Choice Rules Research Articles

Original position arguments: an axiomatic characterization

Abstract We study original position arguments in the context of social choice under ignorance. First, we present a general formal framework for such arguments. Next, we provide an axiomatic characterization of social choice rules that can be supported by original position arguments. We illustrate this characterization in terms of various well-known social choice rules, some of which do and some of which do not satisfy the axioms in question. Depending on the perspective one takes, our results can be used to argue against certain rules, against Rawlsian theories of procedural fairness, or in support of richer, multidimensional models of individual choice.

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.

The implementability of liberalism

AbstractThis note shows that under the unrestricted domain, there exists a choice liberal and Nash implementable social choice rule if and only if there are at least three players and the outcome set is at least twice as large as the player set. A social choice rule is choice liberal if and only if for every player, there exists at least one pair of outcomes such that if this player strictly prefers one over the other, the one he prefers is socially desirable and the other one is not. A social choice rule is Nash implementable if and only if there exists a mechanism such that at every preference profile, the set of Nash equilibrium outcomes coincides with the set of socially desirable ones. The proof constructs an intuitive Nash implementing mechanism.

WELFARE ANALYSIS VIA MARGINAL TREATMENT EFFECTS

We consider a causal structure with endogeneity, i.e., unobserved confoundedness, where an instrumental variable is available. In this setting, we show that the mean social welfare function can be identified and represented via the marginal treatment effect as the operator kernel. This representation result can be applied to a variety of statistical decision rules for treatment choice, including plug-in rules, Bayes rules, and empirical welfare maximization rules. Focusing on the application of the empirical welfare maximization framework, we provide convergence rates of the worst-case average welfare loss (regret).

An indifference result for social choice rules in large societies

Social choice rules can be defined or derived by minimizing distance-based objective functions. One problem with this approach is that any social choice rule can be derived by selecting an appropriate distance function. Another problem comes from the computational difficulty of determining the solution of some social choice rules. We provide a general positive indifference result when looking at expected average distances by showing that on ‘average’ each social choice rule performs equally well with respect to a very large class of distance functions if the number of voters is large. Our result applies also to the frequently employed Kendall τ, Spearman rank correlation and Spearman footrule ‘distance functions’.

Jednostranná nebo konkludentní? Problematické aspekty volby práva (nejen) v zajišťovacích instrumentech ve světle aktuální judikatury

This article deals with cases of <i>unilateral</i> and <i>tacit</i> choice of law, as less common examples of choice of law. These are entirely separate categories. Unilateral choice reflects the fact that it is the result of the will of only one person, and typically appears in unilateral legal acts (such as a financial guarantee in Czech law). Tacit choice, on the other hand, indicates that the intent to choose the law was expressed in a non-explicit way. Choice of law can be at the same time both unilateral and tacit, although this will not occur very often in practice. In the case of unilateral legal acts in the field of contract and tort law, there is a debate whether their conflict of laws regime falls under the EU’s unified conflict of laws rules (Rome I or Rome II Regulation) or under national law. There is no clear decision on the issue by the CJEU. The Czech Supreme Court has recently been given the opportunity to comment on this and some other issues of unilateral and implied choice of law. However, the Court rather missed this opportunity. It avoided the question of whether the national law or the Rome I Regulation applies to unilateral legal acts similar to a declaration of guarantee by (unfortunately incorrectly) applying the Rome Convention. The Court also applied the rules for a bilateral choice of law to an apparently unilateral choice of law in a rather complex manner. Moreover, its conclusion that the choice subjecting the declaration in question to “Danish statutes” is only an implied choice and not an express one is at least questionable. The article critically assesses this decision and shows in what respects a different (and more correct) course of action should be followed.

Nesterov acceleration‐based iterative method for backward problem of distributed‐order time‐fractional diffusion equation

This paper is concerned with the inverse problem of determining the initial value of the distributed‐order time‐fractional diffusion equation from the final time observation data, which arises in some ultra‐slow diffusion phenomena in applied areas. Since the problem is ill‐posed, we propose an iterated regularization method based on the Nesterov acceleration strategy to deal with it. Convergence rates for the regularized approximation solution are given under both the a priori and a posteriori regularization parameter choice rules. It is shown that the proposed method can always yield the order optimal convergence rates as long as the iteration parameter which appears in the Nesterov acceleration strategy is chosen large enough. In numerical aspect, the main advantage of the proposed method lies in its simplicity. Specifically, due to the Nesterov acceleration strategy, only a few number of iteration steps are required to obtain the approximation solution, and at each iteration step, we only need to numerically solve the standard initial‐boundary value problem for the distributed‐order time‐fractional diffusion equation. Some numerical examples including one‐dimensional and two‐dimensional cases are presented to illustrate the validity and effectiveness of the proposed method.

