Utilitarian Social Welfare Research Articles

How stationarity contradicts intergenerational equity

We show how the condition of stationarity may contradict intergenerational equity. By formalizing the intuition that less sensitivity remains for the continuation of the stream if sensitivity for the interests of the present is combined with stationarity, we point out conflicts (a) between stationarity and the requirement of not letting the present be dictatorial, and (b) between stationarity and equal treatment of generations. We use the results to interpret the non-stationarity of the Chichilnisky and Rank-discounted utilitarian social welfare functions. Non-stationarity combined with time invariance leads to time inconsistency. We illustrate how such non-stationary social welfare functions can be applied in the Ramsey model if time invariance is imposed.

Pseudo-wealth and Consumption Fluctuations

Abstract This paper provides an explanation for situations in which the fundamental state variables describing the economy do not change, but aggregate consumption experiences significant changes. We present a theory of pseudo-wealth—individuals’ perceived wealth that is derived from expectations of gains in bets arising from heterogeneous expectations. This wealth is divorced from society's real assets. The creation of a market for bets necessarily generates positive pseudo-wealth. Changes in the magnitude of differences of prior beliefs will lead to changes in expected wealth and hence to changes in consumption, implying instability in aggregate and individual consumption and ex post intertemporal consumption misallocations. Moreover, ‘completing markets’ through the creation of a new market for bets can increase individual and aggregate risk. With a utilitarian social welfare function, completing markets leads to lower welfare ex post, but the first theorem of welfare economics (evaluating each individual's well-being on the basis of her ex ante beliefs) still holds, raising unsettling questions for welfare analysis. We also show that if the planner uses beliefs that are consistent, then the betting equilibrium would be Pareto inferior.

The Cost of Unemployment from a Social Welfare Approach: The Case of Spain and Its Regions

This paper proposes a protocol to measure the cost of unemployment by taking into account three different aspects: incidence, severity and hysteresis. Incidence refers to the conventional unemployment rate; severity takes into account both unemployment duration and the associated income loss; and hysteresis refers to the probability of remaining unemployed. The cost of unemployment is regarded as a welfare loss, which is measured by a utilitarian social welfare function whose arguments are the individual disutilities of unemployed workers. Each individual disutility is modelled as a function of income loss, unemployment duration and hysteresis. The resulting formula is simple and easy to understand and implement. We apply this assessment protocol to the Spanish labour market, focusing on the regional differences and using the official register of unemployed workers compiled by the Public Employment Service.

Price of Fairness in Budget Division and Probabilistic Social Choice

A group of agents needs to divide a divisible common resource (such as a monetary budget) among several uses or projects. We assume that agents have approval preferences over projects, and their utility is the fraction of the budget spent on approved projects. If we maximize utilitarian social welfare, the entire budget will be spent on a single popular project, even if a substantial fraction of the agents disapprove it. This violates the individual fair share axiom (IFS) which requires that for each agent, at least 1/n of the budget is spent on approved projects. We study the price of imposing such fairness axioms on utilitarian social welfare. We show that no division rule satisfying IFS can guarantee to achieve more than an O(1/√m) fraction of maximum utilitarian welfare, in the worst case. However, imposing stronger group fairness conditions (such as the core) does not come with an increased price, since both the conditional utilitarian rule and the Nash rule match this bound and guarantee an Ώ(1/√m) fraction. The same guarantee is attained by the rule under which the spending on a project is proportional to its approval score. We also study a family of rules interpolating between the utilitarian and the Nash rule, quantifying a trade-off between welfare and group fairness. An experimental analysis by sampling using several probabilistic models shows that the conditional utilitarian rule achieves very high welfare on average.

Generalized Graph k-Coloring Games

We investigate pure Nash equilibria in generalized graphk-coloring games where we are given an edge-weighted undirected graph together with a set of k colors. Nodes represent players and edges capture their mutual interests. The strategy set of each player consists of k colors. The utility of a player v in a given state or coloring is given by the sum of the weights of edges {v, u} incident to v such that the color chosen by v is different than the one chosen by u, plus the profit gained by using the chosen color. Such games form some of the basic payoff structures in game theory, model lots of real-world scenarios with selfish players and extend or are related to several fundamental class of games. We first show that generalized graph k-coloring games are potential games. In particular, they are convergent and thus Nash Equilibria always exist. We then evaluate their performance by means of the widely used notions of price of anarchy and price of stability and provide tight bounds for two natural and widely used social welfare, i.e., utilitarian and egalitarian social welfare.

