Preference Aggregation Problem Research Articles

Satisfying complex top- k fairness constraints by preference substitutions

Given m users (voters), where each user casts her preference for a single item (candidate) over n items (candidates) as a ballot, the preference aggregation problem returns k items (candidates) that have the k highest number of preferences (votes). Our work studies this problem considering complex fairness constraints that have to be satisfied via proportionate representations of different values of the group protected attribute(s) in the top- k results. Precisely, we study the margin finding problem under single ballot substitutions , where a single substitution amounts to removing a vote from candidate i and assigning it to candidate j and the goal is to minimize the number of single ballot substitutions needed to guarantee that the top-k results satisfy the fairness constraints. We study several variants of this problem considering how top- k fairness constraints are defined, (i) MFBinaryS and MFMultiS are defined when the fairness (proportionate representation) is defined over a single, binary or multivalued, protected attribute, respectively; (ii) MF-Multi2 is studied when top- k fairness is defined over two different protected attributes; (iii) MFMulti3+ investigates the margin finding problem, considering 3 or more protected attributes. We study these problems theoretically, and present a suite of algorithms with provable guarantees. We conduct rigorous large scale experiments involving multiple real world datasets by appropriately adapting multiple state-of-the-art solutions to demonstrate the effectiveness and scalability of our proposed methods.

Funding public projects: A case for the Nash product rule

We study a mechanism design problem where a community of agents wishes to fund public projects via voluntary monetary contributions by the community members. This serves as a model for public expenditure without an exogenously available budget, such as participatory budgeting or voluntary tax programs, as well as donor coordination when interpreting charities as public projects and donations as contributions. Our aim is to identify a mutually beneficial distribution of the individual contributions. In the preference aggregation problem that we study, agents with linear utility functions over projects report the amount of their contribution, and the mechanism determines a socially optimal distribution of the money. We identify a specific mechanism—the Nash product rule—which picks the distribution that maximizes the product of the agents’ utilities. This rule is Pareto efficient and incentivizes agents to contribute their entire budget while spending each agent’s contribution only on projects the agent finds acceptable.

A Framework to Incorporate Decision-Maker Preferences Into Simulation Optimization to Support Collaborative Design

In this paper, we are concerned with the use of simulation optimization to handle collaborative design problems where more than one decision-maker is involved. We assume that the designers cannot enumerate all their considerations in closed-form, precise mathematical expressions but they can examine the merits of solutions with respect to their preferences and can compare candidate solutions with one another. We propose a three-stage framework to take the decision-makers' such considerations into account. The first step is to obtain a diverse set of designs that can all be considered efficient in terms of a performance metric (i.e., the objective function values of the simulation optimization model). These solutions are then passed on to the decision-makers to be analyzed in terms of their preferences that could not have been previously considered. Finally, the most appropriate solution is chosen. We address the problem encountered in the first step as a multimodal optimization problem. We address the second and the third subproblems as a preference aggregation problem in the social choice theory. We also illustrate the effectiveness of the proposed approach through a supply chain design problem inspired from the literature. We use the crowding clustering genetic algorithm as an example to demonstrate the first step. We use a multiplicative variant of the popular analytic hierarchy process to illustrate how the second and the third steps can be handled.

Incentive Compatible E-mandi with Large Scale Consumer Producer Matching Using BigData Based on Gale-shapely Algorithm for Perishable Commodities SCM

In this paper, we propose to transform the global matching mechanism in an electronic exchange between the producers and consumers in the SCM system for perishable commodities over large scale data sets. Matching of of consumers and producers satisfactions are mathematically modeled based on preferential evaluations based on the bidding request and the requirements data which is supplied as a matrix to Gale Shapely matching algorithm. The matching works over a very transparent approach in a e-trading environment over large scale data. Since, Bigdata is involved; the global SCM could be much clearer and easier for allocation of perishable commodities. These matching outcomes are compared with the matching and profit ranges obtained using simple English auction method which results Pareto-optimal matches. We are observing the proposed method produces stable matching, which is preference-strategy proof with incentive compatibility for both consumers and producers. Our design involves the preference revelation or elicitation problem and the preference-aggregation problem. The preference revelation problem involves eliciting truthful information from the agents about their types that are used for computation of Incentive compatible results. We are using Bayesian incentive compatible mechanism design in our match-making settings where the agents’ preference types are multidimensional. This preserves profitability up to an additive loss that can be made arbitrarily small in polynomial time in the number of agents and the size of the agents’ type spaces.