Nested replicator dynamics, nested logit choice, and similarity-based learning

We consider a model of learning and evolution in games whose action sets are endowed with a partition-based similarity structure intended to capture exogenous similarities between strategies. In this model, revising agents have a higher probability of comparing their current strategy with other strategies that they deem similar, and they switch to the observed strategy with probability proportional to its payoff excess. Because of this implicit bias toward similar strategies, the resulting dynamics – which we call the nested replicator dynamics – do not satisfy any of the standard monotonicity postulates for imitative game dynamics; nonetheless, we show that they retain the main long-run rationality properties of the replicator dynamics, albeit at quantitatively different rates. We also show that the induced dynamics can be viewed as a stimulus-response model in the spirit of Erev and Roth (1998), with choice probabilities given by the nested logit choice rule of Ben-Akiva (1973) and McFadden (1978). This result generalizes an existing relation between the replicator dynamics and the exponential weights algorithm in online learning, and provides an additional layer of interpretation to our analysis and results.

Origin of rules of law choice: the primitive era

The article explores the concept that the first relations falling under the subject of private international law originated in the primitive period. These relations include exogamy and incest taboos, the institution of hospitality and exchange agreements. Exogamy and incest taboos are fundamental relationships that emerged parallel to the development of society and law, forming he cornerstone of these constructs. These represent the earliest interactions involving “foreign persons” and are characterized by personal non-property character. Hospitality ties are linked to exogamy while exchange relationships follow subsequently. Intergroup agreements serve as primary mechanism for regulating these relations and lay the groundwork for the inception of the initial choice-of-law rules. The conflicts are not interstate but rather intergroup (intercommunal), similar to contemporary interpersonal or interlocal disputes. The author applies a number of methods such as comparative analysis, reconstruction, formal-logical, dialectical, natural science and historical analysis in this research. In conclusion, the author asserts that three key institutions emerged in the pre-state era, forming the foundation of modern PIL: exogamy (cross-border marrital and family relations), hospitality (foreigners’ law), and exchange (international contract law). During this period the first conflict resolution rules also emerged. The principle method for addressing conflict issues in primitive societies is the unified substantive approach through intergroup agreements. Additionally, archaic law incorporated conflicting principles like personal law and the law of the place where the action occurred. These conclusions are drawn through a reconstructive approach and are supported by archeology, genetics, anthropology, as well as domestic and foreign scholarly research on legal genesis.

Unwritten ground rules of school choice: Excavating capital as a regulator of access to educational goods

District leaders in school choice contexts tend to overlook the many hidden costs of selecting schools in terms of mobility, time, liquidity, and labor. Meanwhile, a body of literature on school choice policies and cultural, social, and political capital shows that middle-class parents use the resources they possess to get the school access they want. In this study, I critically examine the complex interplay between school choice policies and forms of capital. This analysis extends our empirical understanding of the political dimensions of families’ school choices—the way parent resources, relationships, and strategies determine “who gets what, when, and how” (Laswell, 1936) in terms of schooling opportunities, and way these policies help structure disproportionate school access. By attending to families’ affordances of cultural, social, and political capital in studies of school choice, authorities may be more likely to design choice supports that address some demand-side inequities.

Trade-off between manipulability and dictatorial power: A proof of the Gibbard–Satterthwaite Theorem

By endowing the class of tops-only and efficient social choice rules with a dual order structure that exploits the trade-off between different degrees of manipulability and dictatorial power rules allow agents to have, we provide a proof of the Gibbard–Satterthwaite Theorem.

Diversity Balance in Centralized Public School Admissions

Parental choice over public schools has become a major educational reform throughout the United States and the world. Most district policies are implemented via admission priorities. Diversity in admissions is a common policy goal. However, it necessitates the violation of some priorities. We develop an axiomatic theory for meeting diversity objectives with a reserves system. We axiomatize the trade-off between diversity and priorities. We characterize the solution that uniquely and optimally achieves the diversity objectives via reserves by minimizing priority violations. The choice rule corresponds to a simple and natural implementation of application orders in a reserves system.

THE CONDITIONAL STABILITY AND AN ITERATIVE REGULARIZATION METHOD FOR A FRACTIONAL INVERSE ELLIPTIC PROBLEM OF TRICOMI-GELLERSTEDT-KELDYSH TYPE

The present paper is devoted to identifying an inaccessible boundary condition for a fractional elliptic problem of Tricomi-Gellerstedt-Keldysh-type. Using the expansion Fourier method, the considered problem can be reformulated as an operator equation of the first kind. To construct a stabilized approximate solution we employ a variant of the iterative method. We also present error estimates between the exact solution and the regularized solution by the a priori and the a posteriori parameter choice rules. Finally, some numerical verifications on the efficiency and accuracy of the proposed algorithm is presented.

