A speaker wishes to persuade a listener to accept a certain request. The conditions under which the request is justified, from the listener’s point of view, depend on the values of two aspects. The values of the aspects are known only to the speaker and the listener can check the value of at most one. A mechanism specifies a set of messages that the speaker can send and a rule that determines the listener’s response, namely, which aspect he checks (...) and whether he accepts or rejects the speaker’s request. We study mechanisms that maximize the probability that the listener accepts the request when it is justified and rejects the request when it is unjustified, given that the speaker maximizes the probability that his request is accepted. We show that a simple optimal mechanism exists and can be found by solving a linear programming problem in which the set of constraints is derived from what we call the L-principle. (shrink)

We study the uncertain dichotomous choice model. In this model a set of decision makers is required to select one of two alternatives, say ‘support’ or ‘reject’ a certain proposal. Applications of this model are relevant to many areas, such as political science, economics, business and management. The purpose of this paper is to estimate and compare the probabilities that different decision rules may be optimal. We consider the expert rule, the majority rule and a few in-between (...) rules. The information on the decisional skills is incomplete, and these skills arise from an exponential distribution. It turns out that the probability that the expert rule is optimal far exceeds the probability that the majority rule is optimal, especially as the number of the decision makers becomes large. (shrink)

In certain judgmental situations where a “correct” decision is presumed to exist, optimal decision making requires evaluation of the decision-makers’ capabilities and the selection of the appropriate aggregation rule. The major and so far unresolved difficulty is the former necessity. This article presents the optimal aggregation rule that simultaneously satisfies these two interdependent necessary requirements. In our setting, some record of the voters’ past decisions is available, but the correct decisions are not known. We observe that (...) any arbitrary evaluation of the decision-makers’ capabilities as probabilities yields some optimal aggregation rule that, in turn, yields a maximum-likelihood estimation of decisional skills. Thus, a skill-evaluation equilibrium can be defined as an evaluation of decisional skills that yields itself as a maximum-likelihood estimation of decisional skills. We show that such equilibrium exists and offer a procedure for finding one. The obtained equilibrium is locally optimal and is shown empirically to generally be globally optimal in terms of the correctness of the resulting collective decisions. Interestingly, under minimally competent (almost symmetric) skill distributions that allow unskilled decision makers, the optimal rule considerably outperforms the common simple majority rule (SMR). Furthermore, a sufficient record of past decisions ensures that the collective probability of making a correct decision converges to 1, as opposed to accuracy of about 0.7 under SMR. Our proposed optimal voting procedure relaxes the fundamental (and sometimes unrealistic) assumptions in Condorcet’s celebrated theorem and its extensions, such as sufficiently high decision-making quality, skill homogeneity or existence of a sufficiently large group of decision makers. (shrink)

How should moral sanctions and moral rewards - the moral sentiments involving feelings of guilt and of virtue - be employed to govern individuals' behavior if the objective is to maximize social welfare? In the model that we examine, guilt is a disincentive to act and virtue is an incentive because we assume that they are negative and positive sources of utility. We also suppose that guilt and virtue are costly to inculcate and are subject to certain constraints on their (...) use. We show that the moral sentiments should be used chiefly to control externalities and further that guilt is best to employ when most harmful acts can successfully be deterred whereas virtue is best when only a few individuals can be induced to behave well. We also contrast the optimal use of guilt and virtue to optimal Pigouvian taxation and discuss extensions of our analysis. (shrink)

Hans Reichenbach made a bold and original attempt to ‘vindicate’ induction. He proposed a rule, the ‘straight rule’ of induction, which would guarantee inductive success if any rule of induction would. A central problem facing his attempt to vindicate the straight rule is that too many other rules are just as good as the straight rule if our only constraint on what counts as ‘success’ for an inductive rule is that it is ‘asymptotic’, i.e. (...) that it converges in the limit to the true limiting frequency (of some type of outcome O in a sequence of events) whenever such a limiting frequency exists. In this paper I consider the consequences of requiring speed-optimality of asymptotic methods, that is, requiring that inductive methods must get to the truth as quickly as possible. Two main results are proved: (1) the straight rule is speed-optimal; (2) there are (uncountably) many non-speed-optimal asymptotic methods. A further result gives a sufficient but not necessary condition for speed-optimality among asymptotic methods. Some consequences and open questions are then discussed. (shrink)