New learning methods for supervised and unsupervised preference aggregation

In this paper we present a general treatment of the preference aggregation problem, in which multiple preferences over objects must be combined into a single consensus ranking. We consider two instances of this problem: unsupervised aggregation where no information about a target ranking is available, and supervised aggregation where ground truth preferences are provided. For each problem class we develop novel learning methods that are applicable to a wide range of preference types. Specifically, for unsupervised aggregation we introduce the Multinomial Preference model (MPM) which uses a multinomial generative process to model the observed preferences. For the supervised problem we develop a supervised extension for MPM and then propose two fully supervised models. The first model employs SVD factorization to derive effective item features, transforming the aggregation problems into a learning-to-rank one. The second model aims to eliminate the costly SVD factorization and instantiates a probabilistic CRF framework, deriving unary and pairwise potentials directly from the observed preferences. Using a probabilistic framework allows us to directly optimize the expectation of any target metric, such as NDCG or ERR. All the proposed models operate on pairwise preferences and can thus be applied to a wide range of preference types. We empirically validate the models on rank aggregation and collaborative filtering data sets and demonstrate superior empirical accuracy.

Application of prioritized aggregation operators in preference voting

This paper clarifies, how a preference aggregation problem can be solved using the prioritized aggregation operators (PAO), where, a given group of candidates should be aggregated based upon their satisfaction for a collection of ranked places. The comparison results show that the proposed method can accurate aggregate a preference ranking system with less computation and without the need to solve any mathematical model. Also, a metasearch application shows the usefulness of applying the PAO for a preference aggregation. © 2010 Wiley Periodicals, Inc.

The topological approach to the aggregation of preferences

(1) A domain of preferences allows for topological aggregation for each number of people if and only if this domain of preferences is contractible. (2) The combination of continuity and the Pareto principle implies the existence of a unique manipulator. (3) Arrow’s theorem can be translated into the previous statement. All of these results are obtained via algebraic topology. This paper introduces some of the tools developed in topology and applies them upon the problem of preference aggregation.

Multiperson utility

We approach the problem of preference aggregation by endowing both individuals and coalitions with partially-ordered or incomplete preferences for decision under risk. Restricting attention to the case of complete individual preferences, and assuming complete preferences for some pairs of agents (interpersonal comparisons of utility units), we discover that the Extended Pareto Rule (if two disjoint coalitions A and B prefer x to y, then so does the coalition A ∪ B ) imposes a “no arbitrage” condition in the terms of utility comparison between agents. Furthermore, if all the individuals and pairs have complete preferences and certain non-degeneracy conditions are met, then we witness the emergence of a complete preference ordering for coalitions of all sizes. The corresponding utilities are a weighted sum of individual utilities, with the n − 1 independent weights obtained from the preferences of n − 1 pairs forming a spanning tree in the group.

A generalised model of judgment aggregation

The new field of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements (“if P then Q ”) as material conditionals. In this methodological paper, I present a simple unified model of judgment aggregation in general logics. I show how many realistic decision problems can be represented in it. This includes decision problems expressed in languages of standard propositional logic, predicate logic (e.g. preference aggregation problems), modal or conditional logics, and some multi-valued or fuzzy logics. I provide a list of simple tools for working with general logics, and I prove impossibility results that generalise earlier theorems.

Rousseau's Anti–Agenda-Setting Agenda and Contemporary Democratic Theory

In his recent article, “Rousseau on Agenda-Setting and Majority Rule” (2003), Ethan Putterman examines how the democratic principle of popular majority rule might be reconciled with agenda-setting by legislative experts through an analysis of Rousseau's political theory. He argues that Rousseau accomplishes this reconciliation through a novel separation of powers between the legislative and the executive powers where the sovereign people delegates the exclusive power to initiate laws to the executive. Putterman thereby identifies as a solution to the problem of democratic self-legislation what Rousseau sees as the most important danger to it. At issue is not merely the correct interpretation of Rousseau's theory, for Putterman's argument raises far-reaching questions concerning the compatibility of democratic principles and institutions. After demonstrating that Putterman is incorrect that the sovereign people in Rousseau's state delegate the power of legislative initiative, I examine how Rousseau anticipates and addresses a related question central to contemporary democratic and social choice theory: the problem of preference aggregation through voting in the absence of agenda-setting institutions.

