Utilitarian Aggregation with Heterogeneous Beliefs

The utilitarian aggregation rule requires social utility and beliefs to be a convex combination of individual utilities and beliefs, respectively. Since, in the case of belief heterogeneity, the standard Pareto condition is incompatible with such a separate aggregation, a new condition, called the belief-proof Pareto condition, is proposed to alleviate occurrences of spurious agreement by restricting unanimity to beliefs that can be considered reasonable by society. Then, we show, in the Anscombe-Aumann and the Savage framework, that the belief-proof Pareto condition is equivalent to separate aggregation of individual beliefs and tastes. (JEL D11, D71, D83)

Strategic manipulation in judgment aggregation under higher-level reasoning

We analyse the incentives of individuals to misrepresent their truthful judgments when engaged in collective decision-making. Our focus is on scenarios in which individuals reason about the incentives of others before choosing which judgments to report themselves. To this end, we introduce a formal model of strategic behaviour in logic-based judgment aggregation that accounts for such higher-level reasoning as well as the fact that individuals may only have partial information about the truthful judgments and preferences of their peers. We find that every aggregation rule must belong to exactly one of three possible categories: it is either (i) immune to strategic manipulation for every level of reasoning, or (ii) manipulable for every level of reasoning, or (iii) immune to manipulation only for every kth level of reasoning, for some natural number k greater than 1.

The median rule in judgement aggregation

A judgement aggregation rule takes the views of a collection of voters over a set of interconnected issues and yields a logically consistent collective view. The median rule is a judgement aggregation rule that selects the logically consistent view which minimizes the average distance to the views of the voters (where the “distance” between two views is the number of issues on which they disagree). In the special case of preference aggregation, this is called the Kemeny rule. We show that, under appropriate regularity conditions, the median rule is the unique judgement aggregation rule which satisfies three axioms: Ensemble Supermajority Efficiency, Reinforcement, and Continuity. Our analysis covers aggregation problems in which the consistency restrictions on input and output judgements may differ. We also allow for issues to be weighted, and provide numerous examples in which issue weights arise naturally.

Algorithm and Software for Building Aggregated Rankings

When deciding on the choice of any alternative, it is necessary to find out which of the considered options will be better. In this perspective it is important to establish the assessment criteria and to determine the scale. In this case, the attention should be paid to the non-compensatory nature of the values of the criteria. The method of threshold aggregation allows considering these nuances. Using it, one can build a ranking that will reflect the comparative importance of various alternatives for the enterprise. The use of this method will prevent from compensating the low scores of experts with other higher scores on other criteria. The article presents a noncompensatory aggregation model to compile rankings, which is based on the threshold aggregation rule. A diagram of the assessment stages for this model and an algorithm for the development of software «Compiling an Aggregated Ranking» are presented. This model was programmed in C # in the Visual Studio 2019 environment

On the impossibility of using “the correct” cost–benefit aggregation rule

PurposeThe purpose of this paper is to deal with one of the technical difficulties of private and social cost–benefit analysis, i.e. the choice of the proper cost–benefit aggregation rule (or method) to use, when a private capital investment decision has to be taken or a public project appraisal has to be carried out.Design/methodology/approachAlthough the considerable amount of existing literature, the problem of the choice of the right mathematical aggregation rule is still an open one. The majority of authors claim that net present value is a superior method and thus it is the one to be always used. Other authors try to show that various aggregation methods, under specific conditions, arrive at the same recommendation. An exceptional case is the field of education economics where the internal rate of return is widely used.FindingsThis paper offers a survey of this controversial topic which focuses on some clear cut formal properties of the various aggregation methods and considers the empirical characteristics of the different fields of application. Its main conclusion is that no “correct” aggregation rule, always applicable in all decision frameworks, can exist.Originality/valueIts main objective is to supply clear guidelines to orient practitioners and help the teaching on this topic. Its main conclusion is that no “correct” aggregation rule, always applicable in all decision frameworks, can exist. On the contrary, even if one restricts her/himself to a particular class of investments, often no clear-cut selection can be made.

Neutrality and relative acceptability in judgment aggregation

One of the fundamental normative principles in social choice theory is that of neutrality. In the context of judgment aggregation, neutrality is encoded in the form of an axiom expressing that, when two possible judgments enjoy the same support amongst the individuals, then either both or neither of them should be accepted. This is a reasonable requirement in many scenarios. However, we argue that for scenarios in which individuals are asked to pass judgment on very diverse kinds of propositions, a notion of relative acceptability is better suited. We capture this notion by a new axiom that hinges on a binary “acceptability” relation A between propositions: if a given coalition accepting a proposition p entails the collective acceptance of p, then the same should be true for every other proposition q related to p via A. Intuitively, pAq means that p is at least as acceptable as q. Classical neutrality is then a special case where all propositions are equally acceptable. We show that our new axiom allows us to circumvent a classical impossibility theorem in judgment aggregation for certain scenarios of practical interest. Also, we offer a precise characterisation of all scenarios that are safe, in the sense that any aggregation rule respecting the relative acceptability between propositions will always return logically consistent outcomes.

Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory

To address issues involving inconsistencies, this paper proposes a stochastic multi-criteria group decision making algorithm based on neutrosophic soft sets, which includes a pair of asymmetric functions: Truth-membership and false-membership, and an indeterminacy-membership function. For integrating an inherent stochastic, the algorithm expresses the weights of decision makers and parameter subjective weights by neutrosophic numbers instead of determinate values. Additionally, the algorithm is guided by the prospect theory, which incorporates psychological expectations of decision makers into decision making. To construct the prospect decision matrix, this research establishes a conflict degree measure of neutrosophic numbers and improves it to accommodate the stochastic multi-criteria group decision making. Moreover, we introduce the weighted average aggregation rule and weighted geometric aggregation rule of neutrosophic soft sets. Later, this study presents an algorithm for neutrosophic soft sets in the stochastic multi-criteria group decision making based on the prospect theory. Finally, we perform an illustrative example and a comparative analysis to prove the effectiveness and feasibility of the proposed algorithm.

Aggregation of Information by Binary Voting Rules

A group of individuals faces the choice of an alternative out of a set of alternatives. Each member of the group holds an opinion regarding the most suitable (best) alternative for which he or she votes. In this setting, the individual votes are based on their decisional competencies, which hinge on the information to which they are exposed and on their ability to make use of that information. The main question is how to translate the group members’ voting profile to a single collective choice. This chapter studies different aspects of this question in the context of binary voting where the group faces only two alternatives. The selection of an appropriate aggregation rule is a central issue in the fields of social choice, public choice, voting theory, and collective decision making. Since the votes are based on the individual competencies, the applied aggregation rule should take into account not only the voting profile but also the competency profile. In fact, it should also take into consideration any other relevant environmental information such as the asymmetry between the feasible alternatives, the dependence between individual votes, decision-making costs, and the available past record of the voters’ decisions. The chapter focuses on the clarification of the relationship between the performance of binary aggregation rules and the relevant variables and parameters. This has direct normative implications regarding the desirable mode of collective decision making and, in particular, regarding the desirable aggregation rule and the size and the composition of the decision-making body.