Preference aggregation and statistical estimation

Yugoslav Journal of Operations Research, 2008

Within the frame of decision aid literature, decision making problems with multiple sources of information have drawn the attention of researchers from a wide spectrum of disciplines. In decision situations with multiple individuals, each one has his own knowledge of the decision problem alternatives. The use of information assessed in different domains is not a seldom situation. This non-homogeneous information can be represented by values belonging to domains with different nature as linguistic, numerical and interval valued or can be values assessed in label sets with different granularity and multigranular linguistic information.

Journal of Mathematical Psychology, 1985

He is a specialist in issues of representation and reapportionment and has written on a variety of topics dealing with collective decision-making. His most recent co-edited books are Information Pooling and Group Decision-Making, 1985, and Electoral Laws and Their Political Consequences,

International Journal of Advanced Trends in Computer Science and Engineering ( IJATCSE ), 2019

Most of recommender systems rely on the users' preferences to recommend items. With the increase of data and the number of users on the internet, the task of recommender system becomes more and more sophisticated. The fusion of users' preferences is a solution to facilitate that task. The resolution of this issue, helps in decreasing the run time of a recommender system. This research focuses on the issue of preference fusion in the context of social network. The aim of this research is to determine the collective preferences of users belonging to a given community based on their individual preferences. In particular, researchers are interested here in the representation of individual preferences, taking into account the uncertainty and imprecision phenomenon. In this research two methods are proposed: majority vote method and the Dempster Shafer theory of evidence. Experiments on generated datasets would highlight the interest of the proposed solution.

We study various methods of aggregating individual judgments and individual priorities in group decision making with the AHP. The focus is on the empirical properties of the various methods, mainly on the extent to which the various aggregation methods represent an accurate approximation of the priority vector of interest. We identify five main classes of aggregation procedures which provide identical or very similar empirical expressions for the vectors of interest. We also propose a method to decompose in the AHP response matrix distortions due to random errors and perturbations caused by cognitive biases predicted by the mathematical psychology literature. We test the decomposition with experimental data and find that perturbations in group decision making caused by cognitive distortions are more important than those caused by random errors. We propose methods to correct the systematic distortions.

2009

Collective decision-making is a familiar feature of our social, political, and economic lives. It ranges from the relatively trivial (e.g. the choice of the next family car) to the globally significant (e.g. whether or not a country should go to war). Yet, whether trivial or globally significant, such decisions involve a number of challenging problems. These problems arise in the standard social choice setting, where individuals differ in their preferences. They also arise in the standard decision-making setting, where individuals share the same preferences, but differ in their decisional capabilities. The distinctive feature of Collective Preference and Choice is that it looks at classical aggregation problems that arise in three closely related areas: social choice theory, voting theory, and group decision-making under uncertainty. Using a series of exercises and examples, the book explains these problems with reference to a number of important contributions to the study of collec...

Decision‐making Process, 2009

Many organizations face such complex and important management problems that they sometimes want their decisions to be somehow supported by a 'scientific approach', sometimes called a decision analysis. The analyst in charge of this preparation faces many diverse tasks: stakeholders identification, problem statement, elaboration of a list of possible actions, definition of one or several criteria for evaluating these actions, information gathering, sensitivity analysis, elaboration of a recommendation (for instance a ranking of the actions or a subset of 'good' actions), etc. The desire or necessity to take multiple conflicting viewpoints into account for evaluating the actions often makes this task even more difficult. In that case, we speak of multicriteria decision aiding [POM 93, ROY 85, VIN 89]. The expert must then try to synthesize the partial preferences (modeled by each criterion) into a global preference on which a recommendation can be based. This is called preference aggregation.

Cooperative Approaches, 2011

Omega, 2018

Most of classical decision making processes aim at selecting the "best" alternative or at ranking alternatives based on the opinions of decision makers. Often, such a process occurs among people (experts or decision makers) who are expected to achieve some shared consensus in ranking the alternatives. However, this is not likely to happen (especially for a large and heterogeneous collection of people) and decision makers tend to reveal groups characteristics derived from their different opinions. A major problem is that inconsistency in opinions arises as each expert has a limited knowledge, errors and misinterpretation of data can occur and thus it is not clear how groups can be identified to be internally consistent and non-conflicting. In this paper, we investigate the conditions under which experts can be split into different subgroups that share coherent and consistent opinions but are mutually in conflict in the ordering of the alternatives. We face this problem by presenting a non-linear integer programming model where each decision maker specifies incomplete preferences on pairs of alternatives and the objective is to obtain groups having the least possible degree of inconsistency. From a theoretical standpoint, we show that the proposed problem is non-convex and NP-Hard. Moreover, we validate the proposed approach with respect to a case study related to the 2018 Italian political elections. Specifically, we analyze the opinions of 33 decision makers and we show that the proposed technique is able to identify subgroups characterized by large internal consistency, i.e., the members of each subgroups express similar judgements upon the different options, while such options are evaluated very differently

