Le travail de recherche présenté dans cette thèse s'inscrit dans le champ de l'aide multicritère à la décision. Ce champ concerne la décision dans un contexte où les alternatives sont jugées sous divers aspects, souvent conflictuels. Notre travail s'insère dans une approche descriptive et cherche à observer l'effet du conflit multicritère sur les préférences exprimées par le décideur. Dans un premier temps, nous proposons une définition de l'intensité du conflit multicritère entre deux alternatives puis nous nous intéressons aux préférences incomplètes et identifions deux classes de modèles de préférences incomplètes. Notre principale contribution est ensuite d'observer et analyser l'effet du conflit lors du recueil des préférences d'un décideur. Nous avons pour cela conçu et mené deux expérimentations permettant de tester le recueil de préférences à travers des comparaisons par paires, et à travers des matchings. La première expérimentation nous permet de mettre en évidence une forme d'intransitivité de l'indifférence le long des chaînes d'isopréférence. Un fort conflit multicritère conduit les sujets à exprimer des préférences incomplètes. Les résultats obtenus lors de cette expérimentation sont en cours de publication (Deparis et al. [2012]). La seconde expérimentation nous permet de montrer que les asymétries déjà observées dans la littérature en réponse à un bi-matching sont fortement amplifiées par l'effet du conflit multicritère. Nous discutons des implications de ces résultats en termes d'élicitation des préférences. Enfin, nous analysons les résultats expérimentaux au regard de la labilité des préférences qu'ils révèlent. Au-delà de cette contribution, notre thèse permet de mieux comprendre les interactions qui peuvent exister entre les approches normative, descriptive et prescriptive en décision multicritère. / The research presented in this thesis lies in the field of multicriteria decision aid. This field deals with decision in a context where several aspects, usually in conflict, are considered when judging the alternatives. Our work stands in the descriptive approach and aims at observing the effect of multicriteria conflict on the preferences expressed by decision-makers. First, we propose a definition of the intensity of inter-alternative multicriteria conflict and then we consider incomplete preferences and identify two types of incomplete preference models. Our main contribution is then to observe and analyse the effect of conflict when assessing the preferences of a decision-maker. In order to do so, we designed and led two experiments allowing to test the assessment of preferences through pairwise comparisons and matchings. The first experiment allows us to exhibit an intransitivity of indifference along isopreference chains. A large multicriteria conflict leads subjects to express incomplete preferences. Results obtained from this experiment are under publication (Deparis et al. [2012]). The second experiment allows us to show that asymmetries already observed in the literature in response to bimatchings are strongly amplified by multicriteria conflict. We discuss the implications of these results on elicitation of preferences. Finally, we analyse the experimental results with regard to the lability of preferences that they reveal. Beyond this contribution, our thesis sheds a light on the interactions that exist between the normative, descriptive and prescriptive approaches in multicriteria decision-making.

The main objective of this thesis is to develop a martingale-type solution to optimal consumption--investment choice problems ([Merton, 1969] and [Merton, 1971]) under time-varying incomplete preferences driven by externalities such as patience, socialization effects, and market volatility. The market is composed of multiple risky assets and multiple consumption goods, while in addition there are multiple fluctuating preference parameters with inexact values connected to imprecise tastes. Utility maximization becomes a multi-criteria problem with possibly function-valued criteria. To come up with a complete characterization of the solutions, first we motivate and introduce a set-valued stochastic process for the dynamics of multi-utility indices and formulate the optimization problem in a topological vector space. Then, we modify a classical scalarization method allowing for infiniteness and randomness in dimensions and prove results of equivalence to the original problem. Illustrative examples are given to demonstrate practical interests and method applicability progressively. The link between the original problem and a dual problem is also discussed, relatively briefly. Finally, by using Malliavin calculus with stochastic geometry, we find optimal investment policies to be generally set-valued, each of whose selectors admits a four-way decomposition involving an additional indecisiveness risk-hedging portfolio. Our results touch on new directions for optimal consumption--investment choices in the presence of incomparability and time inconsistency, also signaling potentially testable assumptions on the variability of asset prices. Simulation techniques for set-valued processes are studied for how solved optimal policies can be computed in practice. / 2025-05-12T00:00:00Z

