nep-upt New Economics Papers
on Utility Models and Prospect Theory
Issue of 2016‒10‒02
twenty papers chosen by

  1. Asset allocation with judgment By Manganelli, Simone
  2. On the concavity of the consumption function with liquidity constraints By Martin Blomhoff Holm
  3. When 0 + 1/3+1/3>2/3, but 0 + 0 +1/3 By Krzysztof Kontek; Michael Birnbaum
  4. Ambiguity Aversion Without Asymmetric Information By Chen, Daniel L.; Schonger, Martin
  5. A Simpler Theory of Optimal Capital Taxation By Emmanuel Saez; Stefanie Stantcheva
  6. Can Culture Account for Investment Expectations? By Michaël Lainé
  7. Optimal Risk Sharing with Optimistic and Pessimistic Decision Makers By Aloisio Araujo; Jean-Marc Bonnisseau; Alain Chateauneuf; Rodrigo Novinski
  8. Rational Herding toward the Poor: Evidence from Location Decisions of Microfinance Institutions within Pakistan By Jérôme Monne; Céline Louche; Christophe Villa
  9. Dual Decision Processes: Retrieving Preferences when some Choices are Intuitive By Francesco Cerigioni
  10. Long-term optimal portfolio allocation under dynamic horizon-specific risk aversion By Olmo, José; Gonzalo, Jesús
  11. Dual Decision Processes and Noise Trading By Francesco Cerigioni
  12. Optimality, Equilibrium, and Curb Sets in Decision Problems without Commitment By Herings, Jean-Jacques; Meshalkin, Andrey; Predtetchinski, Arkadi
  13. Cognitive ability and the effect of strategic uncertainty By Nobuyuki Hanaki; Nicolas Jacquemet; Stéphane Luchini; Adam Zylbersztejn
  14. Estimating Risky Behavior with Multiple-Item Risk Measures: An Empirical Examination By Lukas Menkhoff; Sahre Sakha
  15. Reason-based choice and context-dependence: An explanatory framework By Franz Dietrich; Christian List
  16. Cost Competitiveness of Residential Solar PV: The Impact of Net Metering Restrictions By Comello, Stephen; Reichelstein, Stefan
  17. Trust under the Prospect Theory and Quasi-Hyperbolic Preferences: A Field Experiment in Vietnam By Quang Nguyen; Marie Claire Villeval; Hui Xu
  18. How Quantifying Probability Assessments Influences Analysis and Decision Making: Experimental Evidence from National Security Professionals By Friedman, Jeffrey A.; Lerner, Jennifer S.; Zeckhauser, Richard
  19. Risk-Consistent Conditional Systemic Risk Measures By Hannes Hoffmann; Thilo Meyer-Brandis; Gregor Svindland
  20. A comparison of the GAI model and the Choquet integral with respect to a k-ary capacity By Christophe Labreuche; Michel Grabisch

  1. By: Manganelli, Simone
    Abstract: This paper shows how to incorporate judgment in a decision problem under uncertainty, within a classical framework. The method relies on the specification of a judgmental decision with associated confidence level and application of hypothesis testing. The null hypothesis tests whether marginal deviations from the judgmental decision generate negative changes in expected utility. The resulting estimator is always at the boundary of the confidence interval: beyond that point the probability of decreasing the expected utility becomes greater than the chosen confidence level. The decision maker chooses the confidence level as a mapping from the p-value of the judgmental decision into the unit interval. I show how the choice of priors in Bayesian estimators is equivalent to the choice of this confidence level mapping. I illustrate the implications of this new framework with a portfolio choice between cash and the EuroStoxx50 index. JEL Classification: C1, C11, C12, C13, D81
    Keywords: judgmental estimation, out-of-sample, portfolio selection, statistical risk propensity
    Date: 2016–08
  2. By: Martin Blomhoff Holm (BI Norwegian Business School and Norges Bank (Central Bank of Norway))
    Abstract: Carroll and Kimball (1996) prove that the consumption function is concave if infinitely-lived risk-averse households have a utility function which exhibits Hyperbolic Absolute Risk Aversion (HARA), face income uncertainty, and are prudent. However, the empirical evidence is inconclusive about the importance of income uncertainty for households. On the other hand, empirical results suggest that liquidity and liquidity constraints are important determinants of household behavior. In this paper, I prove that the consumption function is strictly concave in wealth for infinitelylived risk-averse households with a utility function of the HARA class if there exists a liquidity constraint which binds for some level of wealth. This result is independent of prudence. Furthermore, the introduction of a liquidity constraint always reduces consumption and increases the marginal propensity to consume out of wealth.