Limiting Dictatorial rules

We consider the preference aggregation problem in infinite societies. In our model, there are arbitrarily many agents and alternatives, and admissible coalitions may be restricted to lie in an algebra. In this framework (which includes the standard one), we characterize, in terms of Strict Neutrality, the Ultrafilter Property of preference aggregation rules. Based on this property, we define the concept of Limiting Dictatorial rules, which are characterized by the existence of arbitrarily small decisive coalitions. We show that, in infinite societies which can be well approximated by finite ones, any Arrovian rule is limiting.

Community preferences and social choice

This paper gives necessary and sufficient conditions for the aggregation of preferences, extending an earlier treatment of aggregation by Stolper, Gorman, Samuelson and Chipman. Such aggregation procedures are intended to deal with the problem of aggregating demand functions in econometrics, where the aggregate is required to be independent to the income distribution. Thus, it is usually assumed in this form of aggregation that all consumers face the same prices, but that the distribution of income is unrestricted. In order to establish the characterisation result, we present a new approach to preference aggregation which involves summing certain subsets of the graphs of the preferences, viewed as subsets of a Euclidean space. This procedure has a clear geometrical interpretation, and a number of useful applications. In particular, it enables us to analyse the possibility of aggregation when prices are not constrained to be the same for all consumers, a case of possible empirical significance. We also show that the Stolper-Gorman-Samuelson-Chipman construction of community indifference curves coincides with a special case of this procedure. Finally, this approach allows us to develop the relationship between these forms of aggregation and the preference aggregation problem as it occurs in social choice theory.

DIFFERENT APPROACHES TO THE AGGREGATION OF PREFERENCES

The investigation of how individual preference orderings might be used to construct a social ordering acceptable to the individuals came to a premature end with the discovery of Arrow's impossibility theorem. An extensive body of literature has subsequently been addressed to „suitable” modifications of Arrow's axiom system. A different approach would have been to investigate the question „What means acceptable?”. In the following we propose an exact procedure for the aggregation of preferences under the majority principle. We then discuss briefly an attempt in the literature to interpret impossibility problems like Arrow's as consequences of the unsolvability of the stop-problem of Turing machines. Finally, we give an introduction into the theory of abstract Finite automata with preference-a new approach to the problem of preference aggregation.

Aggregation of preferences: a review

This paper presents a review and a classification of the main theoretical results obtained up to now in the important field of the aggregation of preferences. (Let us mention that multicriteria analysis is not considered here, as it essentially consists of methods for the aggregation of preferences). Section 1 describes a tableau, each square of which corresponds to a particular type of preference aggregation problem, and gives, for each of them, a list of references. The different types of problems are obtained by considering the various kinds of informations which can be obtained concerning the global preferences of a committee and the preferences of the individual members. Sections 2, 3 and 4 present some comments respectively on Arrow's problem (three first columns of the tableau), on the theory of choice functions (fourth column) and voting procedures (fifth column). In the bibliography, each reference is associated, in terms of its subject, to one particular square of the tableau.

A proposed solution to the voters preference aggregation problem

A proposed solution to the voters preference aggregation problem

Plurality distortion and majority rule

Discussions of the implications of Arrow's theorem for majority rule have typically focused on calculating the probability of the paradox of voting. In doing so, these analyses have ignored another significant problem of preference aggregation in n-way (n > 2) elections, the existence of non-Condorcet winners, when a Condorcet alternative is available, under a simple plurality criterion. At the level of the democratic political system, e.g., a proposed national presidential primary or any electoral subsystem, e.g., state presidential primaries, gubernatorial, senatorial elections, the simple plurality criterion may distort electoral preferences by failing to select an available Condorcet candidate. An algorithm for calculating the probability of such plurality distortion is offered, and probability calculations for three-way elections for small electorates are presented. Most notable is the discovery that single-peaked preferences, while reducing or eliminating the probability of the paradox, lead to a concomitant increase in the probability of plurality distortion. In instances in which no candidate receives half the vote and preferences are single-peaked, the probability of plurality distortion is actually greater than the probability of plurality-Condorcet coincidence. These results cast some doubt on the validity of the plurality criterion as a voting procedure as well as indicating some of the difficulties inherent in the Condorcet criterion. Alternatives to the plurality criterion are discussed, and some preliminary tests of these alternatives are made.