on the measurement of polarization suppose that a population of individuals may be grouped according to some vector of characteristics into clusters such that each cluster is very similar in terms of the attributes of its members but different clusters have members with very dissimilar attributes in that case we say that the society is polarized our purpose is to study polarization and to provide a theory of its measurement our contention is that polarization as conceptualized here is closely related to the generation of social tensions to the possibilities of revolution and revolt and to the existence of social unrest in general we take special care to distinguish our theory from the theory of inequality measurement we derive measures of polarization that are easily applicable to distributions of characteristics such as income and wealth

tabu search directed by direct search methods for nonlinear global optimization abstract in recent years there has been a great deal of interest in metaheuristics in the optimization community tabu search ts represents a popular class of metaheuristics however compared with other metaheuristics like genetic algorithm and simulated annealing contributions of ts that deals with continuous problems are still very limited in this paper we introduce a continuous ts called directed tabu search dts method in the dts method direct search based strategies are used to direct a tabu search these strategies are based on the well known nelder mead method and a new pattern search procedure called adaptive pattern search moreover we introduce a new tabu list conception with anti cycling rules called tabu regions and semi tabu regions in addition diversification and intensification search schemes are employed numerical results show that the proposed method is promising and produces high quality solutions

estimating effective elasticity tensors from christoffel equations we consider the problem of obtaining the orientation and elasticity parameters of an effective tensor of particular symmetry that corresponds to measurable traveltime and polarization quantities these quantities the wavefront slowness and polarization vectors are used in the christoffel equation a characteristic equation of the elastodynamic equation that brings seismic concepts to our formulation and relates experimental data to the elasticity tensor to obtain an effective tensor of particular symmetry we do not assume its orientation thus the regression using the residuals of the christoffel equation results in a nonlinear optimization problem we find the absolute extremum and to avoid numerical instability of a global search obtain an accurate initial guess using the tensor of given symmetry closest to the generally anisotropic tensor obtained from data by linear regression the issue is twofold first finding the closest tensor of particular symmetry without assuming its orientation is challenging second the closest tensor is not the effective tensor in the sense of regression because the process of finding it carries neither seismic concepts nor statistical information rather it relies on an abstract norm in the space of elasticity tensors to include seismic concepts and statistical information we distinguish between the closest tensor of particular symmetry and the effective one the former is the initial guess to search for the latter

preference for flexibility in a savage framework we study preferences over savage acts that map states to opportunity sets and satisfy the savage axioms preferences over opportunity sets may exhibit a preference for flexibility due to an implicit uncertainty about future preferences reflecting anticipated unforeseen contingencies the main result of this paper characterizes maximization of the expected indirect utility in terms of an indirect stochastic dominance axiom that expresses a preference for more opportunities in expectation the key technical tool of the paper a version of mobius inversion has been imported from the theory of nonadditive belief functions it allows an alternative representation using choquet integration and yields a simple proof of kreps 1979 classic result

maximum entropy approach for modeling random uncertainties in transient elastodynamics a new approach is presented for analyzing random uncertainties in dynamical systems this approach consists of modeling random uncertainties by a nonparametric model allowing transient responses of mechanical systems submitted to impulsive loads to be predicted in the context of linear structural dynamics the information used does not require the description of the local parameters of the mechanical model the probability model is deduced from the use of the entropy optimization principle whose available information is constituted of the algebraic properties related to the generalized mass damping and stiffness matrices which have to be positive definite symmetric matrices and the knowledge of these matrices for the mean reduced matrix model an explicit construction and representation of the probability model have been obtained and are very well suited to algebraic calculus and to monte carlo numerical simulation in order to compute the transient responses of structures submitted to impulsive loads the fundamental properties related to the convergence of the stochastic solution with respect to the dimension of the random reduced matrix model are analyzed finally an example is presented

non gaussian positive definite matrix valued random fields for elliptic stochastic partial differential operators this paper deals with the construction of a class of non gaussian positive definite matrix valued random fields whose mathematical properties allow elliptic stochastic partial differential operators to be modeled the properties of this class is studied in details and the numerical procedure for constructing numerical realizations of the trajectories is explicitly given such a matrix valued random field can directly be used for modeling random uncertainties in computational sciences with a stochastic model having a small number of parameters the class of random fields which can be approximated is presented and their experimental identification is analyzed an example is given in three dimensional linear elasticity for which the fourth order elasticity tensor valued random field is constructed for a random non homogeneous anisotropic elastic material