    Keywords: consumption, liquidity constraints
    JEL: D11 D52 D91
    Date: 2016–09–22
  3. By: Krzysztof Kontek; Michael Birnbaum
    Abstract: This paper presents the results of two experiments that exhibit monotonicity violations: some lotteries with three equally likely outcomes are valued more than a superior two-outcome lottery, while others are valued less than an inferior two-outcome lottery. Moreover the experimental data provide compelling evidence that lottery valuation strongly depends on the value(s) of the middle outcome(s). This contradicts the claim of Cumulative Prospect Theory (CPT) that middle outcomes are assigned lower weights than the extreme ones. Both effects can be observed in the case of four-outcome lotteries. The patterns are persistent for various payoff schedules, and have been observed for subjects from both Poland and California. Incorporating the median outcome value into any modeling of risky decision-making enables these effects to be explained. This paper demonstrates that a simple weighted Expected Utility - Median model describes data involving two- three-, and four-outcome lotteries more accurately than CPT. Moreover, it offers an alternative explanation of ''overweighting'' of small probabilities, and ''underweighting'' of large ones – phenomena postulated by CPT.
    Keywords: decision – making under risk, monotonicity violations, Expected Utility Theory (EUT), Cumulative Prospect Theory, median
    JEL: D81
    Date: 2016–09
  4. By: Chen, Daniel L.; Schonger, Martin
    Abstract: Ambiguity aversion has been used to explain a wide range of phenomena in law and policy: incomplete contracts, stock market volatility, abstention from voting, and why prosecutors offer and defendants accept harsh plea bargains. This paper presents evidence problematizing the experimental basis for ambiguity aversion. Ambiguity aversion is the interpretation of the experimental finding (Ellsberg paradox) that most subjects violate probabilistic sophistication: They prefer betting on events whose probabilities are known (objective) to betting on events whose probabilities are unknown to them (subjective). However in typical experiments these unknown probabilities are known and often determined by the experimenter. Thus the typical Ellsberg experiment is a situation of asymmetric information. People may try to avoid situations where they are the less informed party in an asymmetric situation setting. Indeed doing so is often normatively appropriate. Thus avoidance of situations of informational asymmetry is a potential confound in typical Ellsberg experiments. Paying to avoid information asymmetry in an Ellsberg experiment would constitute the misapplication of a heuristic to the unfamiliar experimental situation. To eliminate this confound, this paper proposes a new source of ambiguity: participant generated ambiguity. Instead of the experimenter filling an Ellsberg urn, the opaque Ellsberg urn is filled by the other subjects in a laboratory session. We find that eliminating asymmetric information while leaving ambiguity in place, makes subjects more than willing to choose the ambiguous bet rather than the objective one. This is despite the fact that choosing the objective bet is costless. These results have fundamental implications for individual decision making and for the empirical predictions of theoretical models incorporating Knightian uncertainty.
    Keywords: uncertainty aversion, probabilistic sophistication, sources of ambiguity, Ellsberg paradox
    JEL: C91 D81 G11
    Date: 2016
  5. By: Emmanuel Saez; Stefanie Stantcheva
    Abstract: This paper develops a theory of optimal capital taxation that expresses optimal tax formulas in sufficient statistics following the methodology of optimal labor income taxation. We first consider a simple model with utility functions linear in consumption and featuring heterogeneous utility for wealth. In this case, there are no transitional dynamics, the steady-state is reached immediately and has finite elasticities of capital with respect to the net-of-tax rate. This allows for a simple and transparent optimal tax analysis with formulas expressed in terms of empirical elasticities and social preferences (as in the optimal labor income tax theory). These formulas have the advantage of being easily taken to the data to simulate optimal taxes, which we do using U.S. tax return data on labor and capital incomes. Second, we show how these results can be extended to a much broader class of utility functions and models. The same types of formulas carry over.