We argue that many optimization methods can be viewed as representatives of “forcing”, a methodological approach that attempts to bridge the gap between data and mathematics on the basis of an a priori trust in the power of a mathematical technique, even when detailed, credible models of a phenomenon are lacking or do not justify the use of this technique. In particular, we show that forcing is implied in particle swarms optimization methods, and in modeling image processing problems through optimization. (...) From these considerations, we extrapolate a principle for general data analysis methods, what we call ‘Brandt’s principle’, namely the assumption that an algorithm that approaches a steady state in its output has found a solution to a problem, or needs to be replaced. We finally propose that biological systems, and other phenomena that respect general rules of morphogenesis, are a natural setting for the application of this principle. (shrink)

This paper reports completeness results for dyadic deontic logics in the tradition of Hansson’s systems. There are two ways to understand the core notion of best antecedent-worlds, which underpins such systems. One is in terms of maximality, and the other in terms of optimality. Depending on the choice being made, one gets different evaluation rules for the deontic modalities, but also different versions of the so-called limit assumption. Four of them are disentangled, and compared. The main observation of this paper (...) is that, even in the partial order case, the contrast between maximality and optimality is not as significant as one could expect, because the logic remains the same whatever notion of best is used. This is established by showing that, given analogous properties for the betterness relation, the same system is sound and complete with respect to its intended modelling. The chief result of this paper concerns Åqvist’s system F supplemented with the principle of cautious monotony. It is established that, under the maximality rule, F + is sound and complete with respect to the class of models in which the betterness relation is required be reflexive and smooth . From this, a number of spin-off results are obtained. First and foremost, it is shown that a similar determination result holds for optimality; that is, under the optimality rule, F + is also sound and complete with respect to the class of models in which the betterness relation is reflexive and smooth . Other spin-off results concern classes of models in which further constraints are placed on the betterness relation, like totalness and transitivity. (shrink)

We investigate two formalizations of Optimality Theory, a successful paradigm in linguistics.We first give an order-theoretic counterpart for the data and processinvolved in candidate evaluation.Basically, we represent each constraint as a function that assigns every candidate a degree of violation.As for the second formalization, we define (after Samek-Lodovici and Prince) constraints as operations that select the best candidates out of a set of candidates.We prove that these two formalizations are equivalent (accordingly, there is no loss of generality with using violation (...) marks and dispensing with them is only apparent).Importantly, we show that the second formalization is equivalent with a class of operations over sets of formulas in a given logical language.As a result, we prove that Optimality Theory can be characterized by certain cumulative logics.So, applying Optimality Theory is shown to be reasoning by the rules of cumulative logics. (shrink)

Assuming that votes are independent, the epistemically optimal procedure in a binary collective choice problem is known to be a weighted supermajority rule with weights given by personal log-likelihood-ratios. It is shown here that an analogous result holds in a much more general model. Firstly, the result follows from a more basic principle than expected-utility maximisation, namely from an axiom (Epistemic Monotonicity) which requires neither utilities nor prior probabilities of the ‘correctness’ of alternatives. Secondly, a person’s input need (...) not be a vote for an alternative, it may be any type of input, for instance a subjective degree of belief or probability of the correctness of one of the alternatives. The case of a profile of subjective degrees of belief is particularly appealing, since here no parameters such as competence parameters need to be known. (shrink)

In a homogeneous jury, in which each vote is correct with the same probability, and each pair of votes correlates with the same correlation coefficient, there exists a correlation-robust voting quota, such that the probability of a correct verdict is independent of the correlation coefficient. For positive correlation, an increase in the correlation coefficient decreases the probability of a correct verdict for any voting rule below the correlation-robust quota, and increases that probability for any above the correlation-robust quota. The (...) jury may be less competent under the correlation-robust rule than under simple majority rule and less competent under simple majority rule than a single juror alone. The jury is always less competent than a single juror under unanimity rule. (shrink)

A broad range of intellectual perspectives may be brought to bear on any important social institution. To this general rule, the institution of private property is no exception. The desirability of private property has been endlessly debated across the disciplines: philosophical, historical, economic, and legal. Yet there is very little consensus over its proper social role and limitations. Is it possible to find a unique solution to questions of property and private ownership, good for all resources and for all (...) times? The famous defense of private property that is found in chapter 5 of John Locke's Second Treatise of Government answers this question in the affirmative, for Locke writes as though all property was given to mankind in common, and then seeks to find the quickest and most expeditious way to convert all common property into private property. His implicit, but undefended, assumption is that common forms of property are both undesirable and unstable, while private forms of ownership are always just the opposite. Yet his preferred method for moving from a commons to a regime of private property—the unilateral decision to appropriate by each actor—is one that has been frequently condemned as a sop to unbridled egotism, even though it is subject to two constraints: the first against waste, and the second requiring the appropria-tor to leave “enough, and as good” for others. (shrink)

