Social Choice: Recent Developments

In the past quarter century, there has been a dramatic shift of focus in social choice theory, with structured sets of alternatives and restricted domains of the sort encountered in economic problems coming to the fore. This article provides an overview of some of the recent contributions to four topics in normative social choice theory in which economic modelling has played a prominent role: Arrovian social choice theory on economic domains, variable-population social choice, strategy-proof social choice, and axiomatic models of resource allocation.

Priorities in the Location of Multiple Public Facilities

A collective decision problem is described by a set of agents, a profile of single-peaked preferences over the real line and a number k of public facilities to be located. We consider public facilities that do not su¤er from congestion and are non-excludable. We provide a characterization of the class of rules satisfying Pareto-efficiency, object-population monotonicity and sovereignty. Each rule in the class is a priority rule that selects locations according to a predetermined priority ordering among interest groups. We characterize each of the subclasses of priority rules that respectively satisfy anonymity, hiding-proofness and strategy-proofness. In particular, we prove that a priority rule is strategy-proof if and only if it partitions the set of agents into a fixed hierarchy. Alternatively, any such rule can be viewed as a collection of fixed-populations generalized peak-selection median rules (Moulin, 1980), that are linked across populations, in a way that we describe.

Allocation via Deferred-Acceptance under Responsive Priorities

In many economic environments - such as college admissions, student placements at public schools, and university housing allocation - indivisible objects with capacity constraints are assigned to a set of agents when each agent receives at most one object and monetary compensations are not allowed. In these important applications the agent-proposing deferred-acceptance algorithm with responsive priorities (called responsive DA-rule) performs well and economists have successfully implemented responsive DA-rules or slight variants thereof. First, for house allocation problems we characterize the class of responsive DA-rules by a set of basic and intuitive properties, namely, unavailable type invariance, individual rationality, weak non-wastefulness, resource-monotonicity, truncation invariance, and strategy-proofness. We extend this characterization to the full class of allocation problems with capacity constraints by replacing resource- monotonicity with two-agent consistent con ict resolution. An alternative characterization of responsive DA-rules is obtained using unassigned objects invariance, individual rationality, weak non-wastefulness, weak consistency, and strategy-proofness. Various characterizations of the class of "acyclic" responsive DA-rules are obtained by using the properties efficiency, group strategy-proofness, and consistency.

Top trading with fixed tie-breaking in markets with indivisible goods

We study markets with indivisible goods where monetary compensations are not possible. Each individual is endowed with an object and a preference relation over all objects. When preferences are strict, Gale's top trading cycle algorithm finds the unique core allocation. When preferences are not necessarily strict, we use an exogenous profile of tie-breakers to resolve any ties in individuals' preferences and apply Gale's top trading cycle algorithm for the resulting profile of strict preferences. We provide a foundation of these simple extensions of Gale's top trading cycle algorithm from strict preferences to weak preferences. We show that Gale's top trading cycle algorithm with fixed tie-breaking is characterized by individual rationality, strategy-proofness, weak efficiency, non-bossiness, and consistency. Our result supports the common practice in applications to break ties in weak preferences using some fixed exogenous criteria and then to use a 'good and simple' rule for the resulting strict preferences. This reinforces the market-based approach even in the presence of indifferences because always competitive allocations are chosen.

Single-Plateaued Choice

Single-plateaued preferences generalize single-peaked preferences by allowing for multiple best elements. These preferences have played an important role in areas such as voting, strategy-proofness and matching problems. We examine the notion of singleplateauedness in a choice-theoretic setting. Single-plateaued choice is characterized by means of a collinear interval continuity property in the presence of independence of irrelevant alternatives. Further results establish that our notion of single-plateauedness conforms to the motivation underlying the term and we analyze the consequences of alternative continuity properties. The importance of basic assumptions such as closedness and convexity is discussed. Journal of Economic Literature Classification Nos.: D11, D71.

Single-plateaued choice

Single-plateaued preferences generalize single-peaked preferences by allowing for multiple best elements. These preferences have played an important role in areas such as voting, strategy-proofness and matching problems. We examine the notion of single-plateauedness in a choice-theoretic setting. Single-plateaued choice is characterized by means of a collinear interval continuity property in the presence of independence of irrelevant alternatives. Further results establish that our notion of single-plateauedness conforms to the motivation underlying the term and we analyze the consequences of alternative continuity properties. The importance of basic assumptions such as closedness and convexity is discussed. Journal of Economic Literature Classification Nos.: D11, D71.

Single-basined choice

Single-basined preferences generalize single-dipped preferences by allowing for multiple worst elements. These preferences have played an important role in areas such as voting, strategy-proofness and matching problems. We examine the notion of single-basinedness in a choice-theoretic setting. In conjunction with independence of irrelevant alternatives, single-basined choice implies a structure that conforms to the motivation underlying our definition. We also establish the consequenes of requiring single-basined choice correspondences to be upper semicontinuous, and of the revealed preference relation to be Suzumura consistent. Journal of Economic Literature.

House allocation via deferred-acceptance

We study the simple model of assigning indivisible and heterogenous objects (e.g., houses, jobs, offi ces, etc.) to agents. Each agent receives at most one object and monetary compensations are not possible. For this model, known as the house allocation model, we characterize the class of rules satisfying unavailable object invariance, individual rationality, weak non-wastefulness, resource-monotonicity, truncation invariance, and strategy-proofness: any rule with these properties must allocate objects based on (implicitly induced) objects' priorities over agents and the agent-proposing deferred-acceptance-algorithm.