    JEL: H20 H21
    Date: 2016–09
  6. By: Michaël Lainé (CEPN - Centre d'Economie de l'Université Paris Nord - Université Paris 13 - Université Sorbonne Paris Cité (USPC) - CNRS - Centre National de la Recherche Scientifique, GREThA;Groupe de Recherche en Économie Théorique et Appliquée - CNRS - Centre National de la Recherche Scientifique)
    Abstract: Until recently, risk-taking in investment decisions has been explained by cognitive biases and emotional urges. I would like to propose an alternative explanation, based on the work of Pierre Bourdieu, who links cultural capital to risk-taking. His concept of cultural capital has a very broad meaning, as it encompasses technical skills, aesthetic preferences, verbal facility, general cultural awareness, educational credentials, and artistic competencies. On theoretical grounds, one can assume that a high level of cultural capital enables the taming of uncertainty and allows for temporal horizons that cover longer terms. I test this hypothesis by conducting and analyzing a survey of 307 entrepreneurs. I define risktaking in two ways: (i) in a somewhat mainstream way, on the basis of expected utility, and (ii) in a heterodox way, in a qualitative, context-dependent setting. I find that, in both cases, there seems to be a link between cultural capital and risktaking. Furthermore, it seems to make financing issues more salient. I conclude by opening a discussion about the heterogeneity of entrepreneurs and their animal spirits.
    Keywords: Bourdieu, cultural capital, entrepreneur, investment expectations, risktaking
    Date: 2016
  7. By: Aloisio Araujo (IMPA - Instituto Nacional de Matemática Pura e Aplicada - Instituto Nacional de matematica pura e aplicada, FGV-EPGE - Universidad de Brazil); Jean-Marc Bonnisseau (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics); Alain Chateauneuf (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics); Rodrigo Novinski (Faculdades Ibmec - Faculdades Ibmec)
    Abstract: We prove that under mild conditions individually rational Pareto optima will exist even in presence of non-convex preferences. We consider decision makers dealing with a countable flow of payoffs or choosing among financial assets whose outcomes depend on the realization of a countable set of states of the world. Our conditions for the existence of Pareto optima can be interpreted as a requirement of impatience in the first context and of some pessimism or not unrealistic optimism in the second context. A non-existence example is provided when, in the second context, some decision maker is too optimistic. We furthermore show that at an individually rational Pareto optimum at most one strictly optimistic decision maker will avoid ruin at each state or date. Considering a risky context this entails that even is risk averters will share risk in a comonotonic way as usual, at most one classical strong risk lover will avoid ruin at each state or date. Finally some examples illustrate circumstances when a risk averter could take advantage of sharing risk with a risk lover rather than with a risk averter.
    Abstract: Nous montrons que sous des conditions peu contraignantes des optima de Pareto individuellement rationnels existent même en présence de préférences non-convexes. Nous considérons des décideurs munis de flux dénombrables de paiements ou choisissant parmi des actifs financiers dont les gains dépendent de la réalisation d'un ensemble dénombrable d'états du monde. Nos conditions pour l'existence d'optima de Pareto peuvent s'interpréter comme une exigence d'impatience dans le premier contexte et d'un certain pessimisme ou d'un optimisme non irréaliste dans le second contexte. Un exemple de non-existence est proposé lorsque dans le second contexte l'un des décideurs est trop optimiste. De plus, nous montrons qu'à un optimum de Pareto individuellement rationnel au plus un décideur strictement optimiste évitera la ruine à chaque date ou dans chaque état. Finalement, quelques exemples illustrent dans quelles circonstances un adversaire du risque aurait avantage à partager ses risques avec un joueur plutôt qu'avec un adversaire du risque.
    Keywords: Pareto optimum,optimistic,Risk sharing,optimiste,optimum de Pareto,Partage de risque
    Date: 2015–09
  8. By: Jérôme Monne (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - UN - Université de Nantes, Audencia Business School); Céline Louche (Audencia Business School); Christophe Villa (Audencia Business School)
    Abstract: Analyzing the geographical location of almost all the microfinance institutions (MFIs) within Pakistan, this paper gives further evidence that microfinance activities do not reach the poorest rural areas. Especially, we explore how this result is driven by the uncertainty faced by MFIs in their location decision i.e. they can hardly predict accurately whether or not they will perform financially. Furthermore, we find that MFIs are spatially clustered and identify three main reasons for this: common attraction factors i.e. the characteristics of one area place fits to the preferences of all MFIs so that they are all located in the same areas; payoff externalities to be collocated; and herd behaviour, i.e. MFIs follows one another. Most importantly, we find that a significant part of this herding process is rational, i.e. early locations of MFIs convey information used by later ones such that it reverses or neutralizes the negative impact of uncertainty resulting then in more locations in needier areas. Since it allows them to be located in poorer areas, MFIs improve the achievement of their social goal. This latter result is rather good news for those who reckon that a better access to financial services enhances economic growth and fosters poverty alleviation. Indeed, rational herding constitutes an endogenous moderator effect to the big issue that financial services penetration is too weak in the poorest rural areas.
