Representation and aggregation of preferences under uncertainty

We axiomatize in the Anscombe–Aumann setting a wide class of preferences called rank-dependent additive preferences that includes most known models of decision under uncertainty as well as state dependent versions of these models. We prove that aggregation is possible and necessarily linear if and only if (society's) preferences are uncertainty neutral. The latter means that society cannot have a non-neutral attitude toward uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate multiple prior agents, even when they all have the same set of priors. A number of ways to restore the possibility of aggregation are then discussed.Aggregation; Uncertainty

On the impossibility of preference aggregation under uncertainty

We provide a general theorem on the aggregation of preferences under uncertainty. We study, in the Anscombe-Aumann setting a wide class of preferences, that includes most known models of decision under uncertainty (and state-dependent versions of these models). We prove that aggregation is possible and necessarily linear if (society's) preferences are "smooth". The latter means that society cannot have a non-neutral attitude towards uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate maxmin expected utility maximizers, even when they all have the same set of priors. We show that dropping a weak notion of monotonicity on society's preferences allows one to restore the possibility of aggregation of non-smooth preferences.Aggregation, Harsanyi, uncertainty, multiple priors.

Vive la Différence? Structural Diversity as a Challenge for Metanormative Theories

Decision-making under normative uncertainty requires an agent to aggregate the assessments of options given by rival normative theories into a single assessment that tells her what to do in light of her uncertainty. But what if the assessments of rival theories differ not just in their content but in their structure -- e.g., some are merely ordinal while others are cardinal? This paper describes and evaluates three general approaches to this "problem of structural diversity": structural enrichment, structural depletion, and multi-stage aggregation. All three approaches have notable drawbacks, but I tentatively defend multi-stage aggregation as least bad of the three

A Generalised Model of Investment under Uncertainty: Aggregation and Estimation

We propose a structural model of investment which is based on the aggregation of (S,s) investment projects within firms. This encompasses the findings that whilst firm level investment is smooth, plant level investment is lumpy and frequently zero. We undertake stochastic aggregation and derive a structural firm level investment estimator. The empirical performance and fit of this estimator on a panel of manufacturing firms is encouraging and provides an avenue for general policy simulation. This model also explains the rich non-linear dynamics of firm level investment data and the frequent simultaneity of firm level investment and disinvestment. This approach provides an alternative structural estimator to the standard convex adjustment cost models, such as Tobin's Q and the Euler equation. The is important because these estimators, which assume quadratic adjustment costs, appear to be misspecified and subject to a fallacy of composition between smooth firm level investment and lumpy plant level investment. For completeness we also consider time aggregation as an alternative source of smoothing but statistically reject this as being insufficient to smooth investment alone. This test also rejects most plant level data, such as the US\ LRD and UK\ ARD, as being generated from a single (S,s) process.

On the impossibility of preference aggregation under uncertainty

URL des Cahiers : https://halshs.archives-ouvertes.fr/CAHIERS-MSECahiers de la MSE 2005.12 - Série Verte - ISSN : 1624-0340We provide a general theorem on the aggregation of preferences under uncertainty. We study, in the Anscombe-Aumann setting a wide class of preferences, that includes most known models of decision under uncertainty (and state-dependent versions of these models). We prove that aggregation is possible and necessarily linear if (society's) preferences are "smooth". The latter means that society cannot have a non-neutral attitude towards uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate maxmin expected utility maximizers, even when they all have the same set of priors. We show that dropping a weak notion of monotonicity on society's preferences allows one to restore the possibility of aggregation of non-smooth preferences.Nous établissons un résultat général donnant les conditions sous lesquelles l'agrégation des préférences dans l'incertain est possible. Dans un cadre à la Anscombe-Aummann, nous considérons une classe très large de préférences, incluant la plupart des modèles de décision (et leur version dépendant de l'état). Nous montrons que l'agrégation des préférences n'est possible, et nécessairement linéaire, que si les préférences agrégées possèdent une propriété assez restrictive pouvant s'interpréter comme de la neutralité face à l'incertitude. Un corollaire de notre théorème est qu'il n'est pas possible d'agréger des préférences du type maxmin utilité espérée. Nous montrons que relâcher une condition faible de monotonie sur les préférences de la société restaure la possibilité d'agréger des préférences non neutres par rapport à l'incertitude

Scenarios and Policy Aggregation in Optimization under Uncertainty

A common approach in coping with multiperiod optimization problems under uncertainty where statistical information is not really strong enough to support a stochastic programming model, has been to set up and analyze a number of scenarios. The aim then is to identify trends and essential features on which a robust decision policy can be based. This paper develops for the first time a rigorous algorithmic procedure for determining such a policy in response to any weighting of the scenarios. The scenarios are bundled at various levels to reflect the availability of information, and iterative adjustments are made to the decision policy to adapt to this structure and remove the dependence on hindsight

Characterization of Cynara cardunculus L. flower from Alentejo as a coagulant agent for cheesemaking

The cardoon (Cynara cardunculus L.) is a mandatory vegetable coagulant for certain Protected Designation of Origin Portuguese cheeses. It grows wild in Portugal and is used without any type of control regarding flower picking or extract preparation, representing some uncertainty in cheese manufacture. The variability in technological properties, in the context of traditional cheese manufacture, of cardoon flower ecotypes from the Alentejo region was evaluated, including milk clotting and proteolytic activities, coagulation properties and potential cheesemaking yield of flower extracts. Multivariate statistics highlighted the variability of flower properties for cheesemaking, but allowed the aggregation of the ecotypes into five groups under the major influence of milk clotting activity and effect on gel firmness and micellar aggregation rate, followed by proteolytic activity. These differences may have an impact on cheese properties and therefore can allow the selection of cardoon flower for the manufacture of different types of cheese

Measure and integral with purely ordinal scales

We develop a purely ordinal model for aggregation functionals for lattice valued functions, comprising as special cases quantiles, the Ky Fan metric and the Sugeno integral. For modeling findings of psychological experiments like the reflection effect in decision behaviour under risk or uncertainty, we introduce reflection lattices. These are complete linear lattices endowed with an order reversing bijection like the reflection at $0$ on the real interval $[-1,1]$. Mathematically we investigate the lattice of non-void intervals in a complete linear lattice, then the class of monotone interval-valued functions and