Solving the fair electric load shedding problem in developing countries

Often because of limitations in generation capacity of power stations, many developing countries frequently resort to disconnecting large parts of the power grid from supply, a process termed load shedding. This leaves households in disconnected parts without electricity, causing them inconvenience and discomfort. Without fairness being taken into due consideration during load shedding, some households may suffer more than others. In this paper, we solve the fair load shedding problem (FLSP) by creating solutions which connect households to supply based on some fairness criteria (i.e., to fairly connect homes to supply in terms of duration, their electricity needs, and their demand), which we model as their utilities. First, we briefly describe some state-of-art household-level load shedding heuristics which meet the first criteria. Second, we model the FLSP as a resource allocation problem, which we formulate into two Mixed Integer Programming (MIP) problems based on the Multiple Knapsack Problem. In so doing, we use the utilitarian, egalitarian and envy-freeness social welfare metrics to develop objectives and constraints that ensure our FLSP solutions results in fair allocations that consider the utilities of agents. Then, we solve the FLSP and show that our MIP models maximize the groupwise and individual utilities of agents, and minimize the differences between their pairwise utilities under a number of experiments. When taken together, our endeavour establishes a set of benchmarks for fair load shedding schemes, and provide insights for designing fair allocation solutions for other scarce resources.

Automated peer-to-peer negotiation for energy contract settlements in residential cooperatives

This paper presents an automated peer-to-peer negotiation strategy for settling energy contracts among prosumers in a Residential Energy Cooperative considering heterogeneity prosumer preferences. The heterogeneity arises from prosumers’ evaluation of energy contracts through multiple societal and environmental criteria and the prosumers’ private preferences over those criteria. The prosumers engage in bilateral negotiations with peers to mutually agree on periodical energy contracts/loans consisting of the energy volume to be exchanged at that period and the return time of the exchanged energy. The negotiating prosumers navigate through a common negotiation domain consisting of potential energy contracts and evaluate those contracts from their valuations on the entailed criteria against a utility function that is robust against generation and demand uncertainty. From the repeated interactions, a prosumer gradually learns about the compatibility of its peers in reaching energy contracts that are closer to Nash solutions. Empirical evaluation on real demand, generation and storage profiles – in multiple system scales – illustrates that the proposed negotiation based strategy can increase the system efficiency (measured by utilitarian social welfare) and fairness (measured by Nash social welfare) over a baseline strategy and an individual flexibility control strategy representing the status quo strategy. We thus elicit system benefits from peer-to-peer flexibility exchange already without any central coordination and market operator, providing a simple yet flexible and effective paradigm that complements existing markets.

Cake cutting: Explicit examples for impossibility results

In this article we suggest a model of computation for the cake cutting problem. In this model the mediator can ask the same queries as in the Robertson–Webb model but he or she can only perform algebraic operations as in the Blum–Shub–Smale model. All existing algorithms described in the Robertson–Webb model can be described in this new model.We show that in this model there exist explicit couples of measures for which no algorithm outputs an equitable fair division with connected parts.We also show that there exist explicit sets of measures for which no algorithm in this model outputs a fair division which maximizes the utilitarian social welfare function.The main tool of our approach is Galois theory.

Distributional Impacts of State and Local Tax Policy in a Heterogeneous-agent Model

This article presents a dynamic heterogeneous-agent life-cycle model with housing demand to evaluate the economic implications of reforming US state and local personal tax structures. Because of the extensive reliance of state and local governments on income, sales, and property tax revenue, those three taxes are explicitly modeled to generate a baseline and varied to evaluate alternative policy proposals. The results of the model show that the sales tax burden falls evenly across the distribution of income earners, while the property tax burden falls more heavily on the highest income earners. By design, the model’s income tax is progressive, so the tax burden shares rise with income. Results also show that the property tax generally improves utilitarian social welfare relative to income and sales taxation, but the magnitude of these gains depends on the availability of a state and local tax deduction on federal income taxes.