In this dissertation we focus on two main topics. Under the first topic, we develop a new framework for stochastic network interdiction problem to address ambiguity in the defender risk preferences. The second topic is dedicated to computational studies of two-stage stochastic integer programs. More specifically, we consider two cases. First, we develop some solution methods for two-stage stochastic integer programs with continuous recourse; second, we study some computational strategies for two-stage stochastic integer programs with integer recourse. We study a class of stochastic network interdiction problems where the defender has incomplete (ambiguous) preferences. Specifically, we focus on the shortest path network interdiction modeled as a Stackelberg game, where the defender (leader) makes an interdiction decision first, then the attacker (follower) selects a shortest path after the observation of random arc costs and interdiction effects in the network. We take a decision-analytic perspective in addressing probabilistic risk over network parameters, assuming that the defender's risk preferences over exogenously given probabilities can be summarized by the expected utility theory. Although the exact form of the utility function is ambiguous to the defender, we assume that a set of historical data on some pairwise comparisons made by the defender is available, which can be used to restrict the shape of the utility function. We use two different approaches to tackle this problem. The first approach conducts utility estimation and optimization separately, by first finding the best fit for a piecewise linear concave utility function according to the available data, and then optimizing the expected utility. The second approach integrates utility estimation and optimization, by modeling the utility ambiguity under a robust optimization framework following \cite{armbruster2015decision} and \cite{Hu}. We conduct extensive computational experiments to evaluate the performances of these approaches on the stochastic shortest path network interdiction problem. In third chapter, we propose partition-based decomposition algorithms for solving two-stage stochastic integer program with continuous recourse. The partition-based decomposition method enhance the classical decomposition methods (such as Benders decomposition) by utilizing the inexact cuts (coarse cuts) induced by a scenario partition. Coarse cut generation can be much less expensive than the standard Benders cuts, when the partition size is relatively small compared to the total number of scenarios. We conduct an extensive computational study to illustrate the advantage of the proposed partition-based decomposition algorithms compared with the state-of-the-art approaches. In chapter four, we concentrate on computational methods for two-stage stochastic integer program with integer recourse. We consider the partition-based relaxation framework integrated with a scenario decomposition algorithm in order to develop strategies which provide a better lower bound on the optimal objective value, within a tight time limit.

L'objet de cette thèse est l'étude des aspects algorithmiques du vote par approbation. Il s'agit principalement d'une étude théorique des enjeux computationnels soulevés par le vote par approbation dans des contextes de décisions variés. Cependant, j'étudie aussi des questions plus proches de la théorie classique du choix social et je conduis de brèves études expérimentales.Dans un premier temps, l'étude se porte sur une famille générale de règles de vote pour les élections de comités et les référendums multiples à l'aide du vote par approbation. Dans un second temps, je porte mon attention sur un contexte plus général, le vote par approbation sur domaines combinatoires en se basant sur des préférences conditionnelles. Finalement, je me place dans le cadre du vote avec préférences incomplètes pour étudier les problèmes de vainqueurs possibles et nécessaires dans le vote par approbation. / The subject of this thesis is the study of computational aspects of approval voting. Most of the works are theoretical results about computational issues raised by approval voting, in many different settings. However, I also study some questions that are more related to classical choice theory, and some problems are investigated through experimental analysis.Firstly, I study a general family of rules for approval voting in the context of committee elections and multiple referenda. Secondly, I focus on a more general setting, approval voting in combinatorial domains, based on conditional preferences. Finally, I consider approval voting in the context of incomplete preferences, to study the possible and necessary winner problems.

This thesis consists of three independent papers. They are put in reverse chronological order according to when they were initiated. The first paper, which is a joint work with Özgür Evren, extends the standard rational choice framework with the option to postpone the act of selecting an alternative. In that paper, we propose an axiomatic model of choice over risky prospects that restricts the classical rationality axioms solely to those instances in which the decision maker does not defer. The cardinal approach we follow allows us to identify the preference relation of the decision maker over lotteries, even if the choice data is very scarce due to deferral. Moreover, we also derive the value of deferring choice from a given set of options, which turns out to be an affine utility function over choice sets. At each choice situation, the decision maker compares the utility of each available alternative with that of deferral so as to decide on opting for an alternative immediately. The second paper is a model of status quo bias with choice avoidance. It describes the choice behavior of an otherwise standard decision maker whose choices are affected by the presence of a status quo alternative. The status quo emerges as a temporary choice, which may be reversed upon arrival of new (introspective or objective) information, or upon finding new alternatives. The third paper considers the network formation problem from a matching perspective. In that paper, agents want to link with each other and each has preferences over the subsets of others. We consider various solution concepts regarding the stability of a matching between the agents, establish relations between these concepts under several preference restrictions, and provide sufficient conditions for these solutions to be nonempty. / Diss. Stockholm : Handelshögskolan i Stockholm, 2011