Social Choice Functions Research Articles

A Borda count for partially ordered ballots

The application of the theory of partially ordered sets to voting systems is an important development in the mathematical theory of elections. Many of the results in this area are on the comparative properties between traditional elections with linearly ordered ballots and those with partially ordered ballots. In this paper we present a scoring procedure, called the partial Borda count, that extends the classic Borda count to allow for arbitrary partially ordered preference rankings. We characterize the partial Borda count in the context of weighting procedures and in the context of social choice functions.

Dynamic Social Choice with Evolving Preferences

Social choice theory provides insights into a variety of collective decision making settings, but nowadays some of its tenets are challenged by internet environments, which call for dynamic decision making under constantly changing preferences. In this paper we model the problem via Markov decision processes (MDP), where the states of the MDP coincide with preference profiles and a (deterministic, stationary) policy corresponds to a social choice function. We can therefore employ the axioms studied in the social choice literature as guidelines in the design of socially desirable policies. We present tractable algorithms that compute optimal policies under different prominent social choice constraints. Our machinery relies on techniques for exploiting symmetries and isomorphisms between MDPs.

The Wisdom of Crowds in Bioinformatics: What Can We Learn (and Gain) from Ensemble Predictions?

The combination of distinct algorithms expertise to improve prediction accuracy, inspired by the theory of wisdom of crowds, has been increasingly discussed in literature. However, its application to bioinformatics-related tasks is still in its infancy. This thesis aims at investigating the potential and limitations of ensemble-based solutions for two bioinformatics prediction tasks, namely inference of gene regulatory networks and prediction of microRNAs targets, as well as propose new integration methods. We approach this by considering heterogeneity in the contexts of data and methods, and adopting machine learning methods and concepts from multiagent systems, such as social choice functions, for integration purposes.

Approximate Implementation in Markovian Environments

This paper considers dynamic implementation problems with evolving private information (according to Markov processes). A social choice function is approximately implementable if there exists a dynamic mechanism such that the social choice function is implemented by an arbitrary large number of times with arbitrary high probability in every communication equilibrium. We show that if a social choice function is strictly efficient in the set of social choice functions that satisfy an undetectable condition, then it is approximately implementable. We revisit the classical monopolistic screening problem and show that the monopolist can extract the full surplus in almost all periods with arbitrary high probability.

A maximal domain for strategy-proof and no-vetoer rules in the multi-object choice model

Following “Barberà et al. (1991, Econometrica 59:595–609)”, we study rules (or social choice functions) through which agents select a subset from a set of objects. We investigate domains on which there exist nontrivial strategy-proof rules. We establish that the set of separable preferences is a maximal domain for the existence of rules satisfying strategy-proofness and no-vetoer.

Strategic Manipulability of Self-­Selective Social Choice Rules

We provide exact relations giving the probability of individual and coalitional manipulation of three specific social choice functions (Borda rule, Copeland rule, Plurality rule) in three-alternative elections when the notion of self-selectivity is imposed. The results suggest that the Borda rule is more vulnerable to coalitional manipulation than the Copeland rule and the Plurality rule. However, Plurality rule seems to be more vulnerable to individual manipulability when the number of voters is greater than a certain threshold value. In addition, the probability of individual and coalitional manipulation tends to vanish significantly when the notion of self-selectivity is imposed.

An Impossibility Result for Virtual Implementation with Status Quo

In this paper, virtual implementation is restricted so that only a socially optimal outcome or some fixed outcome (a status quo) can be delivered on the equilibrium path. Under such a restriction, any unanimous and implementable social choice function is almost-dictatorial. That is, there is an agent who obtains the most preferable outcome as long as this outcome is better than status quo outcome for all agents. If the range of social choice functions is restricted to pure outcomes only, the result extends to outcomes that are worse than the status quo.

Truthful implementation and preference aggregation in restricted domains

In a setting where agents have quasi-linear utilities over social alternatives and a transferable commodity,we consider three properties that a social choice function may possess: truthful implementation (in dominant strategies); monotonicity in differences; and lexicographic affine maximization. We introduce the notion of a flexible domain of preferences that allows elevation of pairs and study which of these conditions implies which others in such domain. We provide a generalization of the theorem of Roberts (1979) [36] in restricted valuation domains. Flexibility holds (and the theorem is not vacuous) if the domain of valuation profiles is restricted to the space of continuous functions defined on a compact metric space, or the space of piecewise linear functions defined on an affine space, or the space of smooth functions defined on a compact differentiable manifold. We provide applications of our results to public goods allocation settings, with finite and infinite alternative sets.