Theory and Decision, 1977

DEFINITION 1 : ~> is a difference relation on S iff for every x, y, z, w, r, s in S, (1) (x, y) >~ (z, w) or (z,w) >~ (x,y). (2) If (x, y) >~ (z, w), then (w, z) >1 (y, x). 1> is a transitive difference relation on S if also (3) If (x,y.) >/(z, w) and (z, w) i> (r, s), then (x,y) >I (r, s).

European Journal of Operational Research, 2014

We study various methods of aggregating individual judgments and individual priorities in group decision making with the AHP. The focus is on the empirical properties of the various methods, mainly on the extent to which the various aggregation methods represent an accurate approximation of the priority vector of interest. We identify five main classes of aggregation procedures which provide identical or very similar empirical expressions for the vectors of interest. We also propose a method to decompose in the AHP response matrix distortions due to random errors and perturbations caused by cognitive bias predicted by the mathematical psychology literature. We test the decomposition with experimental data and find that perturbations in group decision making caused by cognitive distortions are more important than those caused by random errors. We propose methods to correct systematic distortions.

Knowledge-Based Systems, 2009

This article presents some systematic sorting and ordering of approaches dealing with fuzzy aggregation and fuzzy averaging from different authors. The aggregation of fuzzy information from a group of experts for developing collective opinion or verdict is the important question in the expert systems theory and practice. This is to obtain a more comprehensive and realistic solution to the given decision problem. This note tries to outline an overall formal umbrella to various methods to aggregate several fuzzy sets, which describe the individual points of view of experts, or results of judgements from the various characteristics.

2014

We consider the situation where there are several alternatives for investing a quantity of money to achieve a set of objectives. The choice of which alternative to apply depends on how citizens and political representatives perceive that such objectives should be achieved. All citizens with the right to vote can express their preferences in the decision-making process. These preferences may be incomplete. Political representatives represent the citizens who have not taken part in the decision-making process. The weight corresponding to political representatives depends on the number of citizens that have intervened in the decision-making process. The methodology we propose needs the participants to specify for each alternative how they rate the different attributes and the relative importance of attributes. On the basis of this information an expected utility interval is output for each alternative. To do this, an evidential reasoning approach is applied. This approach improves the insightfulness and rationality of the decision-making process using a belief decision matrix for problem modeling and the Dempster-Shafer theory of evidence for attribute aggregation. Finally, we propose using the distances of each expected utility interval from the maximum and the minimum utilities to rank the alternative set. The basic idea is that an alternative is ranked first if its distance to the maximum utility is the smallest, and its distance to the minimum utility is the greatest. If only one of these conditions is satisfied, a distance ratio is then used.

The aim of judgment aggregation is to make collective decisions based on the judgments of individual agents. Some rationality conditions governing the expected behavior of the aggregation function must be considered. However, impossibility theorems show that designing an aggregation function satisfying all desirable properties is not feasible. While some rationality conditions are very natural ones, other ones are more disputable. We show that this is the case of the systematicity condition that prevents from electing issues with more votes than others. We rather promote a neutrality and a swap optimality condition. Swap optimality ensures that among two possible results, the one with the best support (number of votes) is chosen. We propose a new family of judgment aggregation methods based on the support (number of votes) that receives each issue.

Information Sciences, 1998

People give information about their personal preferences in many different ways, depending on their background. This paper deals with group decision making problems in which the solution depends on information of a different nature, i.e., assuming that the experts express their preferences with numerical or linguistic values. The aim of this paper is to present a proposal for this problem. We introduce a fusion operator for numerical and linguistic information. This operator combines linguistic values (assessed in the same label set) with numerical ones (assessed in the interval [0,1]). It is based on two transformation methods between numerical and linguistic values, which are defined using the concept of the characteristic values proposed in this paper. Its application to group decision making problems is illustrated by means of a particular fusion operator guided by fuzzy majority. Considering that the experts express their opinions by means of fuzzy or linguistic preference relations, this operator is used to develop a choice process for the alternatives, allowing solutions to be obtained in line with the majority of the experts' opinions.