Information is a peculiar quantity. Unlike matter and energy, which are conserved by the laws of physics, the aggregation of knowledge from many sources can in fact produce more information (synergy) or less (redundancy) than the sum of its parts. This feature can endow groups with problem‐solving strategies that are superior to those possible among noninteracting individuals and, in turn, may provide a selection drive toward collective cooperation and coordination. Here we explore the formal properties of information aggregation as a (...) general principle for explaining features of social organization. We quantify information in terms of the general formalism of information theory, which also prescribes the rules of how different pieces of evidence inform the solution of a given problem. We then show how several canonical examples of collective cognition and coordination can be understood through principles of minimization of uncertainty (maximization of predictability) under information pooling over many individuals. We discuss in some detail how collective coordination in swarms, markets, natural language processing, and collaborative filtering may be guided by the optimal aggregation of information in social collectives. We also identify circumstances when these processes fail, leading, for example, to inefficient markets. The contrast to approaches to understand coordination and collaboration via decision and game theory is also briefly discussed. (shrink)

In a three-candidate election, a scoring rule s (s in [0,1]) assigns 1, s, and 0 points (respectively) to each first, second and third place in the individual preference rankings. The Condorcet efficiency of a scoring rule is defined as the conditional probability that this rule selects the winner in accordance with Condorcet criteria (three Condorcet criteria are considered in the paper). We are interested in the following question: What rule s has the greatest Condorcet efficiency? (...) After recalling the known answer to this question, we investigate the impact of social homogeneity on the optimal value of ?. One of the most salient results we obtain is that the optimality of the Borda rule (s=1/2) holds only if the voters act in an independent way. (shrink)

The level of enjoyment in participating in sports activities is one component that causes young athletes to decide to stop or become more motivated to pursue sports activities. Practicing and participating in competitions are the main activities in sports coaching interactions towards optimal performance. This study aims to determine the effect of modifying the match rules implemented in youth soccer competitions on the level of enjoyment of players. Using an experimental method with 20 soccer schools participating in a competition (...) with modified game rules. Players registered by his team amounted to an average of 13.8 players aged 9-12 years. The number of players who are willing to fill out the pleasure level questionnaire is 238 players. Each player was asked to fill out a questionnaire before and after the competition, the questionnaire was analyzed using the mean and percentage test technique. The results of data analysis showed the average score before participating in the competition was 4.10 while after participating in the competition it was 4.47, which means an increase of 8.88%. The results showed that the level of enjoyment of the players increased after participating in the competition. Modification of the rule of the game in competition affects the level of enjoyment of players in the interaction of youth soccer coaching. Coaches, administrators, and match organizers are expected to have a positive paradigm of thinking and policy making towards the organization of competitions for young soccer players. (shrink)

Considering three monetary policy rules, together with two endogenous macroprudential policies that are credit constraints for households and counter-cyclical capital for bankers, this paper establishes a dynamic stochastic general equilibrium model. Based on the welfare analysis of different combinations of macroprudential rules and monetary policy rules, this paper identifies the optimal policy combinations and analyzes the coordination effects between macroprudential policies and monetary policies. The results show that no matter what kind of monetary policy rules is implemented, the introduction (...) of macroprudential rules has improved the level of total social welfare. In the optimal “two pillars” framework of monetary policies and macroprudential rules, the main objective of monetary policy is to stabilize price inflation, and the macroprudential policy to be implemented is the CRR macroprudential policy. This combination can effectively promote the stability of the real estate market, financial market, and macroeconomy, while maximizing the improvement of total social welfare. (shrink)

