Consistency Axiom Research Articles

Infinite-horizon social evaluation with variable population size

We present an infinite-horizon extension of the framework of variable-population social choice. Our first main result is the welfarism theorem using the axiom of intratemporal anonymity. By this theorem, the ranking of social alternatives is determined by an intratemporally anonymous and finitely complete quasi-ordering [which we call social welfare relation (SWR)] defined on the set of all streams of utility vectors of generations. We introduce three SWRs: the critical-level generalized utilitarian (CLGU) SWR, the critical-level generalized overtaking (CLGO) SWR, and the critical-level generalized catching-up (CLGC) SWR. They are infinite-horizon extensions of the critical-level generalized utilitarianism. We characterize (in terms of subrelation) the CLGU SWR with five axioms: Strong Pareto, Finite Anonymity, Weak Existence of Critical Levels, Restricted Continuity, and Existence Independence. Further, the CLGO and the CLGC SWRs are characterized by adding consistency axioms. We also present infinite-horizon reformulations of some population ethics axioms. In particular, we characterize the CLGO and the CLGC SWRs associated with a positive critical level by using the axiom of avoidance of the repugnant conclusion.

Entropy, desegregation, and proportional rationing

An assignment of students to schools displays zero-segregation if all schools have the same distribution of the different types of students (ethnic, geographical, gender). We axiomatize the choice of an optimally desegregated assignment under arbitrary capacity constraints. The celebrated Consistency axiom, together with standard rational choice requirements, identify the choice rule minimizing a canonical index of proportional fairness: the entropy of the assignment matrix. This is an alternative vindication of the Mutual Information index of segregation recently characterized in Frankel and Volij (2011).A similar result holds in the capacity-constrained extension of the bipartite rationing model: there we must minimize the entropy of the rationing matrix augmented by individual deficits.

Random scheduling with deadlines under dichotomous preferences

A group of individuals share a deterministic server which is capable of serving one job per unit of time. Every individual has a job and a cut off time slot (deadline) where service beyond this slot is as worthless as not getting any service at all. Individuals are indifferent between slots which are not beyond their deadlines (compatible slots). A schedule (possibly random) assigns the set of slots to individuals by respecting their deadlines. We only consider the class of problems where for every set of relevant slots (compatible with at least one individual) there are at least as many individuals who have a compatible slot in that set: we ignore the case of underdemand. For this class, we characterize the random scheduling rule which attaches uniform probability to every efficient deterministic schedule (efficient uniform rule) by Pareto efficiency, equal treatment of equals, and probabilistic consistency (Chambers, 2004). We also show that a weaker version of the probabilistic consistency axiom is enough to achieve our result. Finally we show that efficient uniform rule is strategyproof.

Sequential rationalization of multivalued choice

This paper contributes to the theory of rational choice under sequential criteria. Following the approach initiated by Manzini and Mariotti (2007) for single-valued choice functions, we characterize choice correspondences that are rational by two sequential criteria under a mild consistency axiom. Rationales ensuring the sequential rationalization are explicitly constructed and a uniquely determined, canonical solution is provided.

A complexity question in justification logic

Bounds for the computational complexity of major justification logics were found in papers by Buss, N. Krupski, Kuznets, and Milnikel: logics J, J4, JT, LP and JD were established to be Σ2p-complete. A corresponding lower bound is also known for JD4, the system that includes the consistency axiom and positive introspection. However, no upper bound has been established so far for this logic. Here, the missing upper bound for the complexity of JD4 is established through an alternating algorithm. It is shown that using Fitting models of only two worlds is adequate to describe JD4; this helps to design an effective tableau procedure and essentially is what distinguishes the new algorithm from existing ones.

Reexamination on updating Choquet beliefs

Eichberger et al. (2007) characterize the full Bayesian update rule for capacities. This paper shows that a conditional preference relation represented by the Choquet expected utility with respect to the updated capacity through the rule does not satisfy the axiom of Conditional Certainty Equivalence Consistency. A counterexample is provided and it is proved that a relaxation of the axiom maintains their results.

The Limit of Discounted Utilitarianism

This paper presents an infinite-horizon version of intergenerational utilitarianism that is both satisfactorily complete and consistent. By studying discounted utilitarianism as the discount factor tends to one, a generalized criterion is obtained, which we completely characterize in terms of Finite Anonymity, Strong Pareto, Partial Unit Comparability and three additional consistency axioms. Its construction leads to an extended concept of utility difference for infinite utility streams, from which an ethical principle of compensations is rigorously derived. Through the principle of compensations, the concept of extended utility is proposed as a replacement for the extended axioms of anonymity that have been introduced in previous studies.