canonical representation of set functions the representation of a cooperative transferable utility game as a linear combination of unanimity games may be viewed as an isomorphism between no necessarily additive set functions on the players space and additive ones on the coalitions space or alternatively between nonadditive probability measures on a state space and additive ones on the space of events we extend the unanimity basis representation to general infinite spaces of players study spaces of games which satisfy certain properties and provide some conditions for additivity of the resulting additive set function on the space at coalitions these results also allow us to extend some representations of the choquet integral from finite to infinite spaces

statistical inference for stochastic dominance and for the measurement of poverty and inequality we derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty welfare and inequality this includes estimators of most of the poverty indices currently in use as well as estimators of the curves used to infer stochastic dominance of any order these curves can be used to determine whether poverty inequality or social welfare is greater in one distribution than in another for general classes of indices and for ranges of possible poverty lines we also derive the sampling distribution of the maximal poverty lines up to which we may confidently assert that poverty is greater in one distribution than in another the sampling distribution of convenient dual estimators for the measurement of poverty is also established the statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes our results are briefly illustrated using data for four countries drawn from the luxembourg income study data bases

a differential evolution algorithm with self adaptive strategy and control parameters based on symmetric latin hypercube design for unconstrained optimization problems abstract this paper presents a differential evolution de algorithm namely slade with self adaptive strategy and control parameters for unconstrained optimization problems in slade the population is initialized by symmetric latin hypercube design slhd to increase the diversity of the initial population moreover the trial vector generation strategy assigned to each target individual is adaptively selected from the strategy candidate pool to match different stages of the evolution according to their previous successful experience slade employs cauchy distribution and normal distribution to update the control parameters cr and f to appropriate values during the evolutionary process a large amount of simulation experiments and comparisons have been made by employing a set of 25 benchmark functions experimental results show that slade is better than or at least comparable to other classic or adaptive de algorithms and slhd is effective for improving the performance of slade

evidence based modelling of strategic fit an introduction to rcarbs this paper presents an important development of a novel non parametric object classification technique namely carbs classification and ranking belief simplex to enable regression type analyses termed rcarbs it is as with carbs an evidence based technique with its mathematical operations based on the dempster shafer theory of evidence its exposition is demonstrated here by modelling the strategic fit of a set of public organizations in addition to the consideration of the predictive fit of a series of models graphical exploration of the contribution of individual variables in the derived models is also undertaken when using rcarbs comparison analyses including through fivefold cross validation are carried out using multiple regression and neural networks models the findings highlight that rcarbs achieves parity of test set predictive fit with regression and better fit than neural networks the rcarbs technique can also enable researchers to explore non linear relationships contributions between variables in greater detail than either regression or neural networks models

polarization concepts measurement estimation distributions can be described using density functions the main theorem uniquely characterizes a class of polarization measures that fits into what we call the identityalienation framework and simultanously satisfies a set of axioms second we provide sample estimators of population polarization indices that can be used to compare polarization across time or entities distribution free statistical inference results are also used in order to ensure that the orderings of polarization across entities are not simply due to sampling noise an illustration of the use of these tools using data from 21 countries shows that polarization and inequality orderings can often differ in practice

symmetry characterization and measurement errors of elasticity tensors it is often desirable to approximate a full anisotropic tensor given by 21 independent parameters by one with a higher symmetry if one considers measurement errors of an elasticity tensor the standard approaches of finding the best approximation by a higher symmetric tensor do not produce the most likely tensor to find such a tensor i replace the distance metric used in previous studies with one based on probability distribution functions of the errors of the measured quantities in the case of normally distributed errors the most likely tensor with higher symmetries coincides with the closest higher symmetric tensor using a deviation scaled euclidean metric

mathematical optimization ideas for biodiversity conservation several major environmental issues like biodiversity loss and climate change currently concern the international community these topics that are related to the development of human societies have become increasingly important since the united nations conference on environment and development unced or earth summit in rio de janeiro in 1992 in this article we are interested in the first issue we present here many examples of the help that using mathematical programming can provide to decision makers in the protection of biodiversity the examples we have chosen concern the selection of nature reserves the control of adverse effects caused by landscape fragmentation including the creation or restoration of biological corridors the ecological exploitation of forests the control of invasive species and the maintenance of genetic diversity most of the presented models are or can be approximated with linear quadratic or fractional integer formulations and emphasize spatial aspects of conservation planning many of them represent decisions taken in a static context but temporal dimension is also considered the problems presented are generally difficult combinatorial optimization problems some are well solved and others less well research is still needed to progress in solving them in order to deal with real instances satisfactorily moreover relations between researchers and practitioners have to be strengthened furthermore many recent achievements in the field of robust optimization could probably be successfully used for biodiversity protection a domain in which many data are uncertain

