Collective Choice Rules Research Articles

Escaping Arrow’s theorem: the Advantage-Standard model

AbstractThere is an extensive literature in social choice theory studying the consequences of weakening the assumptions of Arrow’s Impossibility Theorem. Much of this literature suggests that there is no escape from Arrow-style impossibility theorems, while remaining in an ordinal preference setting, unless one drastically violates the Independence of Irrelevant Alternatives (IIA). In this paper, we present a more positive outlook. We propose a model of comparing candidates in elections, which we call the Advantage-Standard (AS) model. The requirement that a collective choice rule (CCR) be representable by the AS model captures a key insight of IIA but is weaker than IIA; yet it is stronger than what is known in the literature as weak IIA (two profiles alike on x, y cannot have opposite strict social preferences on x and y). In addition to motivating violations of IIA, the AS model makes intelligible violations of another Arrovian assumption: the negative transitivity of the strict social preference relation P. While previous literature shows that only weakening IIA to weak IIA or only weakening negative transitivity of P to acyclicity still leads to impossibility theorems, we show that jointly weakening IIA to AS representability and weakening negative transitivity of P leads to no such impossibility theorems. Indeed, we show that several appealing CCRs are AS representable, including even transitive CCRs.

Urban Greening Management Arrangements between Municipalities and Citizens for Effective Climate Adaptation Pathways: Four Case Studies from The Netherlands

The transition towards nature-based cities has increasingly become a central focus in political–environmental agendas and urban design practices, aiming to enhance climate adaptation, urban biodiversity, spatial equilibrium, and social well-being as part of the ongoing socio-ecological urban transition process. Climate adaptation in cities is a complex problem and one of the main collective challenges for society, but the relationships between city managers and citizens as to urban green care still face many challenges. Parks design guided by technical-expert and globalised criteria; inflexibility from bureaucratic inertia; and citizens’ demands to participate in the urban green transition, sometimes without the necessary knowledge or time, are some of the challenges that require further research. In this study, we examine four long-lasting approaches to green-space management in four cities in the Netherlands, ranging from municipality-driven to community-driven management forms, and encompassing diverse spatial configurations of greenery within the urban fabric. Utilising the theoretical lens of the Social–Ecological Systems Framework, we employ a multiple-case-study approach and ethnographic fieldwork analysis to gain a comprehensive understanding of the norms, collective-choice rules, and social conventions embodied in each urban green management arrangement. The purpose of this research is applied, that is, to provide urban managers and decision-makers with a deeper understanding of drivers to promote effective collaborative management approaches, focusing on specific organisational rules that may contribute to more sustained planning and maintenance pathways for urban green spaces, regardless of changes in political leadership or significant external funding sources. The results of the investigated cases show that long-lasting collaborative management of forests and parks has established a set of collective-choice rules for resource transfer between municipalities and citizens, including non-monetary resources (such as pruning-training courses or guided tours that attract tourists and researchers). Additionally, these arrangements have been favoured by the existence of legal norms that enable co-ownership of the land, and monitoring and sanctioning mechanisms that offer a slightly different interpretation from the evidence identified so far in the scientific literature on collective resource management and organisational studies.

Past, present and future of the Smart City in India: An institutional perspective

The present contribution analyses the Smart City Mission launched in the year 2015 in India from an institutional perspective and examines how it is mobilized for coordinated action. Relying on theoretical guidance provided by Ostrom's (2005) ‘Institutional Analysis and Development’ (IAD) framework and González-Arellano's (2022) and Scott's (2008) formulation of ‘Institutional Construction of Futures of Cities’, we analyse a corpus of empirical data to suggest that SC has historical precedents in the way it is institutionalized. Further, to substantiate our findings, a structured literature review of empirical contributions (34 nos.) within the SCOPUS database is undertaken. In conceptual terms, the anticipatory praxis of Smart City Mission leverages the institutional structure of doing flagship programmes and a cultural-cognitive affirmation of neutrality in data-driven governance. The initiative blurs the political city as the action arenas of structuring SC initiatives at the local levels lack operational rules to construct desired outcomes. The paper argues for a need to make the action-to-outcome linkage legible and endow agency to participants to act and control the outcomes by framing collective choice rules. Strengthening action arenas at the city level emboldens the capacity to envision collaborative futures and bridge the gap between anticipation and experience.