Rethinking Economics Using Complexity Theory

In this paper we argue that if we want to find a more satisfactory approach to tackling the major socio-economic problems we are facing, we need to thoroughly rethink the basic assumptions of macroeconomics and financial theory. Making minor modifications to the standard models to remove “imperfections” is not enough, the whole framework needs to be revisited. Let us here enumerate some of the standard assumptions and postulates of economic theory. 1. An economy is an equilibrium system. In other words, it is a system in which all markets systematically clear at each point of time, but where the equilibrium may be perturbed, from time to time by exogenous shocks. 2. Selfish or greedy behaviour of individuals yields a result that is beneficial to society – a modern, widespread, but inaccurate reformulation of the principle of the “invisible hand”. 3. Individuals and companies decide rationally. By this it is meant that individuals optimize under the constraints they are facing and that their choices satisfy some standard consistency axioms. 4. The behaviour of all the agents together can be treated as corresponding to that of an average or representative individual. 5. When the financial sector is analysed, it is assumed that financial markets are efficient. Efficiency here means that all the relevant information concerning an asset is reflected in the price of that asset. 6. For financial markets it is assumed that they function better if their liquidity is greater. 7. In financial markets, the more connected the network of individuals and institutions the more it reduces risks and the more stable and robust is the system. Below, we discuss the fundamental problems with these assumptions and outline some of the policy implications of improved assumptions.

Efficiency and Consistency in Group Decisions

The paper introduces a concept of “efficiency set" in the context of group decisions and analyses its properties. If the set contains a single element, then the Borda rule finds it. Otherwise, the group needs a value function to choose from the efficient alternatives. Two value functions, with considerations for the number of participants who are badly affected by the choice, have been discussed. It turns out that the consistency axiom of group choice imposes a constraint, on the form of the value function, with questionable normative significance.

Preferences, rational choices and economic valuation: Some empirical tests

This study focuses on the respondent rationality hypothesis, usually assumed to be true in Discrete Choice Experiments. We examine lexicographic preferences, the influence of consistency, and the role of task complexity in the individual choice process. To this end, we carry out rationality tests in a survey on forest recreation. Results show that choice set orderings do not impact on choice probability. If a violation of continuity or consistency axioms does impact on choice probability, the Willingness-To-Pay estimators calculated using the total sample and the sub-samples of “irrational” respondents are not significantly different. This serves as a basis for discussing the traditional concept of rationality.

On interference abstractions

Interference is the bane of both concurrent programming and analysis. To avoid considering all possible interferences between concurrent threads, most automated static analysis employ techniques to approximate interference, e.g., by restricting the thread scheduler choices or by approximating the transition relations or reachable states of the program. However, none of these methods are able to reason about interference directly. In this paper, we introduce the notion of interference abstractions (IAs), based on the models of shared memory consistency, to reason about interference efficiently. IAs differ from the known abstractions for concurrent programs and cannot be directly modeled by these abstractions. Concurrency bugs typically involve a small number of unexpected interferences and therefore can be captured by small IAs. We show how IAs, in the form of both over- and under-approximations of interference, can be obtained syntactically from the axioms of sequential consistency. Further, we present an automatic method to synthesize IAs suitable for checking safety properties. Our experimental results show that small IAs are often sufficient to check properties in realistic applications, and drastically improve the scalability of concurrent program analysis in these applications.

Inconsistency Pays?: Time-Inconsistent Subjects and EU Violators Earn More

Experimental choice data from 881 subjects based on 40 time-tradeoff items and 32 risky choice items reveal that most subjects are time-inconsistent and most violate the axioms of expected utility theory. These inconsistencies cannot be explained by well-known theories of behavioral inconsistency, such as hyperbolic discounting and cumulative prospect theory. Aggregating expected payoffs and the risk associated with each subjects’ 72 choice items, the statistical links between inconsistency and total payoffs are reported. Time-inconsistent subjects and those who violate expected utility theory both earn substantially higher expected payoffs, and these positive associations survive largely undiminished when included together in total payoff regressions. Consistent subjects earn lower than average payoffs because most of them are consistently impatient or consistently risk averse. Positive payoffs from inconsistency cannot, however, be fully explained by greater risk taking. Controlling for the total risk of each subject’s risk choices as well as for socio-economic differences among subjects, time inconsistent subjects earn significantly more money, in statistical and economic terms. So do expected utility violators. Positive returns to inconsistency extend outside the domain in which inconsistencies occurs, with time-inconsistent subjects earning more on risky choice items, and expected utility violators earning more on time-tradeoff items. The results seem to call into question whether axioms of internal consistency—and violations of these axioms that behavioral economists frequently focus on—are economically relevant criteria for evaluating the quality of decision making in human populations.

Consistent comparison of pro-poor growth

This article contributes to the literature of pro-poor growth measurement by introducing and characterizing a growth-rate consistency axiom. The axiom states that if one growth pattern is judged to be more pro-poor than another growth pattern at a given growth rate, then the pro-poor ranking between the two growth patterns should remain the same at a higher growth rate. We show that summary pro-poor measures such as poverty-growth elasticities may violate this axiom. We then characterize a special dominance condition under which a given summary pro-poor measure will satisfy the growth-rate consistency axiom. Finally, we establish a general growth-rate dominance condition under which all summary pro-poor measures will respect the growth-rate consistency axiom.

