Olivier Cailloux

Eliciting Electre Tri category limits for a group of decision makers

Multiple criteria sorting aims at assigning alternatives evaluated on several criteria to predefined ordered categories. In this paper, we consider a well known multiple criteria sorting method, Electre Tri, which involves three types of preference parameters: (1) category limits defining the frontiers between consecutive categories, (2) weights and majority level specifying which coalitions form a majority, and (3) veto thresholds characterizing discordance effects. We propose an elicitation procedure to infer category limits from assignment examples provided by multiple decision makers. The procedure computes a set of category limits and vetoes common to all decision makers, with variable weights for each decision maker. Hence, the method helps reaching a consensus among decision makers on the category limits and veto thresholds, whereas finding a consensus on weights is left aside. The inference procedure is based on mixed integer linear programming and performs well even for datasets corresponding to real-world decision problems. We provide an illustrative example of the use of the method and analyze the performance of the proposed algorithms.

Constrained multicriteria sorting method applied to portfolio selection

The paper focuses on portfolio selection problems which aim at selecting a subset of alternatives considering not only the performance of the alternatives evaluated on multiple criteria, but also the performance of portfolio as a whole, on which balance over alternatives on specific attributes is required by the Decision Makers (DMs). n nWe propose a two-level method to handle such decision situation. First, at the individual level, the alternatives are evaluated by the sorting model Electre Tri which assigns alternatives to predefined ordered categories by comparing alternatives to profiles separating the categories. The DMs preferences on alternatives are expressed by some assignment examples they can provide, which reduces the DMs cognitive efforts. Second, at the portfolio level, the DMs preferences express requirements on the composition of portfolio and are modeled as constraints on category size. The method proceeds through the resolution of a Mixed Integer Program (MIP) and selects a satisfactory portfolio as close as possible to the DMs preference. n nThe usefulness of the proposed method is illustrated by an example which integrates a sorting model with assignment examples and constraints on the portfolio definition. The method can be used widely in portfolio selection situation where the decision should be made taking into account the performances of individual alternatives and portfolio simultaneously.

Operational tools to build a multicriteria territorial risk scale with multiple stakeholders

Evaluating and comparing the threats and vulnerabilities associated with territorial zones according to multiple criteria (industrial activity, population, etc.) can be a time-consuming task and often requires the participation of several stakeholders. Rather than a direct evaluation of these zones, building a risk assessment scale and using it in a formal procedure permits to automate the assessment and therefore to apply it in a repeated way and in large-scale contexts and, provided the chosen procedure and scale are accepted, to make it objective. One of the main difficulties of building such a formal evaluation procedure is to account for the multiple decision makers preferences. The procedure used in this article, Electre Tri, uses the performances of each territorial zone on multiple criteria, together with preferential parameters from multiple decision makers, to qualitatively assess their associated risk level. We also present operational tools in order to implement such a procedure in practice, and show their use on a detailed example.

A data model for algorithmic multiple criteria decision analysis

Various software tools implementing multiple criteria decision analysis (MCDA) methods have appeared over the last decades. Although MCDA methods share common features, most of the implementing software have been developed independently from scratch. Majority of the tools have a proprietary storage format and exchanging data among software is cumbersome. Common data exchange standard would be useful for an analyst wanting to apply different methods on the same problem. The Decision Deck project has proposed to build components implementing MCDA methods in a reusable and interchangeable manner. A key element in this scheme is the XMCDA standard, a proposal that aims to standardize an XML encoding of common structures appearing in MCDA models, such as criteria and performance evaluations. Although XMCDA allows to present most data structures for MCDA models, it almost completely lacks data integrity checks. In this paper we present a new comprehensive data model for MCDA problems, implemented as an XML schema. The data model includes types that are sufficient to represent multi-attribute value/utility models, ELECTRE III/TRI models, and their stochastic extensions, and AHP. We also discuss use of the data model in algorithmic MCDA.

Reasons and Means to Model Preferences as Incomplete

Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review some of the reasons that have been put forward to justify more complex modeling, and review some of the techniques that have been proposed to obtain models of such preferences.

Eliciting a suitable voting rule via examples

We address the problem of specifying a voting rule by means of a series of examples. Each example consists of the answer to a simple question: how should the rule rank two alternatives, given the positions at which each voter ranks the two alternatives? To be able to formalise this elicitation problem, we develop a novel variant of classical social choice theory in terms of associations of alternatives with vectors of ranks rather than the common associations of voters with preference orders. We then define and study a class of voting rules suited for elicitation using such answers. Finally, we propose and experimentally evaluate several elicitation strategies for arriving at a good approximation of the target rule with a reasonable number of queries.