Potential rationality in collective decision-making

This study investigates Suzumura consistency as a condition for the rationality of social preferences. A preference is said to be Suzumura-consistent when all preference cycles include only indifference relations. This condition is equivalent to transitivity in the presence of completeness, but, in general, it is substantially weaker than transitivity when preference is incomplete. Notably, Suzumura consistency is especially significant for a preference because it is necessary and sufficient for the existence of an ordering (transitive and complete preference) that is compatible with the original preference. This coherency property can be regarded as a requirement for potential rationality. In this study, we examine the implications of shifting from actual rationality to potential rationality in collective decision-making. We introduce the concept of an alternative-dependent coherent collection in order to obtain a representation of a class of Suzumura-consistent collective choice rules that satisfy the axioms imposed in Arrow’s impossibility theorem. This demonstrates that the power structure to determine social choice can be alternative-dependent.

Independent, neutral, and monotonic collective choice: the role of Suzumura consistency

We examine the impact of Suzumura’s (Economica 43:381–390, 1976) consistency property when applied in the context of collective choice rules that are independent of irrelevant alternatives, neutral, and monotonic. An earlier contribution by Blau and Deb (Econometrica 45:871–879, 1977) establishes the existence of a vetoer if the collective relation is required to be complete and acyclical. The purpose of this paper is to explore the possibilities that result if completeness and acyclicity are dropped and Suzumura consistency is imposed instead. A conceptually similar but logically independent version of the combined axiom that requires the collective decision mechanism to be independent, neutral, and monotonic is employed. In the case of a finite population, we obtain an alternative impossibility theorem if a collective choice rule is assumed to be non-degenerate and a modified no veto requirement is imposed instead of Blau and Deb’s (1977) condition. If the population is countably infinite, the impossibility can be avoided but it resurfaces if our new no veto property is extended to a coalitional variant.

Games Played by Teams of Players

We develop a general framework for analyzing games where each player is a team and members of the same team all receive the same payoff. The framework combines noncooperative game theory with collective choice theory, and is developed for both strategic form and extensive form games. We introduce the concept of team equilibrium and identify conditions under which it converges to Nash equilibrium with large teams. We identify conditions on collective choice rules such that team decisions are stochastically optimal: the probability the team chooses an action is increasing in its equilibrium expected payoff. The theory is illustrated with some binary action games. (JEL C72, D71)

How do governance arrangements matter in the circular economy? Lessons from five methanation projects based on the social-ecological system framework

As the circular economy (CE) is a viable solution to address environmental issues, academics and policy makers aim to have a better understanding of the drivers and barriers related to its development. Nonetheless, what is still missing in this discussion is what governance arrangements at the micro level would be conducive for the CE. In other words, how actors should interact to apply, form, and reform rules to organize activities inherent in the development of the CE. This study aims to investigate this question by mobilizing the Socio-Ecological Systems framework to examine five methanation projects carried out in the Brittany and Normandy regions of France. As these projects are characterized by different outcomes, a comparative analysis is conducted to identify a set of governance arrangement factors that are key to the success of the CE. First, in terms of actors, the results highlight the importance of (i) the participation of all relevant stakeholders in the governance process, especially local inhabitants, (ii) facilitative leadership, (iii) sufficient technological expertise. Second, there should be effective collaboration through frequent information sharing and self-organizing activities. Third, actors apply constitutional rules while elaborating collective choice rules that allow a collaborative and bottom-up governance.

Collective choice rules on restricted domains based on a priori information

We consider restricted domains where each individual has a domain of preferences containing some partial order. This partial order might differ for different individuals. Necessary and sufficient conditions are formulated under which these restricted domains admit unanimous, strategy-proof and non-dictatorial choice rules.

Two‐stage majoritarian choice

We propose a class of decisive collective choice rules that rely on a linear ordering to partition the majority relation into two acyclic relations. The first of these relations is used to pare down the set of the feasible alternatives into a shortlist while the second is used to make a final choice from the shortlist. Rules in this class are characterized by four properties: two classical rationality requirements (Sen's Expansion Consistency and Manzini and Mariotti's Weak WARP); and adaptations of two classical collective choice requirements (Arrow's Independence of Irrelevant Alternatives and Saari and Barney's No Preference Reversal Bias). These rules also satisfy some other desirable properties, including an adaptation of May's Positive Responsiveness.