On the coefficient of variation as a predictor of risk sensitivity: Behavioral and neural evidence for the relative encoding of outcome variability

Cox and Vjollca (2010) argue that the coefficient of variation (CV) fails as a normative criterion for risk taking in risky choice because it predicts violations of dominance. They suggest that it fails also on descriptive grounds because such violations are not observed in a study they conducted and because people’s choices in two other situations were not predicted by the CV. This paper counters the normative argument by suggesting that occasional violations of dominance might be the price that organisms with only limited processing capacity pay to achieve a broad set of goals. The consistency axioms of rational choice theory have a long history of falling short of accounting for such tradeoffs. The paper then addresses the three instances of descriptive failures of the CV to predict risk taking provided by Cox and Sadiraj, showing them to be inappropriate or inconclusive arguments against the use of the CV as a measure of risk in risk-return models of human and animal risk taking. Finally, the paper reviews new behavioral and neuroscience evidence in support of the CV as a predictor of risk taking, especially in decisions from experience, for which the model was developed.

Updating claims in bankruptcy problems

We re-examine the consistency axiom in bankruptcy problems and propose arguments in favor of an alternative definition of a reduced problem. The classical definition updates the size of the estate while keeping agents’ claims unaffected. Instead, we suggest updating agents’ claims along with the estate. The resulting consistency axiom characterizes the well-known Random Arrival rule as the unique bilateral consistent extension of the Contested Garment rule to many agents.

Characterization of the Banzhaf Value Using a Consistency Axiom

Una de las propiedades importantes caracterizando soluciones de juegos cooperativos es con- sistencia. Esta nocion establece conexiones entre los vectores solucion de un juego cooperativo y aquellos de su juego reducido. Este ultimo es obtenido a partir del juego inicial al remover uno o mas jugadores y asignandoles pagos de acuerdo a un principio especifico. Consistencia de una solucion significa que la restriccion de una solucion del juego inicial a cualquier coalicion, pertenece al conjunto de soluciones del correspondiente juego reducido. En este articulo, mostramos que consistencia junto con estandarizacion para juegos de dos personas caracterizan el valor de Banzhaf.

Compressed Environments: Unbounded Optimizers Should Sometimes Ignore Information

Given free information and unlimited processing power, should decision algorithms use as much information as possible? A formal model of the decision-making environment is developed to address this question and provide conditions under which informationally frugal algorithms, without any information or processing costs whatsoever, are optimal. One cause of compression that allows optimal algorithms to rationally ignore information is inverse movement of payoffs and probabilities (e.g., high payoffs occur with low probably and low payoffs occur with high probability). If inversely related payoffs and probabilities cancel out, then predictors that correlate with payoffs and consequently condition the probabilities associated with different payoffs will drop out of the expected-payoff objective function, severing the link between information and optimal action rules. Stochastic payoff processes in which rational ignoring occurs are referred to as compressed environments, because optimal action depends on a reduced-dimension subset of the environmental parameters. This paper considers benefits and limitations of economic models versus other methods for studying links between environmental structure and the real-world success of simple decision procedures. Different methods converge on the normative proposition of ecological rationality, as opposed to axiomatic rationality based on informational efficiency and internal consistency axioms, as a superior framework for comparing the effectiveness of decision strategies and prescribing decision algorithms in application.

Characteristic properties of FPTP systems

In this article, we model FPTP systems as social preference rules and give two characterizations. We show that a social preference rule is an FPTP system if, and only if, it satisfies the axioms of subset consistency, district consistency, subset cancellation, and district cancellation. The second characterization consists of the axioms of subset consistency, subset anonymity, neutrality, topsonlyness, Pareto optimality, district consistency and district cancellation. The characterizations give us an opportunity to compare the characteristic properties of FPTP systems to the characteristic properties that we found for list systems of proportional representation (list PR systems) in Hout et al. (Social Choice and Welfare, 27:459–475, 2006), where we modelled those systems also as social preference rules. We find that consistency and anonymity distinguish list PR systems from FPTP systems. On the other hand, it is district cancellation that distinguishes FPTP systems from list PR systems.

Bargaining among groups: an axiomatic viewpoint

We introduce a model of bargaining among groups, and characterize a family of solutions using a Consistency axiom and a few other invariance and monotonicity properties. For each solution in the family, there exists some constant α ≥ 0 such that the “bargaining power” of a group is proportional to c α, where c is the cardinality of the group.

Kautilya: a forerunner of neoclassical price theory

PurposeThe purpose of this paper is to establish Kautilya as a genuine contender to be a forerunner of the neoclassical price theory.Design/methodology/approachRational reconstruction approach is used to present Kautilya's understanding of several most basic concepts in economics.FindingsKautilya's understanding of the law of diminishing returns is at par with the classicists. His applications of concepts like opportunity cost, and of demand and supply framework, are closer to those of the neoclassicals. His understanding of the rules (axioms) of comparison and consistency and the exploration of substitution possibilities is way ahead of the classicists.Research limitations/implicationsThe current research in the history of economic thought concentrates too heavily on the exploration of Western history of economic thought.Practical implicationsKautilya's Arthashastra is a new source of knowledge and the profession should encourage the exploration of other ancient contributions outside of Europe.Originality/valueThe paper revises the history of economic thought.