Weak Pareto Principle Research Articles

Strong dictatorship via ratio-scale measurable utilities: a simpler proof

Tsui and Weymark (Econ Theory 10:241–256, 1997, https://doi.org/10.1007/s001990050156) have shown that the only continuous social welfare orderings on the whole Euclidean space which satisfy the weak Pareto principle and are invariant to individual-specific similarity transformations of utilities are strongly dictatorial. Their proof relies on functional equation arguments which are quite complex. This note provides a simpler proof of their theorem.

Collective choice rules with social maximality

We consider social choice on a non-empty, finite set X where all elements of X are available; society will not be required to make a choice from a strict subset of X. Arrow assumes that the social preference relation is an ordering of the alternatives in X. However, under the assumption that the collective choice rule satisfies unrestricted domain, independence of irrelevant alternatives and the weak Pareto principle, this can be weakened to the requirement that (i) the social preference relation generates a non-empty set of maximal alternatives, and (ii) every maximal alternative is strictly socially preferred to every non-maximal alternative. Requirement (ii) can be weakened further when there are four or more alternatives. When only property (i) is satisfied, we characterize all collective choice rules that output complete social preferences and satisfy unrestricted domain, Pareto, neutrality and anonymity. These collective choice rules are related to the S rules of Bossert and Suzumura (2008). Finally, we prove some equivalence theorems relating the various binary relations considered in the paper to existing coherence conditions on social preferences.

Acyclicity, anonymity, and prefilters

We analyze the decisiveness structures associated with acyclical collective choice rules. In particular, we examine the consequences of adding anonymity to weak Pareto, thereby complementing earlier results on acyclical social choice. Both finite and countably infinite populations are considered. As established in contributions by Donald Brown and by Jeffrey Banks, acyclical social choice is closely linked to prefilters in the presence of the weak Pareto principle. We introduce the notion of a conditional prefilter and use it to generalize their results. In the finite-population case, adding anonymity implies that the collection of decisive sets is a special case of a conditional prefilter. We then identify the decisiveness structure that results from adding anonymity to the weak Pareto principle. Moving to infinite populations, we obtain the decisive set that consists of the entire population as a possibility, along with a new class of prefilters that we refer to as symmetric free Fréchet prefilters. The choice of the term Fréchet prefilter is motivated by the observation that they share a defining property with the well-known Fréchet filter—namely, that all sets in the requisite collection are such that their complement is finite.

Nash welfarism and the distributive implications of informational constraints

We study two informational simplicity conditions for aggregating von Neumann–Morgenstern preferences. When the best relevant alternative for each individual cannot be ascertained with confidence (as when allocating an uncertain endowment of goods), Independence of Harmless Expansions requires that the social ranking of lotteries be unaffected by the addition of any alternative that every agent deems at least as good as the one she originally found worst. This axiom, along with the Weak Pareto Principle and Anonymity, characterizes bottom-calibrated Nash welfarism: utilities are calibrated so that the worst alternative is worth zero and lotteries are ranked according to the product of such bottom-calibrated utilities. When the worst relevant alternatives are difficult to identify, replacing Independence of Harmless Expansions by the dual axiom of Independence of Useless Expansions yields a characterization of top-calibrated Nash welfarism: lotteries are ranked according to the opposite of the product of the absolute values of top-calibrated utilities. The distributive implications of our two informational simplicity axioms are thus drastically different: while bottom-calibrated Nash welfarism recommends randomizing between two alternatives that it deems equally good, top-calibrated Nash welfarism is randomization-averse.

Belief-weighted Nash aggregation of Savage preferences

The belief-weighted Nash social welfare functions are methods for aggregating Savage preferences defined over a set of acts. Each such method works as follows. Fix a 0-normalized subjective expected utility representation of every possible preference and assign a vector of individual weights to each profile of beliefs. To compute the social preference at a given preference profile, rank the acts according to the weighted product of the individual 0-normalized subjective expected utilities they yield, where the weights are those associated with the belief profile generated by the preference profile. We show that these social welfare functions are characterized by the weak Pareto principle, a continuity axiom, and the following informational robustness property: the social ranking of two acts is unaffected by the addition of any outcome that every individual deems at least as good as the one she originally found worst. This makes the belief-weighted Nash social welfare functions appealing in contexts where the best relevant outcome for an individual is difficult to identify.

Rawls’s maximin rule and Arrow’s impossibility theorem

Rawls’s maximin rule is closely related to Arrow’s impossibility theorem. When there are at least three social states and three social members, a social welfare functional with full domain is the maximin rule if and only if it satisfies anonymity, binary independence, weak ordinal non-comparability, the weak Pareto principle, and the Pareto indifference principle.