Majority Rule or Dictatorship? How Collective-Choice Rules Affect Institutional Design and Cooperation

Majority Rule or Dictatorship? How Collective-Choice Rules Affect Institutional Design and Cooperation

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.

Polycentric structures nurturing adaptive food quality governance - Lessons learned from geographical indications in the European Union

In contrast to harmonised international food quality standards, local producers of food that is protected as geographical indication can adapt production rules. In a comparative multi-method case study approach, we analyse how constitutional and collective choice rules affect the negotiation of diverse interests and the adaptability of food quality standards in France, Italy and Austria. In France, a national organisation with a plurality of technical expertise guarantees the coherence of geographical indications based on notions of terroir and heritage. Italy's rural development approach secures very elaborated voting rules for producer groups and broader interaction on the regional level to accomplish broadly legitimated decisions. In the Austrian intellectual property rights approach, producers self-define the constitutional and collective choice rules and have the fullest autonomy and responsibility in standard setting. We conclude that polycentric interlinkages across scales and sectors – though delaying adaptation – support the long-term conservation of the products' identity via broad legitimisation. Both, the autonomy of local producers to innovatively adapt to change as well as a strong product identity are key for the long-term viability of geographical indications.

The organizations management multi-criteria objects aggregate rating construction

The article deals with the higher education institutions national aggregate rating constructing problem. This task is relevant in terms of improving management processes in educational organizations. This problem is formulated as a collective choice problem. Proposed to use voting in small groups as aggregation procedures, which satisfies the Condorcet principle. Three collective choice rules description is given in the paper. Obtained on the Bord, Copeland and Kemeny basis procedure salternatives final orderings stability is illustrated by concrete examples. The empirical mean is considered as a Kemeny median approximation. The Bord procedure instability with respect to changes in the initial scores obtained by universities in the ranking mechanisms under consideration is illustrated by examples. This paper presents the results of applying the described small-group voting procedures to a limited sample. This sample consists of data from 15 higher educational institutions from one of the Russian Federation regions. Universities constructed three aggregated ranks proximity degree was evaluated using two metrics - Kendall's rank correlation coefficient and Kemeny's distance. Based on the obtained results comparative analysis, it was made a conclusion about the expediency of using Condorcet-consistent collective selection procedures when constructing educational organizations aggregate ranking.

Pairwise Justifiable Changes in Collective Choices

Consider the following principle regarding the performance of collective choice rules. If a rule selects alternative x in situation 1, and alternative y in situation 2, there must be an alternative z, and some member of society whose appreciation of z relative to x has increased when going from situation 1 to situation 2. This principle requires a minimal justification for the fall of x in the consideration of society: someone must have decreased its appreciation relative to some other possible alternative. We study the consequences of imposing this requirement of pairwise justifiability on a large class of collective choice rules that includes social choice and social welfare functions as particular cases. When preference profiles are unrestricted, it implies dictatorship, and both Arrow's and the Gibbard-Satterthwaite theorems become corollaries of our general result. On appropriately restricted domains, pairwise justifiability, along with anonymity and neutrality, characterize Condorcet consistent rules, thus providing a foundation for the choice of the alternatives that win by majority over all others in pairwise comparisons, when they exist.

Superset-robust collective choice rules

A new property of collective choice rules that we refer to as superset robustness is introduced, and we employ it in several characterization results. The axiom requires that if all individual preference orderings expand weakly (in the sense of set inclusion), then the corresponding social preference relation must also expand weakly. In other words, if a given profile is changed by adding instances of weak preference to some individual relations, then the social weak preference relation for the expanded profile must contain the social weak preference relation for the original—that is, the social relation cannot contract in response to the addition of pairs to the individual relations. We begin by examining social welfare functions (that is, collective choice rules such that the resulting social preferences are orderings) and then move on to rules that generate transitive (but not necessarily complete) social rankings. The remaining results of the paper focus on Suzumura-consistent collective choice rules. In all of these cases, it turns out that the property of superset robustness is closely related to classes of agreement-based collective choice rules. These are rules such that the social relation is determined by collecting the pairs on whose relative rankings the members of the decisive sets agree.