Several recent studies and initiatives have emphasized the importance of a strong ethical organizational DNA (ODNA) to create and promote an effective corporate governance culture of trust, integrity and intellectual honesty. This paper highlights the drawbacks of an excessively heavy reliance on rules-based approaches that increase the cost of doing business, overshadow essential elements of good corporate governance, create a culture of dependency, and can result in legal absolutism. The paper makes the case that the way forward for effective corporate (...) governance is to strike an optimal balance between rules-based and principles-based approaches. The recent corporate scandals have demonstrated that the ethical ODNA is critical to the driving force and basis of legal and regulatory requirements. Effective governance means adhering to ethical principles, not merely complying with rules, and is a crucial guardian of a firm’s reputation and integrity. It is through an effective corporate governance program (that is, one that optimally captures and integrates the appropriate aspects of rules-based and principles-based approaches, and identifies and assesses the related risks) that an organization can reconfigure its ODNA for improved performance. Focusing on the ethical ODNA as the basis of new governance measures provides an opportunity to develop a competitive advantage as it represents a potential source of differentiation, strengthens the relationship with all stakeholders of the organization by building a culture of trust and integrity, and re-instills investor confidence. This paper employs dialectical reasoning that links the ODNA through principles-driven rules in developing a risks-based approach. A comparison from a risk assessment perspective between rules-based and principles-based approaches is presented. Although there have been few applications employing dialectical reasoning in business research, this methodology can be extremely useful in isolating ethical issues and integrating them into the business process. The risks-based approach captures the benefits of both rules-based and principles-based approaches, and incorporates trust-based principles such␣as solidarity, subsidiarity and covenantal relationships. (shrink)

In this paper, we derive necessary and sufficient conditions on team based tasks in order for a selection criterion applied to individuals to produce optimal teams. We assume only that individuals have types and that a team’s performance depends on its size and the type composition of its members. We first derive the selection principle which states that if a selection criterion exists, it must rank types by homogeneous team performance, the performance of a team consisting only of that (...) type. We then prove that a selection criterion exists if and only if replacing the team’s lowest ranked type, as measured by homogeneous team performance, with a higher ranked type increases team performance. Finally, we show that the replace the lowest ranked property rules out most common types of team complementarities, including benefits to diverse types and types that fill structural holes. (shrink)

In cloud security, intrusion detection system (IDS) is one of the challenging research areas. In a cloud environment, security incidents such as denial of service, scanning, malware code injection, virus, worm, and password cracking are getting usual. These attacks surely affect the company and may develop a financial loss if not distinguished in time. Therefore, securing the cloud from these types of attack is very much needed. To discover the problem, this paper suggests a novel IDS established on a combination (...) of a leader-based k-means clustering (LKM), optimal fuzzy logic system. Here, at first, the input dataset is grouped into clusters with the use of LKM. Then, cluster data are afforded to the fuzzy logic system (FLS). Here, normal and abnormal data are inquired by the FLS, while FLS training is done by the grey wolf optimization algorithm through maximizing the rules. The clouds simulator and NSL-Knowledge Discovery and DataBase (KDD) Cup 99 dataset are applied to inquire about the suggested method. Precision, recall, and F-measure are conceived as evaluation criteria. The obtained results have denoted the superiority of the suggested method in comparison with other methods. (shrink)

In a three-candidate election, a scoring rule λ, λ∈[0,1], assigns 1,λ and 0 points (respectively) to each first, second and third place in the individual preference rankings. The Condorcet efficiency of a scoring rule is defined as the conditional probability that this rule selects the winner in accordance with Condorcet criteria (three Condorcet criteria are considered in the paper). We are interested in the following question: What rule λ has the greatest Condorcet efficiency? After recalling the (...) known answer to this question, we investigate the impact of social homogeneity on the optimal value of λ. One of the most salient results we obtain is that the optimality of the Borda rule (λ=1/2) holds only if the voters act in an independent way. (shrink)

In many voting systems, voters’ preferences on a set of candidates are represented by linear orderings. In this context, scoring rules are well-known procedures to aggregate the preferences of the voters. Under these rules, each candidate obtains a fixed number of points, sk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s_k$$\end{document}, each time he/she is ranked k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}th by one voter and the candidates are ordered according to the total number of (...) points they receive. In order to identify the best scoring rule to use in each situation, we need to know which properties are met by each of these procedures. Although some properties have been analyzed extensively, there are other properties that have not been studied for all scoring rules. In this paper, we consider two desirable social choice properties, the Pareto-optimality and the immunity to the absolute loser paradox, and establish characterizations of the scoring rules that satisfy each of these specific axioms. Moreover, we also provide a proof of a result given by Saari and Barney, where the scoring rules meeting reversal symmetry are characterized. From the results of characterization, we establish some relationships among these properties. Finally, we give a characterization of the scoring rules satisfying the three properties. (shrink)