a decremental stochastic fractal differential evolution for global numerical optimization the aim of hybridization in the context of evolutionary computation is to combine appropriate operators from different evolutionary computation paradigms to form a single technique that enjoys a statistically superior performance over a wide range of optimization problems this paper introduces a novel hybridization between differential evolution and update processes of the stochastic fractal search algorithm the diffusion property of the fractal search algorithm is applied in random fractals followed by two novel update processes to explore the search space more efficiently in this algorithm a diffusion process based on differential evolution algorithm is used instead of random fractals in the original stochastic fractal search algorithm a new success based scheme is used to utilize the update processes and to solve the burden of extra computations during the search this new algorithm captures the strengths of both component algorithms and produces a greater explorative power as compared to the original algorithms to verify the performance of our algorithm a challenging test suite of 30 benchmark functions from the ieee cec2014 real parameter single objective competition is used the results affirm the effectiveness and robustness of the proposed approach compared to the original stochastic fractal search and other recent state of the art algorithms the proposed algorithm enjoys a statistically superior performance over most of the tested benchmarks especially hybrid and composition test functions compared to the other contestant algorithms

evolutionary optimization of transition probability matrices for credit decision making statistical transition probability matrices tpms which indicate the likelihood of obligor credit state migration over a certain time horizon have been used in various credit decision making applications a standard approach of calculating tpms is to form a one year empirical tpm and then project it into the future based on markovian and time homogeneity assumptions however the one year empirical tpm calculated from historical data generally does not satisfy desired properties we propose an alternative methodology by formulating the problem as a constrained optimization problem requiring satisfaction of all the desired properties and minimization of the discrepancy between predicted multi year tpms and empirical evidence the problem is high dimensional non convex and non separable and is not effectively solved by nonlinear programming methods to address the difficulty we investigated evolutionary algorithms eas and problem representation schemas a self adaptive differential evolution algorithm jade together with a new representation schema that automates constraint satisfaction is shown to be the most effective technique

distance of a stiffness tetrad to the symmetry classes of linear elasticity abstract in the scope of linear anisotropic elasticity the fourth order elasticity tensor or tetrad has to be identified this can be done either by measurements or by numerical simulations an important task is then to identify a given tetrad probably with some experimental or numerical scattering with one of the symmetry classes for this purpose one needs a distance function between a given tetrad and the class of all tetrads with a particular symmetry which is zero if the tetrad obeys this symmetry or non zero otherwise in this paper we present a fast method to solve these problems we firstly introduce the 8th order projectors that map any stiffness tetrad into the part that is invariant under the action of a specific fixed symmetry group for this purpose we consider the seven out of the eight symmetry classes that are distinguishable in linear elasticity secondly since the symmetry axes of the specific stiffness tensor under consideration is generally not aligned with the used tensorial basis of the projector we need to rotate the sample stiffness the optimal orientation is obtained when the distance between the rotated stiffness and the rotated and projected stiffness is minimal thus we need to apply only linear mappings and minimize over three euler angles the latter is quite simple as the domain of the euler angles is periodic and the number of local minima is limited this procedure has the advantage that it is applicable in an algorithmic manner and does not require an a priori identification of symmetry planes symmetry axes or component symmetries which are only apparent under special choices for the tensorial basis

on the interpretation of sarin and wakker s a simple axiomatization of nonadditive expected utility in an interesting recent paper sarin and wakker 1992 henceforth s w have provided a new axiomatization of expected utility maximization with capacities ceu its simplicity is attractive in that it provides a constructive interpretation of the role of capacities and choquet integration in the main representation theorem an important issue raised by the paper is the interpretation of the key axiom p4 cumulative dominance s w suggest an appreciation of the axiom as an adaptation of stochastic dominance principles to nonadditive probability contexts most eloquently on page 1260 if viable such an interpretation would supply the ceu model with a powerful intuitive foundation that has been lacking so far this note argues that a stochastic dominance interpretation can be maintained only at the price of either an arbitrary choice of specification which undermines its intuitive force or alternatively of an unintended restriction of the class of characterized preferences two logically independent arguments are presented the first points out an arbitrariness in the definition of the more likely than relation in terms of preferences proposition 1 the second shows a similar arbitrariness in the definition of a stochastic dominance relation in terms of a more likely than relation proposition 2 in each case the invoked symmetry conditions yield a characterization of ceu preferences with symmetric capacities a nontrivial generalization of the seu model that has received little attention in the literature for notation and definitions the reader is referred to s w s paper s w s concern is to develop an intuitively convincing axiomatization of ceu representable preference relations their key axiom p4 is formulated in terms of a more likelythan relation on the algebra v of events that is defined in terms of the preference relation a on the set of acts y to facilitate the subsequent discussion their definition is introduced here formally as a condition on the pair of relations a

generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions a new generalized probabilistic approach of uncertainties is proposed for computational model in structural linear dynamics and can be extended without difficulty to computational linear vibroacoustics and computational non linear structural dynamics this method allows the prior probability model of each type of uncertainties model parameter uncertainties and modeling errors to be separately constructed and identified the modeling errors are not taken into account with the usual output prediction error method but with the nonparametric probabilistic approach of modeling errors recently introduced and based on the use of the random matrix theory the theory an identification procedure and a numerical validation are presented then a chaos decomposition with random coefficients is proposed to represent the prior probabilistic model of random responses the random germ is related to the prior probability model of model parameter uncertainties the random coefficients arc related to the prior probability model of modeling errors and then depends on the random matrices introduced by the nonparametric probabilistic approach of modeling errors a validation is presented finally a future perspective is introduced when experimental data are available the prior probability model of the random coefficients can be improved in constructing a posterior probability model using the bayesian approach

a theory of diversity how can diversity be measured what does it mean to value biodiversity can we assist noah in constructing his preferences to address these questions we propose a multi attribute approach under which the diversity of a set of species is the sum of the values of all attributes possessed by some species in the set we develop the basic intuitions and requirements for a theory of diversity and show that the multi attribute approach satisfies them in a flexible yet tractable manner a natural starting point is to think of the diversity of a set as an aggregate of the pairwise dissimilarities between its elements the multi attribute framework allows one to make this program formally precise it is shown that the program can be realized if and only if the family of relevant attributes is well ordered acyclic moreover there is a unique functional form aggregating dissimilarity into diversity the length of a minimum spanning tree examples are taxonomic hierarchies and lines representing uni dimensional qualities in multi dimensional settings pairwise dissimilarity information among elements is insufficient to determine their diversity by consequence the qualitative and quantitative behavior of diversity differs fundamentally

generalized stochastic approach for constitutive equation in linear elasticity a random matrix model this work is concerned with the construction of stochastic models for random elasticity matrices allowing either for the generation of elasticity tensors exhibiting some material symmetry properties almost surely integrating the statistical dependence between the random stiffness components or for the modeling of random media that requires the mean of a stochastic anisotropy measure to be controlled apart from the level of statistical fluctuations to this aim we first introduced a decomposition of the stochastic elasticity tensor on a deterministic tensor basis and considered the probabilistic modeling of the random components having recourse to the maxent principle strategies for random generation and estimation were further reviewed and the approach was exemplified in the case of a material that was transversely isotropic almost surely in a second stage we made use of such derivations to propose a generalized model for random elasticity matrices that took into accountconstraints on both the level of stochastic anisotropy and the level of statistical fluctuations

a stochastic model for elasticity tensors with uncertain material symmetries in this paper we consider the probabilistic modeling of media exhibiting uncertainties on material symmetries more specifically we address both the construction of a stochastic model and the definition of a methodology allowing the numerical simulation and consequently the inverse experimental identification of random elasticity tensors whose mean distance in a sense to be defined to a given class of material symmetry is specified following the eigensystem characterization of the material symmetries the proposed approach relies on the probabilistic model derived in mignolet and soize 2008 allowing the variance of selected eigenvalues of the elasticity tensor to be partially prescribed in this context a new methodology regarding in particular the parametrization of the model is defined and illustrated in the case of transversely isotropic materials the efficiency of the approach is demonstrated by computing the mean distance of the random elasticity tensor to a given material symmetry class the distance and projection onto the space of transversely isotropic tensors being defined by considering the riemmanian metric and the euclidean projection respectively it is shown that the methodology allows the above distance to be partially reduced as the overall level of statistical fluctuations increases no matter the initial distance of the mean model used in the simulations a comparison between this approach and the initial nonparametric approach introduced in soize 2008 is finally provided