    Keywords: panel Poisson regression,rational herding,poverty,microfinance institutions,location decisions,uncertainty
    Date: 2016
  9. By: Francesco Cerigioni
    Abstract: Evidence from cognitive sciences shows that some choices are conscious and reflect individual preferences while others tend to be intuitive, driven by analogies with past experiences. Under these circumstances, usual economic modeling might not be valid because not all choices are the consequence of individual tastes. We here propose a behavioral model that can be used in standard economic analysis that formalizes how conscious and intuitive choices arise by presenting a decision maker composed by two systems. One system compares past decision problems with the one the decision maker faces, and it replicates past behavior when the problems are similar enough (Intuitive choices). Otherwise, a second system is activated and preferences are maximized (Conscious choices). We then present a novel method capable of finding conscious choices just from observed behavior and finally, we provide a choice theoretical foundation of the model and discuss its importance as a general framework to study behavioral inertia.
    Keywords: Dual Processes, Fast and Slow Thinking, Similarity, Revealed Preferences, memory, Intuition
    JEL: D01 D03 D60
    Date: 2016–09
  10. By: Olmo, José; Gonzalo, Jesús
    Abstract: This paper studies the long-term asset allocation problem of an individual with risk aversion coefficient that i) varies with economic conditions, and ii) exhibits different risk attitudes towards the short and the long term. To do this, we propose a parametric linear portfolio policy that accommodates an arbitrarily large number of assets in the portfolio and a piecewise linear risk aversion coefficient. These specifications of the optimal portfolio policy and individual's risk aversion allow us to apply GMM methods for parameter estimation and testing. Our empirical results provide statistical evidence of the existence of a short-term and a long-term regime in the individual's risk aversion. Long-term risk aversion is always higher than short-term risk aversion, and it is more statistically significant as the investment horizon increases. The analysis of the optimal portfolio weights also suggests that the allocation to stocks and bonds is strongly negatively correlated, with the magnitude of the portfolio weights and risk aversion coefficients increasing as the investment horizon expands.
    Keywords: Parametric portfolio policies; Intertemporal portfolio theory; Threshold nonlinearity tests; Dynamic risk aversion
    JEL: E62 E52 E32
    Date: 2016–09–01
  11. By: Francesco Cerigioni
    Abstract: Evidence from financial markets suggests that asset prices can be consistently far from their funda-mental value. Prices seem to underreact to news in the short-run and overreact in the long-run. In this paper, we use Dual Process Theory to describe traders behavior. In particular, a part of traders holds wrong beliefs anytime the market environment does not change sufficiently. The proportion of traders with wrong beliefs will depend on how similar past market environments are with the present one. We show that such model not only can be seen as a way of endogenizing noise trading, but also provides a justification for noise traders’ beliefs and it shows that underreaction and overreaction naturally arise in such framework. Finally, we discuss how the model might help understanding the emergence of the equity-premium puzzle and its variation through time.
    Keywords: asset pricing, Dual Processes, noise trading, underreaction, overreaction, equity-premium puzzle
    JEL: G02 G11 G12
    Date: 2016–09
  12. By: Herings, Jean-Jacques (General Economics 1 (Micro)); Meshalkin, Andrey (General Economics 1 (Micro)); Predtetchinski, Arkadi (General Economics 1 (Micro))
    Abstract: The paper considers a class of decision problems with infinite time horizon that contains Markov decision problems as an important special case. Our interest concerns the case where the decision maker cannot commit himself to his future action choices. We model the decision maker as consisting of multiple selves, where each history of the decision problem corresponds to one self. Each self is assumed to have the same utility function as the decision maker. We introduce the notions of Nash equilibrium, subgame perfect equilibrium, and curb sets for decision problems. An optimal policy at the initial history is a Nash equilibrium but not vice versa. Both subgame perfect equilibria and curb sets are equivalent to subgame optimal policies. The concept of a subgame optimal policy is therefore robust to the absence of commitment technologies.