Corrections to “Positively responsive collective choice rules and majority rule: a generalization of May's theorem to many alternatives” (International Economic Review60 (2019), 1489–1504)

Corrections to “Positively responsive collective choice rules and majority rule: a generalization of May's theorem to many alternatives” (<i>International Economic Review</i><b>60</b> (2019), 1489–1504)

A note on Murakami’s theorems and incomplete social choice without the Pareto principle

In Arrovian social choice theory assuming the independence of irrelevant alternatives, Murakami (Logic and social choice, Dover Publications, New York, 1968) proved two theorems about complete and transitive collective choice rules satisfying strict non-imposition (citizens’ sovereignty), one being a dichotomy theorem about Paretian or anti-Paretian rules and the other a dictator-or-inverse-dictator impossibility theorem without the Pareto principle. It has been claimed in the later literature that a theorem of Malawski and Zhou (Soc Choice Welf 11(2):103–107, 1994) is a generalization of Murakami’s dichotomy theorem and that Wilson’s impossibility theorem (J Econ Theory 5(3):478–486, 1972) is stronger than Murakami’s impossibility theorem, both by virtue of replacing Murakami’s assumption of strict non-imposition with the assumptions of non-imposition and non-nullness. In this note, we first point out that these claims are incorrect: non-imposition and non-nullness are together equivalent to strict non-imposition for all transitive collective choice rules. We then generalize Murakami’s dichotomy and impossibility theorems to the setting of incomplete social preference. We prove that if one drops completeness from Murakami’s assumptions, his remaining assumptions imply (i) that a collective choice rule is either Paretian, anti-Paretian, or dis-Paretian (unanimous individual preference implies noncomparability) and (ii) that adding proposed constraints on noncomparability, such as the regularity axiom of Eliaz and Ok (Games Econ Behav 56:61–86, 2006), restores Murakami’s dictator-or-inverse-dictator result.

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.

Nudging and Participation: a Contractualist Approach to Behavioural Policy

As behavioural economics reveals, human decision-making deviates from neoclassical assumptions about human behaviour and people (often) fail to make the ‘right’ welfare-enhancing choice. The purpose of Sunstein and Thaler’s concept of ‘nudge’ is to improve individual welfare. To provide normative justification, they argue that the only relevant normative criterion is whether the individual is ‘better off as judged by themselves’, so that the direction in which people are to be nudged is defined by their own preferences. In light of behavioural findings, however, people’s choices do not provide a sound basis for eliciting preferences and thus for assessing welfare. In this paper, I aim to challenge Sunstein and Thaler’s normative view, arguing that it is unreasonable to rely on conventional welfare economics, particularly considering the given context. Sunstein and Thaler depend on an approach of ‘preference purification’ which assumes informed, latent, and true preferences: As a result they face crucial methodological, epistemological, and practical objections, and cannot show how their approach enhances individual welfare. By building on the concepts of R. Sugden and C. Schubert, I develop an alternative normative framework for behavioural public policy, based on a contractualist perspective in which people may consent to collective choice rules in order to align future behaviour with values, to achieve particular goals or to preserve personal integrity. Individual consent and citizens’ participation and deliberation are crucial to this approach. This contractualist approach may provide a normative justification for behavioural public policy, and help to reconcile behavioural and normative economics.

POSITIVELY RESPONSIVE COLLECTIVE CHOICE RULES AND MAJORITY RULE: A GENERALIZATION OF MAY'S THEOREM TO MANY ALTERNATIVES

AbstractMay's theorem shows that if the set of alternatives contains two members, an anonymous and neutral collective choice rule is positively responsive if and only if it is majority rule. We show that if the set of alternatives contains three or more alternatives only the rule that assigns to every problem its strict Condorcet winner satisfies the three conditions plus Nash's version of “independence of irrelevant alternatives” for the domain of problems that have strict Condorcet winners. We show also that no rule satisfies the four conditions for domains that are more than slightly larger.