Fusion of individual preference orderings in an ordinal semidemocratic decision-making framework

This contribution focuses on the problem of combining multi-agent preference orderings of different alternatives into a single consensus fused ordering, when the agents’ importance is expressed through a rank-ordering and not a set of weights. An enhanced version of the algorithm proposed by Yager in (Fuzzy Sets and Systems, 117(1): 1-12, 2001) is presented. The main advantages of the new algorithm are that: (i) it better reflects the multi-agent preference orderings and (ii) it is more versatile, since it admits preference orderings with omitted or incomparable alternatives. The description of the new algorithm is supported by a realistic example

A paired-comparison approach for fusing preference orderings from rank-ordered agents

The problem of aggregating multi-agent preference orderings has received considerable attention in many fields of research, such as multi-criteria decision aiding and social choice theory; nevertheless, the case in which the agents’ importance is expressed in the form of a rank-ordering, instead of a set of weights, has not been much debated. The aim of this article is to present a novel algorithm – denominated as ‘‘Ordered Paired-Comparisons Algorithm’’ (OPCA), which addresses this decision-making problem in a relatively simple and practical way. The OPCA is organized into three main phases: (i) turning multi- agent preference orderings into sets of paired comparisons, (ii) synthesizing the paired-comparison sets, and (iii) constructing a fused (or consensus) ordering. Particularly interesting is phase two, which introduces a new aggregation process based on a priority sequence, obtained from the agents’ importance rank-ordering. A detailed description of the new algorithm is supported by practical examples

A novel algorithm for fusing preference orderings by rank-ordered agents

Yager proposed an algorithm to combine multi-agent preference orderings of several alternatives into a single consensus fused ordering, when the agents’ importance is expressed through a rank-ordering and not a set of weights. This algorithm is simple and automatable but has some limitations which reduce its range of application, e.g., (i) preference orderings should not include incomparabilities between alternative and/or omissions of some of them, and (ii) the fused ordering may sometimes not reflect the majority of the multi-agent preference orderings. The aim of this article is to present an enhanced version of the Yager’s algorithm, which overcomes the above limitations. Some practical examples support the description of the new algorithm

Preference fusion and Condorcet's Paradox under uncertainty

Facing an unknown situation, a person may not be able to firmly elicit his/her preferences over different alternatives, so he/she tends to express uncertain preferences. Given a community of different persons expressing their preferences over certain alternatives under uncertainty, to get a collective representative opinion of the whole community, a preference fusion process is required. The aim of this work is to propose a preference fusion method that copes with uncertainty and escape from the Condorcet paradox. To model preferences under uncertainty, we propose to develop a model of preferences based on belief function theory that accurately describes and captures the uncertainty associated with individual or collective preferences. This work improves and extends the previous results. This work improves and extends the contribution presented in a previous work. The benefits of our contribution are twofold. On the one hand, we propose a qualitative and expressive preference modeling strategy based on belief-function theory which scales better with the number of sources. On the other hand, we propose an incremental distance-based algorithm (using Jousselme distance) for the construction of the collective preference order to avoid the Condorcet Paradox.Comment: International Conference on Information Fusion, Jul 2017, Xi'an, Chin

Representing Reliability-Based Peer Pressure

Abstract This thesis proposes and explores three strategies for aggregating individual preferences: the non-contentious, majority, and plurality methods. The proposed methods rely on the lexicographic rule but use a reliability ordering over sets of agents instead of only agents. The preservation of properties (reflexivity, transitivity, totality, antisymmetry, and unanimity) by each method are examined and compared. The thesis contributes to understanding preference aggregation strategies and their relevance in real-life decision-making contexts.Masteroppgave i informasjonsvitenskapINFO390MASV-INF

Checking the consistency of the solution in ordinal semi-democratic decision making problems

An interesting decision-making problem is that of aggregating multi-agent preference orderings into a consensus ordering, in the case the agents’ importance is expressed in the form of a rank-ordering. Due to the specificity of the problem, the scientific literature encompasses a relatively small number of aggregation techniques. For the aggregation to be effective, it is important that the consensus ordering well reflects the input data, i.e., the agents’ preference orderings and importance rank-ordering. The aim of this paper is introducing a new quantitative tool – represented by the so-called p indicators – which allows to check the degree of consistency between consensus ordering and input data, from several perspectives. This tool is independent from the aggregation technique in use and applicable to a wide variety of practical contexts, e.g., problems in which preference orderings include omissions and/or incomparabilities between some alternatives. Also, the p indicators are simple, intuitive and practical for comparing the results obtained from different techniques. The description is supported by various application examples

Consistency analysis in quality classification problems with multiple rank-ordered agents

A relatively diffused quality decision problem is that of classifying some objects of interest into predetermined nominal categories. This problem is particularly interesting in the case: (i) multiple agents perform local classifications of an object, to be fused into a global classification; (ii) there is more than one object to be classified; and (iii) agents may have different positions of power, expressed in the form of an importance rank-ordering. Due to the specificity of the problem, the scientific literature encompasses a relatively small number of data fusion techniques. For the fusion to be effective, the global classifications of the objects should be consistent with the agents’ local classifications and their importance rank-ordering, which represent the input data. The aim of this article is to propose a set of indicators, which allow to check the degree of consistency between the global classification and the input data, from several perspectives, e.g., that of individual agents, individual objects, agents’ importance rank-ordering, etc. These indicators are independent from the fusion technique in use and applicable to a wide variety of practical contexts, such as problems in which some of the local classifications are uncertain or incomplete. The proposed indicators are simple, intuitive, and practical for comparing the results obtained through different techniques. The description therein is supported by several practical examples

Possibilistic Boolean games: strategic reasoning under incomplete information

Boolean games offer a compact alternative to normal-form games, by encoding the goal of each agent as a propositional formula. In this paper, we show how this framework can be naturally extended to model situations in which agents are uncertain about other agents' goals. We first use uncertainty measures from possibility theory to semantically define (solution concepts to) Boolean games with incomplete information. Then we present a syntactic characterization of these semantics, which can readily be implemented, and we characterize the computational complexity