    JEL: C61 C62 C73
  13. By: Nobuyuki Hanaki (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis - CNRS - Centre National de la Recherche Scientifique); Nicolas Jacquemet (PSE - Paris School of Economics, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Stéphane Luchini (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales - Université Paul Cézanne - Aix-Marseille 3 - Université de la Méditerranée - Aix-Marseille 2 - CNRS - Centre National de la Recherche Scientifique); Adam Zylbersztejn (GATE - Groupe d'analyse et de théorie économique - UL2 - Université Lumière - Lyon 2 - Ecole Normale Supérieure Lettres et Sciences Humaines - CNRS - Centre National de la Recherche Scientifique)
    Abstract: How is one's cognitive ability related to the way one responds to strategic uncertainty? We address this question by conducting a set of experiments in simple 2 × 2 dominance solvable coordination games. Our experiments involve two main treatments: one in which two human subjects interact, and another in which one human subject interacts with a computer program whose behavior is known. By making the behavior of the computer perfectly predictable, the latter treatment eliminates strategic uncertainty. We find that subjects with higher cognitive ability are more sensitive to strategic uncertainty than those with lower cognitive ability.
    Keywords: Strategic uncertainty,Bounded rationality,Robot,Experiment
    Date: 2016
  14. By: Lukas Menkhoff; Sahre Sakha
    Abstract: We compare seven established risk elicitation methods and investigate how they robustly explain eleven kinds of risky behavior with 760 individuals. Risk measures are positively correlated; however, their performance in explaining behavior is heterogeneous and, therefore, difficult to assess ex ante. To close this knowledge gap, greater diversification across risk measures is helpful. We do, indeed, find that performance increases considerably if single-item risk measures are combined to form multiple-item risk measures. They tend to improve results the more single-item measures they contain and if these single-item risk measures have different framings. Interestingly, survey items perform as well as incentivized experimental items in explaining risky behavior.
    Keywords: Risk, experiments, household survey, testing methods, contexts
    JEL: D81 C93 O12
    Date: 2016
  15. By: Franz Dietrich (PSE - Paris School of Economics, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Christian List (LSE - London School of Economics and Political Science)
    Abstract: We introduce a "reason-based" framework for explaining and predicting individual choices. The key idea is that a decision-maker focuses on some but not all properties of the options and chooses an option whose "motivationally salient" properties he/she most prefers. Reason-based explanations can capture two kinds of context-dependent choice: (i) the motivationally salient properties may vary across choice contexts, and (ii) they may include "context-related" properties, not just "intrinsic" properties of the options. Our framework allows us to explain boundedly rational and sophisticated choice behaviour. Since properties can be recombined in new ways, it also offers resources for predicting choices in unobserved contexts.
    Keywords: Rational choice,reasons,context-dependence,bounded and sophisticated rationality,prediction of choice
    Date: 2016
  16. By: Comello, Stephen (Stanford University); Reichelstein, Stefan (Stanford University)
    Abstract: The policy of net-metering allows the operators of residential- and commercial solar PV systems to sell surplus electricity back to their utility at the going retail rate. This policy has recently been criticized on the grounds that it provides a subsidy for solar installations, a subsidy that is paid for by all ratepayers. In response, public utility commissions have begun to take up this regulatory issue. This paper presents a theoretical and empirical analysis of the effects of net metering restrictions. We examine the impact that feed-in tariffs (FiT), set below the going retail rate, will have on the volume of future residential PV investments. Our calculations focus on three representative locations in the states of California, Nevada and Hawaii. We find that a FiT set at or above the levelized cost of electricity (LCOE) for solar PV power would provide sufficient incentives for investors to continue on the current path of residential solar installations, even though the profitability of these investments would be lowered substantially. At the same time, we find that the LCOE is a tipping point insofar as feed-in tariffs set below that level would have a sharply negative effect on the volume of new installations.