Asymmetrically fair rules for an indivisible good problem with a budget constraint

We study a particular restitution problem where there is an indivisible good (land or property) over which two agents have rights: the dispossessed agent and the owner. A third party, possibly the government, seeks to resolve the situation by assigning rights to one and compensate the other. There is also a maximum amount of money available for the compensation. We characterize a family of asymmetrically fair rules that are immune to strategic behavior, guarantee minimal welfare levels for the agents, and satisfy the budget constraint.

Centralized allocation in multiple markets

We study the problem of centralized allocation of indivisible objects in multiple markets. We show that the set of allocation rules that are group strategy-proof and Pareto-efficient are sequential dictatorships. Therefore, the solution of the joint al-location in multiple markets is significantly narrower than in the single-market case. Our result also applies to dynamic allocation problems. Finally, we provide conditions under which the solution of the single-market allocation coincides with the multiple-market case, and we apply this result to the study of the school choice problem with sibling priorities.

Essays on robust mechanism design

Chapter 1: Under the average common value function, we select almost uniquely the mechanism that gives the seller the largest portion of the true value in the worst situation among all the direct mechanisms that are feasible, ex-post implementable and individually rational. Chapter 2: Strategy-proof, budget balanced, anonymous, envy-free linear mechanisms assign p identical objects to n agents. The efficiency loss is the largest ratio of surplus loss to efficient surplus, over all profiles of non-negative valuations. The smallest efficiency loss is uniquely achieved by the following simple allocation rule: assigns one object to each of the p−1 agents with the highest valuation, a large probability to the agent with the pth highest valuation, and the remaining probability to the agent with the (p+1)th highest valuation. When “envy freeness” is replaced by the weaker condition “voluntary participation”, the optimal mechanism differs only when p is much less than n. Chapter 3: One group is to be selected among a set of agents. Agents have preferences over the size of the group if they are selected; and preferences over size as well as the “stand-outside” option are single-peaked. We take a mechanism design approach and search for group selection mechanisms that are efficient, strategy-proof and individually rational. Two classes of such mechanisms are presented. The proposing mechanism allows agents to either maintain or shrink the group size following a fixed priority, and is characterized by group strategy-proofness. The voting mechanism enlarges the group size in each voting round, and achieves at least half of the maximum group size compatible with individual rationality.

Literacy, security, governmentality: Defining spaces, managing populations – How has education become part of whole of government security strategy?

In this paper I conduct a Foucauldian discourse analysis of a political speech given by Brendon Nelson in 2006 when the Australian Minister for Defence in the Howard Coalition Government. The speech connects conceptualisations of terror, globalization, education and literacy as part of a whole of government security strategy. The analysis examines this speech as an example of a liberal way of governing the conduct of diverse and unpredictable populations. My analysis suggests that the apparatus of government has been strategically used in order to biopolitically contain the rise of complex social forces and protect a set of homogenous cultural values. The purposes of education and uses of literacy are seen as instruments for the inscription of a coded set of values understood to be synonymous with civil society.

Cooperative Profit Sharing in Coalition-Based Resource Allocation in Wireless Networks

We consider a network in which several service providers offer wireless access to their respective subscribed customers through potentially multihop routes. If providers cooperate by jointly deploying and pooling their resources, such as spectrum and infrastructure (e.g., base stations) and agree to serve each others' customers, their aggregate payoffs, and individual shares, may substantially increase through opportunistic utilization of resources. The potential of such cooperation can, however, be realized only if each provider intelligently determines with whom it would cooperate, when it would cooperate, and how it would deploy and share its resources during such cooperation. Also, developing a rational basis for sharing the aggregate payoffs is imperative for the stability of the coalitions. We model such cooperation using the theory of transferable payoff coalitional games. We show that the optimum cooperation strategy, which involves the acquisition, deployment, and allocation of the channels and base stations (to customers), can be computed as the solution of a concave or an integer optimization. We next show that the grand coalition is stable in many different settings, i.e., if all providers cooperate, there is always an operating point that maximizes the providers' aggregate payoff, while offering each a share that removes any incentive to split from the coalition. The optimal cooperation strategy and the stabilizing payoff shares can be obtained in polynomial time by respectively solving the primals and the duals of the above optimizations, using distributed computations and limited exchange of confidential information among the providers. Numerical evaluations reveal that cooperation substantially enhances individual providers' payoffs under the optimal cooperation strategy and several different payoff sharing rules.

Simple Coalitional Strategy Profiles in Repeated Games

This paper is a version of the discussion paper titled "Simple coalitional strategy profiles"

A new approach for multi-agent coalition formation and management in the scope of electricity markets

This paper presents a new methodology for the creation and management of coalitions in Electricity Markets. This approach is tested using the multi-agent market simulator MASCEM, taking advantage of its ability to provide the means to model and simulate VPP (Virtual Power Producers). VPPs are represented as coalitions of agents, with the capability of negotiating both in the market, and internally, with their members, in order to combine and manage their individual specific characteristics and goals, with the strategy and objectives of the VPP itself. The new features include the development of particular individual facilitators to manage the communications amongst the members of each coalition independently from the rest of the simulation, and also the mechanisms for the classification of the agents that are candidates to join the coalition. In addition, a global study on the results of the Iberian Electricity Market is performed, to compare and analyze different approaches for defining consistent and adequate strategies to integrate into the agents of MASCEM. This, combined with the application of learning and prediction techniques provide the agents with the ability to learn and adapt themselves, by adjusting their actions to the continued evolving states of the world they are playing in.