six dimensional orthogonal tensorrepresentation of the rotation about an axis in three dimensions abstract the representation of the classical formula that contains euler s theorem on three dimensionalrigid body rotations as an orthogonal tensor in three dimensions is extended to a six dimensional representation as a tool for accomplishing coordinate transformations of the anisotropic elasticity tensor

the noah s ark problem this paper is about the economic theory of biodiversity preservation a cost effectiveness methodology is constructed which results in a particular formula that can be used as a criterion to rank projects the ranking criterion is sufficiently operational to be useful in suggesting what to look at when determining actual conservation priorities among endangered species at the same time the formula is firmly rooted in a mathematically rigorous optimization framework so that its theoretical underpinnings are clear the underlying model called the noah s ark problem is intended to be a kind of canonical form that hones down to its analytical essence the problem of best preserving diversity under a limited budget constraint

stochastic modeling of uncertainties in computational structural dynamics recent theoretical advances this paper deals with a short overview on stochastic modeling of uncertainties we introduce the types of uncertainties the variability of real systems the types of probabilistic approaches the representations for the stochastic models of uncertainties the construction of the stochastic models using the maximum entropy principle the propagation of uncertainties the methods to solve the stochastic dynamical equations the identification of the prior and the posterior stochastic models the robust updating of the computational models and the robust design with uncertain computational models we present recent theoretical advances in this field concerning the parametric and the nonparametric probabilistic approaches of uncertainties in computational structural dynamics for the construction of the prior stochastic models of both the uncertainties on the computational model parameters and on the modeling uncertainties and for their identification with experimental data we also present the construction of the posterior stochastic model of uncertainties using the bayesian method

standard state space models preclude unawareness we show that a very broad class of models including possibility correspondences necessarily fail to capture very simple and intuitive implications of unawareness we explain why standard state space formulations suffer from this problem illustrating the point with an example of a nonstandard state space model which avoids the difficulty

non gaussian positive definite matrix valued random fields with constrained eigenvalues application to random elasticity tensors with uncertain material symmetries this paper is devoted to the construction of a class of prior stochastic models for non gaussian positive definite matrix valued random fields the proposed class allows the variances of selected random eigenvalues to be specified and exhibits a larger number of parameters than the other classes previously derived within a nonparametric framework having recourse to a particular characterization of material symmetry classes we then propose a mechanical interpretation of the constraints and subsequently show that the probabilistic model may allow prescribing higher statistical fluctuations in given directions such stochastic fields turn out to be especially suitable for experimental identification under material symmetry uncertainties as well as for the development of computational multi scale approaches where the randomness induced by fine scale features may be taken into account we further present a possible strategy for inverse identification relying on the sequential solving of least square optimization problems an application is finally provided copyright c 2011 john wiley sons ltd

elastic moduli approximation of higher symmetry for the acoustical properties of an anisotropic material the issue of how to define and determine an optimal acoustical fit to a set of anisotropic elastic constants is addressed the optimal moduli are defined as those which minimize the mean squared difference in the acoustical tensors between the given moduli and all possible moduli of a chosen higher material symmetry the solution is shown to be identical to minimizing a euclidean distance function or equivalently projecting the tensor of elastic stiffness onto the appropriate symmetry this has implications for how to best select anisotropic constants to acoustically model complex materials

a probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures in this paper we address the construction of a prior stochastic model for non gaussian deterministically bounded positive definite matrix valued random fields in the context of mesoscale modeling of heterogeneous elastic microstructures we first introduce the micromechanical framework and recall in particular huet s partition theorem based on the latter we discuss the nature of hierarchical bounds and define under some given assumptions deterministic bounds for the apparent elasticity tensor having recourse to the maximum entropy principle under the constraints defined by the available information we then introduce two random matrix models it is shown that an alternative formulation of the boundedness constraints further allows constructing a probabilistic model for deterministically bounded positive definite matrix valued random fields such a construction is presented and relies on a class of random fields previously defined we finally exemplify the overall methodology considering an experimental database obtained from ebsd measurements and provide a simple numerical application

decomposition and representation of coalitional games a coalitional game is a real valued set function defined on an algebra f of subsets of a space x such that o 0 we prove the existence of a one to one correspondence between coalitional games bounded with respect to the composition norm and countably additive measures defined on an appropriate space