Liberal approaches to ranking infinite utility streams: when can we avoid interference?

In this work we analyse social welfare relations on sets of finite and infinite utility streams that satisfy various types of liberal non-interference principles. Earlier contributions have established that (finitely) anonymous and strongly Paretian quasiorderings exist that verify non-interference axioms together with weak preference continuity and further consistency. Nevertheless Mariotti and Veneziani (2011) prove that a fully liberal non-interfering view of a finite society leads to dictatorship if the weak Pareto principle is imposed. We first prove that this impossibility result vanishes when we extend the horizon to infinity. Then we investigate a related problem: namely, the possibility of combining “standard” semicontinuity with efficiency in the presence of non-interference. We provide several impossibility results that prove that there is a generalised incompatibility between relaxed forms of continuity and non-interference principles, both under ordinal and cardinal views of the problem.

Pareto principles, positive responsiveness, and majority decisions

This article investigates the relationship among the weak Pareto principle, the strong Pareto principle, and positive responsiveness in the context of voting. First, it is shown that under a mild domain condition, if an anonymous and neutral collective choice rule (CCR) is complete and transitive, then the weak Pareto principle and the strong Pareto principle are equivalent. Next, it is shown that under another mild domain condition, if a neutral CCR is transitive, then the strong Pareto principle and positive responsiveness are equivalent. By applying these results, we obtain a new characterization of the method of majority decision.

A characterization and an impossibility of finite length anonymity for infinite generations

In the context of ranking infinite utility streams, the impartiality axiom of finite length anonymity requires the equal ranking of any two utility streams that are equal up to a finite length permutation ( Fleurbaey and Michel, 2003). We first characterize any finite length permutation as a composition of a fixed step permutation and an “almost” fixed step permutation. We then show that if a binary relation satisfies finite length anonymity, then it violates all the distributional axioms that are based on a segment-wise comparison. Examples of those axioms include the weak Pareto principle and the weak Pigou-Dalton principle.

On the Possibility of Continuous, Paretian and Egalitarian Evaluation of Infinite Utility Streams

There exists a utilitarian tradition a la Sidgwick of treating equal generations equally in the form of anonymity. Diamond showed that no social evaluation ordering over infinite utility streams satisfying the Pareto principle, Sidgwick's equity principle, and the axiom of continuity exists. We introduce two versions of egalitarianism in the spirit of the Pigou-Dalton transfer principle and the Lorenz domination principle, and examine their compatibility with the weak Pareto principle in the presence of a semi-continuity axiom. The social evaluation relation is not assumed to be either complete or transitive, yet Diamond's impossibility strenuously resurfaces.

Non-welfaristic Policy Assessment and the Pareto Principle

A welfaristic method of policy evaluation focuses exclusively on the effect of the policy on individuals' utilities. In contrast, a non-welfaristic way of assessing policies attaches some importance to factors other than the effects of policies on individuals' utilities. This paper develops a general framework to examine alternative approaches to policy assessment and their compatibility with the dominance rule underlying the weak Pareto principle.

How Inconsistent is a Paretian Liberal?

We revisit Sen's (1970) Paradox in its formulation for collective choice rules. It is well-known that under unrestricted domain, binary liberalism (BL) and the global (resp. binary) Weak Pareto principle (GWP/BWP) are incompatible with binary rejection consistency (resp. binariness). We first observe that even minimal contraction consistency is incompatible with BL and BWP, and show that this can be understood as the root of existing impossibility results. We then prove that the strongest expansion consistency condition is compatible with BL and BWP, and demonstrate that even requiring GWP still allows for various expansion consistency.

Arrovian aggregation in economic environments: how much should we know about indifference surfaces?

Arrow's celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and non-dictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about indifference surfaces is needed to construct social ordering functions satisfying the weak Pareto principle and anonymity. We show that local information such as marginal rates of substitution or the shapes “within the Edgeworth box” is not enough, and knowledge of substantially non-local information is necessary.

EQUAL VALUE OF LIFE AND THE PARETO PRINCIPLE

A principle claiming equal entitlement to continued life has been strongly defended in the literature as a fundamental social value. We refer to this principle as ‘equal value of life'. In this paper we argue that there is a general incompatibility between the equal value of life principle and the weak Pareto principle and provide proof of this under mild structural assumptions. Moreover we demonstrate that a weaker, age-dependent version of the equal value of life principle is also incompatible with the weak Pareto principle. However, both principles can be satisfied if transitivity of social preference is relaxed to quasi-transitivity.