Ex post renegotiation-proof mechanism design

We study what kind of equilibria of which mechanisms are ex post renegotiation-proof (EPRP), i.e., robust against the possibility of ex post renegotiation under a variety of renegotiation procedures, and which social choice functions are EPRP implementable. In complete information environments with two agents only budget balanced Groves allocations are EPRP implementable, while with three or more agents – all ex post efficient allocations are. In environments with independent private values essentially only the budget balanced “Groves in expectations” allocations are EPRP implementable, while with three or more agents and correlated beliefs – all ex post efficient allocations are.

Minimalist Impossibility Theorems

We explore the frontier between possibility and impossibility results by analyzing different combinations of pro-socialness and conditions. This exercise delivers stronger versions of four classical impossibility theorems, and offers a thorough understanding of connections among them. We also characterize social choice functions that are independent of irrelevant alternatives, which makes evident that the fundamental difficulty of social choice lies in pairwise consistency requirements. We also introduce a concise pedagogical approach to classical impossibility theorems.

Ex Post Self-Implementation

We consider the implementation problem under incomplete information and interdependent values. This paper provides a necessary and sufficient condition for a social choice function to be ex post self-implementable in general environments. A social choice function is ex post self-implementable if it is fully ex post implemented by the associated direct revelation mechanism. We introduce a new monotonicity condition called restricted monotonicity and show that this and ex post incentive compatibility are necessary and sufficient for ex post self-implementation.

The communication burden of payment determination

In the presence of self-interested parties, mechanism designers typically aim to implement some social-choice function in an equilibrium. This paper studies the cost of such equilibrium requirements in terms of communication. While a certain amount of information x needs to be communicated just for computing the outcome of a certain social-choice function, an additional amount of communication may be required for computing the equilibrium-supporting payments (if exist).Our main result shows that the total amount of information required for this task can be greater than x by a factor linear in the number of players n, i.e., n⋅x (under a common normalization assumption). This is the first known lower bound for this problem. In fact, we show that this result holds even in single-parameter domains. On the positive side, we show that certain classic economic domains, namely, single-item auctions and public-good mechanisms, only entail a small overhead.

Mechanism design and implementation theoretic perspective for interference coupled wireless systems

This article investigates the properties of social choice functions (SCFs) that represent resource allocation strategies for interference coupled wireless systems. The resources can be physical layer parameters such as power vectors or spatial streams. Strategy proofness and efficiency properties of SCFs are used to capture the properties of non-manipulability and Pareto optimality of resource allocation strategies, respectively. This article introduces and investigates the concepts of (strong) intuitive fairness and non-participation in interference coupled systems. The analysis indicates certain inherent limitations when designing strategy proof and efficient resource allocation strategies, if additional desirable and intuitive properties are imposed. These restrictions are investigated in an analytical mechanism design framework for interference coupled wireless systems. The article also investigates the permissible SCFs, which can be implemented by a mechanism in either Nash equilibrium or dominant strategy for utility functions representing interference coupled wireless systems. Among other results, it is shown that a strategy proof and efficient resource allocation strategy cannot simultaneously satisfy continuity and the often encountered property of non-participation.

Strategy-proof voting for multiple public goods

In a voting model where the set of feasible alternatives is a subset of a product set A = A1×⋯×Am of m finite categories, we characterize the set of all strategy-proof social choice functions for three different types of preference domains over A, namely for the domains of additive, completely separable, and weakly separable preferences over A.

Mechanism design and communication networks

This paper studies a mechanism design model where the players and the designer are nodes in a communication network. We characterize the communication networks (directed graphs) for which, in any environment (utilities and beliefs), every incentive compatible social choice function is partially implementable. We show that any incentive compatible social choice function is implementable on a given communication network, in all environments with either common independent beliefs and private values or a worst outcome, if and only if the network is strongly connected and weakly 2-connected. A network is strongly connected if for each player, there exists a directed path to the designer. It is weakly 2-connected if each player is either directly connected to the designer or indirectly connected to the designer through two disjoint paths, not necessarily directed. We couple encryption techniques together with appropriate incentives to secure the transmission of each player's private information to the designer.