differential evolution algorithm with separated groups for multi dimensional optimization problems the classical differential evolution de algorithm one of population based evolutionary computation methods proved to be a successful approach for relatively simple problems but does not perform well for difficult multi dimensional non convex functions a number of significant modifications of de have been proposed in recent years including very few approaches referring to the idea of distributed evolutionary algorithms the present paper presents a new algorithm to improve optimization performance namely de with separated groups de sg which distributes population into small groups defines rules of exchange of information and individuals between the groups and uses two different strategies to keep balance between exploration and exploitation capabilities the performance of de sg is compared to that of eight algorithms belonging to the class of evolutionary strategies covariance matrix adaptation es particle swarm optimization comprehensive learning pso and efficient population utilization strategy pso differential evolution distributed de with explorative exploitative population families self adaptive de de with global and local neighbours and grouping differential evolution and multi algorithms amalgam the comparison is carried out for a set of 10 30 and 50 dimensional rotated test problems of varying difficulty including 10 and 30 dimensional composition functions from cec2005 although slow for simple functions the proposed de sg algorithm achieves a great success rate for more difficult 30 and 50 dimensional problems

nonparametric estimation and inference about the overlap of two distributions this paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques this quantity has been proposed as a measure of economic polarization between two groups anderson 2004 and anderson et al 2010 in ecology it has been used to measure the overlap of species we give the asymptotic distribution theory of our estimator which in some cases of practical relevance is nonstandard due to a boundary value problem we also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider we investigate the finite sample properties of our methods by simulation methods we give an application to the study of polarization within china in recent years using household survey data from two provinces taken in 1987 and 2001 we find a big increase in polarization between 1987 and 2001 according to monetary outcomes but less change in terms of living space

an effective memetic differential evolution algorithm based on chaotic local search this paper proposes an effective memetic differential evolution de algorithm or decls that utilizes a chaotic local search cls with a shrinking strategy the cls helps to improve the optimizing performance of the canonical de by exploring a huge search space in the early run phase to avoid premature convergence and exploiting a small region in the later run phase to refine the final solutions moreover the parameter settings of the decls are controlled in an adaptive manner to further enhance the search ability to evaluate the effectiveness and efficiency of the proposed decls algorithm we compared it with four state of the art de variants and the ipop cma es algorithm on a set of 20 selected benchmark functions results show that the decls is significantly better than or at least comparable to the other optimizers in terms of convergence performance and solution accuracy besides the decls has also shown certain advantages in solving high dimensional problems

toward an empirical analysis of polarization stochastic dominance conditions may be interpreted as a means of defining the degree and nature of separateness of two distributions by describing polarization states in terms of stochastic dominance conditions this paper presents a taxonomy of and tests for polarization both between and within population distributions four examples from the poverty growth and development wage distribution and assortative pairing literatures are used to illustrate how the techniques may be used in empirical applications

a simple axiomatization of nonadditive expected utility textabstractthis paper provides an extension of savage s subjective expected utility theory for decisions under uncertainty it includes in the set of events both unambiguous events for which probabilities are additive and ambiguous events for which probabilities are permitted to be nonadditive the main axiom is cumulative dominance which adapts stochastic dominance to decision making under uncertainty we derive a choquet expected utility representation and show that a modification of cumulative dominance leads to the classical expected utility representation the relationship of our approach with that of schmeidler who uses a two stage formulation to derive choquet expected utility is also explored our work may be viewed as a unification of schmeidler 1989 and gilboa 1987

representing preferences with a unique subjective state space we extend kreps 1979 analysis of preference for flexibility reinterpreted by kreps 1992 as a model of unforeseen contingencies we enrich the choice set consequently obtaining uniqueness results that were not possible in kreps model we consider several representations and allow the agent to prefer commitment in some contingencies in the representations the agent acts as if she had coherent beliefs about a set of possible future ex post preferences each of which is an expected utility preference we show that this set of ex post preferences called the subjectie state space is essentially unique given the restriction that all ex post preferences are expected utility preferences and is minimal even without this restriction because the subjective state space is identified the way ex post utilities are aggregated into an ex ante ranking is also essentially unique hence when a representation that is additive across states exists the additivity is meaningful in the sense that all representations are intrinsically additive uniqueness enables us to show that the size of the subjective state space provides a measure of the agent s uncertainty about future contingencies and that the way the states are aggregated indicates whether these contingencies lead to a desire for flexibility or commitment