    Date: 2016–05
  17. By: Quang Nguyen (Middlesex University [London] - Middlesex University); Marie Claire Villeval (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université Jean Monnet - Saint-Etienne - PRES Université de Lyon - CNRS - Centre National de la Recherche Scientifique); Hui Xu (Beijing Normal University, GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université Jean Monnet - Saint-Etienne - PRES Université de Lyon - CNRS - Centre National de la Recherche Scientifique)
    Abstract: Virtually every commercial transaction has within itself an element of trust, certainly any transaction conducted over a period of time. It can be plausibly argued that much of the economic backwardness in the world can be explained by the lack of mutual confidence. (Arrow 1972)
    Keywords: risk preferences, time preferences, Cumulative Prospect Theory, Vietnam, field experiment, trustworthiness,trust
    Date: 2016
  18. By: Friedman, Jeffrey A. (Dartmouth College); Lerner, Jennifer S. (Harvard University); Zeckhauser, Richard (Harvard University)
    Abstract: National security is one of many fields where public officials offer imprecise probability assessments when evaluating high-stakes decisions. This practice is often justified with arguments about how quantifying subjective judgments would bias analysts and decision makers toward overconfident action. We translate these arguments into testable hypotheses, and evaluate their validity through survey experiments involving national security professionals. Results reveal that when decision makers receive numerals (as opposed to words) for probability assessments, they are less likely to support risky actions and more receptive to gathering additional information, disconfirming the idea of a bias toward action. Yet when respondents generate probabilities themselves, using numbers (as opposed to words) magnifies overconfidence, especially among low-performing assessors. These results hone directions for research among both proponents and skeptics of quantifying probability estimates in national security and other fields. Given that uncertainty surrounds virtually all intelligence reports, military plans, and national security decisions, understanding how national security officials form and interpret probability assessments has wide-ranging implications for theory and practice.
    Date: 2015–02
  19. By: Hannes Hoffmann; Thilo Meyer-Brandis; Gregor Svindland
    Abstract: We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional aggregation and a univariate conditional risk measure. Our studies extend known results for unconditional risk measures on finite state spaces. We argue in favor of a conditional framework on general probability spaces for assessing systemic risk. Mathematically, the problem reduces to selecting a realization of a random field with suitable properties. Moreover, our approach covers many prominent examples of systemic risk measures from the literature and used in practice.
    Date: 2016–09
  20. By: Christophe Labreuche (UMP CNRS/THALES - Unité mixte de physique CNRS/Thalès - THALES - CNRS - Centre National de la Recherche Scientifique); Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)
    Abstract: Two utility models are classically used to represent interaction among criteria: the Choquet integral and the Generalized Additive Independence (GAI) model. We propose a comparison of these models. Looking at their mathematical expression, it seems that the second one is much more general than the first one. The GAI model has been mostly studied in the case where attributes are discrete. We propose an extension of the GAI model to continuous attributes, using the multi-linear interpolation. The values that are interpolated can in fact be interpreted as a k-ary capacity, or its extension – called p-ary capacity – where p is a vector and pi is the number of levels attached to criterion i. In order to push the comparison further, the Choquet integral with respect to a p-ary capacity is generalized to preferences that are not necessarily monotonically increasing or decreasing on the attributes. Then the Choquet integral with respect to a p-ary capacity differs from a GAI model only by the type of interpolation model. The Choquet integral is the Lovász extension of a p-ary capacity whereas the GAI model is the multi-linear extension of a p-ary capacity.
    Abstract: Deux modèles d'utilité sont classiquement utilisés pour représenter l'interaction entre les critères : l'intégrale de Choquet et le modèle de l'indépendance additive généralisée (GAI). Nous proposons une comparaison de ces deux modèles. D'après leur expression mathématique, il semble que le second soit plus général que le premier. Le modèle GAI a été étudié le plus souvent avec des attributs discrets. Nous proposons une extension du modèle GAI pour les attributs continus, par interpolation multi-linéaire. Les valeurs interpolées peuvent être interprétées comme une capacité k-additive ou p-additive, où p est un vecteur et pi le nombre de niveaux attachés au critère i. Pour pousser la comparaison plus loin, l'intégrale de Choquet par rapport à une p-capacité est généralisée aux préférences qui ne sont pas nécessairement monotones croissantes ou décroissantes. Alors l'intégrale de Choquet pour une p-capacité diffère d'un modèle GAI seulement par le type d'interpolation. L'intégrale de Choquet est l'extension de Lovász d'une p-capacité tandis que le modèle GAI est l'extension multi-linéaire d'une p-capacité.
    Keywords: Multiple criteria analysis,Generalized Additive Independence,Choquet integral,interpolation,intégrale de Choquet,Multiple analyse des critères,indépendance additive généralisée
    Date: 2016–01

General information on the NEP project can be found at For comments please write to the director of NEP, Marco Novarese at <>. Put “NEP” in the subject, otherwise your mail may be rejected.
NEP’s infrastructure is sponsored by the School of Economics and Finance of Massey University in New Zealand.