Towards a Utilitarian Social Welfare Function—Income Inequality and National Welfare Growth in China

Since the beginning of the reform period, China's income inequality has increased. However, loss of national welfare and the impact of income inequality on the growth of national welfare has not been adequately assessed. The result is that any development model myopically focusing on efficiency and ignoring equality cannot maximize growth in national welfare. Grounded in utilitarian theory, this paper builds a national welfare function which incorporates the Gini coefficient and demonstrates the negative effects of income inequality on China’s national welfare. We then provide a welfare-loss formula of income inequality and another formula to calculate the influence of income inequality change on national welfare growth. Our calculations show that from 1996 to 2010, the average welfare-loss rate of China’s residents' income inequality was 8.08%, with absolute welfare loss increasing1.44 times; while the relative impact of Gini coefficient increases on national welfare growth was (-) 8.66%.

Low-Distortion Social Welfare Functions

Work on implicit utilitarian voting advocates the design of preference aggregation methods that maximize utilitarian social welfare with respect to latent utility functions, based only on observed rankings of the alternatives. This approach has been successfully deployed in order to help people choose a single alternative or a subset of alternatives, but it has previously been unclear how to apply the same approach to the design of social welfare functions, where the desired output is a ranking. We propose to address this problem by assuming that voters’ utilities for rankings are induced by unknown weights and unknown utility functions, which, moreover, have a combinatorial (subadditive) structure. Despite the extreme lack of information about voters’ preferences, we show that it is possible to choose rankings such that the worst-case gap between their social welfare and that of the optimal ranking, called distortion, is no larger (up to polylogarithmic factors) than the distortion associated with much simpler problems. Through experiments, we identify practical methods that achieve nearoptimal social welfare on average.

Inequity aversion, welfare measurement and the Gini index

Integrating individual inequity aversion (Fehr and Schmidt in Q J Econ 114:817–868, 1999) into a utilitarian social welfare function, we derive a simple welfare measure which comprises both GDP and income inequality as measured by the Gini-index.

Perception-theoretic Foundations of Weighted Utilitarianism

We provide a microfoundation for a weighted utilitarian social welfare function that reflects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopt utilitarian welfare functions, assuming that comparable utility functions can be calibrated, using information beyond consumer choice data. We show that consumer choice data alone are sufficient. As suggested by Edgeworth (1881), just noticeable differences (JNDs) provide a common unit of measure for interpersonal comparisons of utility differences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual JNDs.

When do utilitarianism and egalitarianism agree on evaluation? An intersection approach

We examine the range of the agreement between the utilitarian social welfare ordering (SWO) and leximin SWO by analyzing the intersection of them. We characterize the intersection (in terms of subrelation) using the strong version of Pigou–Dalton equity and a new axiom on the composition of rank-preserving progressive and regressive utility transfers. Then, adding separability and cardinal full comparability, we jointly characterize the leximin SWO and the lexicographic composition of the utilitarian and leximin SWOs that applies the utilitarian SWO first. We also jointly characterize these two SWOs and the utilitarian SWO using the weak version of Pigou–Dalton equity.

Truthful and Near-Optimal Mechanisms for Welfare Maximization in Multi-Winner Elections

Mechanisms for aggregating the preferences of agents in elections need to balance many different considerations, including efficiency, information elicited from agents, and manipulability. We consider the utilitarian social welfare of mechanisms for preference aggregation, measured by the distortion. We show that for a particular input format called threshold approval voting, where each agent is presented with an independently chosen threshold, there is a mechanism with nearly optimal distortion when the number of voters is large. Threshold mechanisms are potentially manipulable, but place a low informational burden on voters. We then consider truthful mechanisms. For the widely-studied class of ordinal mechanisms which elicit the rankings of candidates from each agent, we show that truthfulness essentially imposes no additional loss of welfare. We give truthful mechanisms with distortion O(√m log m) for k-winner elections, and distortion O(√m log m) when candidates have arbitrary costs, in elections with m candidates. These nearly match known lower bounds for ordinal mechanisms that ignore the strategic behavior. We further tighten these lower bounds and show that for truthful mechanisms our first upper bound is tight. Lastly, when agents decide between two candidates, we give tight bounds on the distortion for truthful mechanisms.