Transitions between equilibria in Bilingual Games under Probit Choice

We study the effect of introducing a bilingual strategy on the long run equilibrium outcome in a class of two-strategy coordination games with distinct payoff- and risk-dominant equilibria under the probit choice rule. Existing results show that in the class of two-strategy games under consideration, the inefficient risk dominant equilibrium is selected in the long run under noisy best response models. We show that if the cost of the bilingual option is sufficiently low then the efficient payoff dominant equilibrium will be selected in the long run under the probit choice rule.

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.

Two Regularization Methods for Identifying the Spatial Source Term Problem for a Space-Time Fractional Diffusion-Wave Equation

In this paper, we delve into the challenge of identifying an unknown source in a space-time fractional diffusion-wave equation. Through an analysis of the exact solution, it becomes evident that the problem is ill-posed. To address this, we employ both the Tikhonov regularization method and the Quasi-boundary regularization method, aiming to restore the stability of the solution. By adhering to both a priori and a posteriori regularization parameter choice rules, we derive error estimates that quantify the discrepancies between the regularization solutions and the exact solution. Finally, we present numerical examples to illustrate the effectiveness and stability of the proposed methods.

A discretizing Tikhonov regularization method via modified parameter choice rules

Abstract In this paper, we propose two parameter choice rules for the discretizing Tikhonov regularization via multiscale Galerkin projection for solving linear ill-posed integral equations. In contrast to previous theoretical analyses, we introduce a new concept called the projection noise level to obtain error estimates for the approximate solutions. This concept allows us to assess how noise levels change during projection. The balance principle and Hanke–Raus rule are modified by incorporating the error estimates of the projection noise level. We demonstrate the convergence rate of these two modified parameter choice rules through rigorous proof. In addition, we find that the error between the approximate solution and the exact solution improves as the noise frequency increases. Finally, numerical experiments are provided to illustrate the theoretical findings presented in this paper.

Adaptive minimax optimality in statistical inverse problems via SOLIT—Sharp Optimal Lepskiĭ-Inspired Tuning

We consider statistical linear inverse problems in separable Hilbert spaces and filter-based reconstruction methods of the form fˆα=qαT∗TT∗Y , where Y is the available data, T the forward operator, qαα∈A an ordered filter, and α > 0 a regularization parameter. Whenever such a method is used in practice, α has to be appropriately chosen. Typically, the aim is to find or at least approximate the best possible α in the sense that mean squared error (MSE) E[∥fˆα−f†∥2] w.r.t. the true solution f† is minimized. In this paper, we introduce the Sharp Optimal Lepskiĭ-Inspired Tuning (SOLIT) method, which yields an a posteriori parameter choice rule ensuring adaptive minimax rates of convergence. It depends only on Y and the noise level σ as well as the operator T and the filter qαα∈A and does not require any problem-dependent tuning of further parameters. We prove an oracle inequality for the corresponding MSE in a general setting and derive the rates of convergence in different scenarios. By a careful analysis we show that no other a posteriori parameter choice rule can yield a better performance in terms of the order of the convergence rate of the MSE. In particular, our results reveal that the typical understanding of Lepskiĭ-type methods in inverse problems leading to a loss of a log factor is wrong. In addition, the empirical performance of SOLIT is examined in simulations.

Discrete Legendre spectral projection-based methods for Tikhonov regularization of first kind Fredholm integral equations

In this paper, we apply the discrete Legendre Galerkin and multi-Galerkin methods to find the approximate solution of the Tikhonov regularized equation of the Fredholm integral equations of the first kind. We evaluate the error bounds for the approximate solutions with the exact solution in the infinity norm. We provide an a priori parameter choice strategy to find the convergence rates under the infinity norm. Since smoothness of the solution is not known in applied problems, we discuss an adaptive parameter choice rule to choose the regularization parameter, and then using this regularization parameter, we obtain the order of convergence in infinity norm. We give test examples to justify the theoretical estimates.

Modelling orthographic similarity effects in recognition memory reveals support for open bigram representations of letter coding

A variety of letter string representations has been proposed in the reading literature to account for empirically established orthographic similarity effects from masked priming studies. However, these similarity effects have not been explored in episodic memory paradigms and very few memory models have employed orthographic representation of words. In the current work, through two recognition memory experiments employing word and pseudoword stimuli respectively, we empirically established a set of key orthographic similarity effects for the first time in recognition memory – namely the substitution effect, transposition effect and reverse effect in recognition memory of words and pseudowords, and a start-letter importance in recognition memory of words. Subsequently, we compared orthographic representations from the reading literature including slot coding, closed-bigram, open-bigram and the overlap model. Each of these representations was situated in a global matching model and fitted to recognition performance via Luce’s choice rule in a hierarchical Bayesian framework. Model selection results showed support for the open-bigram representation in both experiments.