The structure of strategy-proof random social choice functions over product domains and lexicographically separable preferences

We characterize the class of dominant-strategy incentive-compatible (or strategy-proof) random social choice functions in the standard multi-dimensional voting model where voter preferences over the various dimensions (or components) are lexicographically separable. We show that these social choice functions (which we call generalized random dictatorships) are induced by probability distributions on voter sequences of length equal to the number of components. They induce a fixed probability distribution on the product set of voter peaks. The marginal probability distribution over every component is a random dictatorship. Our results generalize the classic random dictatorship result in Gibbard (1977) and the decomposability results for strategy-proof deterministic social choice functions for multi-dimensional models with separable preferences obtained in LeBreton and Sen (1999).

Information elicitation and sequential mechanisms

We study an incomplete information mechanism design problem with three peculiarities. First, access to agents’ private information is costly and unobservable. Second, the mechanism may communicate sequentially with the agents. Third, the mechanism designer and all the agents share a common interest. As an example one can think of N geologists that study the potential oil reserves in some tract. The geologists agree on the right course of action, given their N studies. However, carrying out the study may be costly for a geologist and so he may opt to fabricate a study. The oil company that employs these geologists need not contract them simultaneously and may, furthermore, choose to provide some of the results of early studies to geologists employed later on. Finally, the geologists and the oil company would like the joint study to forecast the quantity of oil reserves as accurate as possible. It turns out that, in such settings, what may not be implementable without communication becomes implementable with communication. Clearly, the possibility for sequential communication introduces a lot of complexity to the design problem. However, we provide a result in the spirit of the revelation principle and argue that whenever implementation is possible with communication it is also possible with a simple communication mechanism. Formally, we extend the model and results in Smorodinsky and Tennenholtz (Games Econ Behav 55(2):385–406, 2006) who consider the similar problem but restrict attention to symmetric social choice functions and IID distributions over the private information.

A hybrid model using analytic network process and gray relational analysis for bank's IT outsourcing vendor selection

PurposeConsidering the limitation of the single stage vendor selection model, this paper proposes a two‐stage vendor selection framework for IT outsourcing in microfinance banks.Design/methodology/approachThe paper attempts to realize a complete analysis at company level using grey systems theory for shaping the relations among variables. With the social choice function – Dodgson function, the first stage is a trial phase that helps the decision‐maker find the potential vendors, then, the decision‐maker employs those chosen vendors for the final selection with modified grey relational analysis (GRA) integrated analytic network process (ANP), which emphasizes the interrelation among those selection criteria, and avoids the subjective estimation of experts and practitioners. The case of a microfinance bank IT outsourcing vendor selection is used to verify the proposed approach.FindingsThe results of the empirical study show that the proposed method is practical for ranking competing vendors in terms of their overall performance with respect to multiple interdependence criteria for the bank's IT outsourcing.Practical implicationsThe method exposed in the paper can be used for other supplier selection by modifying some criteria and weight.Originality/valueThe paper provides a method for ranking competing vendors in terms of their overall performance with respect to multiple interdependence criteria for IT outsourcing.

Strategy-proof partitioning

We consider the problem of choosing a partition of a set of objects by a set of agents. The private information of each agent is a strict ordering over the set of partitions of the objects. A social choice function chooses a partition given the reported preferences of the agents. We impose a natural restriction on the allowable set of strict orderings over the set of partitions, which we call an intermediate domain. Our main result is a complete characterization of strategy-proof and tops-only social choice functions in the intermediate domain. We also show that a social choice function is strategy-proof and unanimous if and only if it is a meet social choice function.

Implementation with evidence

We generalize the canonical problem of Nash implementation by allowing agents to voluntarily provide discriminatory signals, i.e., evidence. Evidence can either take the form of hard information or, more generally, have differential but nonprohibitive costs in different states. In such environments, social choice functions that are not Maskin-monotonic can be implemented. We formulate a more general property, evidence monotonicity, and show that this is a necessary condition for implementation. Evidence monotonicity is also sufficient for implementation in economic environments. In some settings, such as when agents have small preferences for honesty, any social choice function is evidence-monotonic. Additional characterizations are obtained for hard evidence. We discuss the relationship between the implementation problem where evidence provision is voluntary and a hypothetical problem where evidence can be chosen by the planner as part of an extended outcome space.