A truthful combinatorial double auction-based marketplace mechanism for cloud computing

Designing market-based mechanism that benefits both the cloud customer and cloud provider in a cloud market is a fundamental but complex problem. Double auction is one such mechanism to allocate resources that prevents monopoly and is used to design an unbiased optimal market strategy for cloud market. This work proposes a truthful combinatorial double auction mechanism for allocation and pricing of computing resources in cloud. For resource allocation, utilitarian social welfare maximization problem is formulated using Integer Linear Programming (ILP) and a near optimal solution is obtained using Linear Programming based padded method. For payment, truthful and novel schemes are designed for both customers and providers. Moreover, the proposed mechanism is individual rational, computationally tractable, weakly budget-balance and asymptotic efficient. Performance evaluation and comparative study exhibit that the proposed mechanism is effective on various performance metrics such as utilitarian social welfare, total utility, customers’ satisfaction, providers’ revenue and hence is applicable in real cloud environments.

Premature Deaths, Accidental Bequests and Fairness

While little agreement exists regarding the taxation of bequests in general, there is a widely held view that accidental bequests should be subject to a confi…scatory tax. We propose to reexamine the optimal taxation of accidental bequests in an economy where individuals care about what they leave to their offspring in case of premature death. We show that, whereas the conventional 100 % tax view holds under the standard utilitarian social welfare criterion, it does not hold under the ex post egalitarian criterion, which assigns a strong weight to the welfare of unlucky short-lived individuals. From an egalitarian perspective, it is optimal not to tax, but to subsidize accidental bequests. We examine the robustness of those results in a dynamic OLG model of wealth accumulation, and show that, whereas the sign of the optimal tax on accidental bequests depends on the form of the joy of giving motive, it remains true that the 100 % tax view does not hold under the ex post egalitarian criterion.

The Social Cost of Unemployment: The Spanish Labour Market from a Social Welfare Approach

This paper proposes a protocol for considering the social cost of unemployment by taking into account three different aspects: incidence, severity and hysteresis. Incidence refers to the conventional unemployment rate; severity takes in both unemployment duration and the associated income loss; and hysteresis refers to the probability of remaining unemployed. The social cost of unemployment is regarded as a welfare loss, which is measured by a utilitarian social welfare function whose arguments are the individual disutilities of unemployed workers. Each individual disutility is modelled as a function of income loss, unemployment duration and hysteresis. The resulting formula is simple and easy to understand and implement. We apply this assessment protocol to the Spanish labour market, using the official register of unemployed workers compiled by the Public Employment Service.

Inequity Aversion, Welfare Measurement and the Gini Index

Over the last decades, research in behavioural economics has demonstrated that individual welfare (utility), as relevant for economic decision making, depends not only on absolut but also on distributional aspects. Moreover, evidence is gathering that something similar holds for aggregate welfare, i.e. that GDP alone is an insufficient predictor for various supposedly welfare related variables on a societal level. This note shows that distributional concerns on an aggregate level can indeed be derived from distributional concerns on an individual level: integrating individual inequity aversion into a utilitarian social welfare function yields a simple welfare measure which comprises both GDP and income inequality as measured by the Gini index.

Levels of other-regarding preferences and the structure of the interaction

The paper contributes to the literature on other-regarding preferences challenging the narrow self-interest assumption. Experimental evidence confirms that the same individuals might express different otherregarding preferences in different situations or contexts. The structure of their interaction, their relative positions in it might trigger different behavioral patterns. In this paper we propose a model of multi-level other-regarding preferences assuming that different levels are actualized depending on the context in which an individual has to take her decision. We analyze the experimental trust game letting the players have multi-level preferences. Under certain parameterization and asymmetric information assumption, we show that the share given up by the leader of the game in favor of the follower is strictly monotonically increasing with altruism of the former. It is also demonstrated that utilitarian social welfare is increasing with the leader’s altruism if the players are not extremely risk-averse. In the case when information for both players is incomplete, a separating equilibrium exists allowing to distinguish between leaders with different other-regarding preferences.