THE IMPOSSIBILITY OF A PARETIAN REPUBLICAN? SOME COMMENTS ON PETTIT AND SEN

Philip Pettit (2001) has suggested that there are parallels between his republican account of freedom and Amartya Sen's (1970) account of freedom as decisive preference. In this paper, I discuss these parallels from a social-choice-theoretic perspective. I sketch a formalization of republican freedom and argue that republican freedom is formally very similar to freedom as defined in Sen's “minimal liberalism” condition. In consequence, the republican account of freedom is vulnerable to a version of Sen's liberal paradox, an inconsistency between universal domain, freedom, and the weak Pareto principle. I argue that some standard escape routes from the liberal paradox – those via domain restriction – are not easily available to the republican. I suggest that republicans need to take seriously the challenge of the impossibility of a Paretian republican.

More on independent decisiveness and Arrow's theorem

Denicolo [2, Theorem 1] strengthens Arrow's [1, p. 97] theorem by replacing the independence of irrelevant alternatives (IIA) condition by a strictly weaker one, relational independent decisiveness (RID). It is shown here that RID can be still substantially weakened. Yet, the new condition is equivalent to RID under the weak Pareto principle P and unrestricted domain U. In fact, any condition that can be put in place of IIA in Arrow's theorem must imply RID in the presence of P and U. Incidentally, it is argued that Denicolo's proof of his Theorem 1 contains an imprecision.

Lexicographic use of Sugeno integrals and monotonicity conditions

The Sugeno integral is very useful but its sensitivity is low. In order to overcome this disadvantage, the author proposes the lexicographic order induced by Sugeno integrals, which is called the LS order. It is an extension of useful orderings such as the ordinary lexicographic order, the leximax (the lexicographic maximax rule), and the leximin (the lexicographic maximin rule). Concerning the sensitivity of orderings, the author discusses three monotonicity conditions: the ordinary monotonicity condition (M), the weak Pareto principle (WP), and the strong Pareto principle (SP). As well known, the Sugeno integral always satisfies (M). The author shows that it satisfies (WP) under a special condition, and that it never satisfies (SP). In addition, he shows necessary and sufficient conditions for an LS order to satisfy (WP) and (SP). By using these conditions one can design LS orders satisfying desired monotonicity conditions.

The Possibility of a Fair Paretian

In my preceding article, I respond to the claim that the weak Pareto principle implies welfarism.1 Louis Kaplow and Steven Shavell make this claim in a series of recent papers.2 In my article, I have consistently adopted the definition of welfarism that is standard among social choice theorists.3 Under this standard definition, welfarism restricts the information that can be utilized in ranking social states to utility information corresponding to those social states.4 In their prior writings, Kaplow and Shavell have indicated that they intend to refer to this same concept.5 They contrast

Social choice with independent subgroup utility scales

In this article, the kinds of utility comparisons that can be made may differ in distinct population subgroups. Within each subgroup, utility is either ordinally or cardinally measurable. Levels and differences of utility may or may not be interpersonally comparable within a subgroup. No utility comparisons are possible between subgroups. Given these informational assumptions, it is shown that any continuous social welfare ordering that satisfies the weak Pareto principle only depends on the utilities of one of the subgroups. The class of social welfare orderings consistent with these assumptions is determined by the scale type of the dictatorial subgroup.

The Theory of Social Choice since 1951 / Die Theorie kollektiver Entscheidungen seit 1951

Summary Starting point for our analysis is Arrow’s famous impossibility result from 1951. Arrow had proved that within an ordinal framework no non-dictatorial social welfare function exists that satisfies the condition of unrestricted domain, the weak Pareto principle and the requirement of independence of irrelevant alternatives. In the first few sections, we discuss what kinds of positive results can be obtained once we relax one or the other of his axioms. The simple majority rule, for example, is an Arrow social welfare function under a domain restriction that is more general than single-peakedness. The Borda rule violates Arrow’s independence axiom but satisfies a weak independence requirement together with some other rather attractive properties. We next look at preference domains that admit the existence of Arrovian social welfare functions, i. e. aggregation rules fulfilling both the Pareto and the independence condition and being nondictatorial. We also characterize domains for non-manipulable voting procedures. The subsequent section analyzes social aggregation functions that allow for an interpersonal comparison of both utility levels and utility gains. Utilitarian rules and the Rawlsian lexicographic maximin principle are discussed in particular. We finally examine the exercise of individual rights within the social choice context, which means that non-utility information is considered as well.