between strictly pseudoconvex domains in the case of biholomorphic mappings between weakly pseudoconvex domains with realanalytic boundaries the result follows from the work of baouendi jacobowitz and treves 5 results in this direction were obtained in recent years by several authors see the papers 4 6 18 22 33 47 49 in this paper we are treating the case when the domains d and d have different dimensions to be specific we assume that d e c and d c c n are bounded pseudoconvex domains with real analytic boundaries and n n l in this situation a proper holomorphic map f d d need not be regular at the boundary for instance there exist proper holomorphic maps of balls of different dimensions

multiple criteria decision making multiattribute utility theory the next ten years management science and decision science have grown exponentially since midcentury two closely related fields central to this growth are multiple criteria decision making mcdm and multiattribute utility theory maut this paper comments on the history of mcdm and maut and discusses topics we believe are important in their continued development and usefulness to management science over the next decade our aim is to identify exciting directions and promising areas for future research

thermodynamics as a theory of decision making with information processing costs perfectly rational decision makers maximize expected utility but crucially ignore the resource costs incurred when determining optimal actions here we propose a thermodynamically inspired formalization of bounded rational decision making where information processing is modelled as state changes in thermodynamic systems that can be quantified by differences in free energy by optimizing a free energy bounded rational decision makers trade off expected utility gains and information processing costs measured by the relative entropy as a result the bounded rational decision making problem can be rephrased in terms of well known variational principles from statistical physics in the limit when computational costs are ignored the maximum expected utility principle is recovered we discuss links to existing decision making frameworks and applications to human decision making experiments that are at odds with expected utility theory since most of the mathematical machinery can be borrowed from statistical physics the main contribution is to re interpret the formalism of thermodynamic free energy differences in terms of bounded rational decision making and to discuss its relationship to human decision making experiments

the predictive utility of generalized expected utility theories many alternative theories have been proposed to explain violations of expected utility eu theory observed in experiments several recent studies test some of these alternative theories against each other formal tests used to judge the theories usually count the number of responses consistent with the theory ignoring systematic variation in responses that are inconsistent we develop a maximum likelihood estimation method which uses all the information in the data creates test statistics that can be aggregated across studies and enables one to judge the predictive utility the fit and parsimony of utility theories analyses of 23 data sets using several thousand choices suggest a menu of theories which sacrifice the least parsimony for the biggest improvement in fit the menu is mixed fanning prospect theory eu and expected value which theories are best is highly sensitive to whether gambles in a pair have the same support eu fits better or not eu fits poorly our method may have application to other domains in which various theories predict different subsets of choices e g refinements of nash equilibrium in noncooperative games