In the State of Bernstein, operating a motor vehicle on a suspended license is a misdemeanor, punishable by permanent loss of one’s license. Officer Krupke arrests everyone who does this, as Tony has. But Tony says, “Gee, Officer Krupke, can’t you bend the rules? I went to your high school, you know.” Tony’s using a euphemism. He’s really asking Krupke to break the rules. Is there, however, a non-euphemistic way to bend a rule of law, without breaking it? More (...) precisely, can we ever bend a rule while still applying it, in some sense, or is this just doubletalk? Consider the case of Maria, whose driver’s license has also been suspended. Maria lives with her mother in a remote area, twenty miles from the nearest doctor. Maria’s mother comes down with a fever of one hundred two. It’s not life-threatening, but Maria wants to spare her mother suffering and hasten recovery, so she drives to the hospital herself, rather than waiting for an ambulance to make the trip out and back. Unfortunately for Maria, the statute contains no applicable exception. I stipulate that this statute is not unjust or otherwise defective, as written. Suppose there are conclusive reasons for legislators not to complicate the statute with exceptions broad enough to cover cases such as Maria’s. Writing such exceptions would encourage sub-optimal misapplication of the exception by judges and sub-optimal misconduct by legal subjects who would anticipate judicial misapplication of the statutory exception. Nevertheless, most will agree that Maria has strong reasons to act as she does. Rare is the writer who insists that rules of law trump all other reasons that bear on legal subjects. Some will insist that we give Maria’s mother a condition more life-threatening before they’ll assent. (shrink)

How, and how well, do people switch between exploration and exploitation to search for and accumulate resources? We study the decision processes underlying such exploration/exploitation trade‐offs using a novel card selection task that captures the common situation of searching among multiple resources (e.g., jobs) that can be exploited without depleting. With experience, participants learn to switch appropriately between exploration and exploitation and approach optimal performance. We model participants' behavior on this task with random, threshold, and sampling strategies, and find (...) that a linear decreasing threshold rule best fits participants' results. Further evidence that participants use decreasing threshold‐based strategies comes from reaction time differences between exploration and exploitation; however, participants themselves report non‐decreasing thresholds. Decreasing threshold strategies that “front‐load” exploration and switch quickly to exploitation are particularly effective in resource accumulation tasks, in contrast to optimal stopping problems like the Secretary Problem requiring longer exploration. (shrink)

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. (shrink)

We use game theory and Santa Fe Artificial Stock Market, an agent-based model of an evolving stock market, to study the optimal frequency for traders to revise their market forecasting rules. We discover two things: There is a unique strategic Nash equilibrium in the game of choosing forecast revision rates, and this equilibrium is sub-optimal in the sense that traders’ earnings are not maximized an the market is inefficient. This strategic equilibrium is due to an analogue of the (...) prisoner’s dilemma; the optimal global state is unstable because each trader has too much incentive to ‘defect’ and use forecasting rules that pull the market into thesub-optimal equilibrium. (shrink)

During the past decade, a small but rapidly growing number of Law&Tech scholars have been applying algorithmic methods in their legal research. This Article does it too, for the sake of saving disclosure regulation failure: a normative strategy that has long been considered dead by legal scholars, but conspicuously abused by rule-makers. Existing proposals to revive disclosure duties, however, either focus on the industry policies (e.g. seeking to reduce consumers’ costs of reading) or on rulemaking (e.g. by simplifying linguistic (...) intricacies). But failure may well depend on both. Therefore, this Article develops a `comprehensive approach', suggesting to use computational tools to cope with linguistic and behavioral failures at both the enactment and implementation phases of disclosure duties, thus filling a void in the Law & Tech scholarship. Specifically, it outlines how algorithmic tools can be used in a holistic manner to address the many failures of disclosures from the rulemaking in parliament to consumer screens. It suggests a multi-layered design where lawmakers deploy three tools in order to produce optimal disclosure rules: machine learning, natural language processing, and behavioral experimentation through regulatory sandboxes. To clarify how and why these tasks should be performed, disclosures in the contexts of online contract terms and privacy online are taken as examples. Because algorithmic rulemaking is frequently met with well-justified skepticism, problems of its compatibility with legitimacy, efficacy and proportionality are also discussed. (shrink)

Scoring rules measure the deviation between a forecast, which assigns degrees of confidence to various events, and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is strictly better than the mathematical expectation of any other forecast q by the lights of p. Forecasts need not satisfy the axioms of the probability calculus, but Predd et al. [9] have shown that given a (...) finite sample space and any strictly proper additive and continuous scoring rule, the score for any forecast that does not satisfy the axioms of probability is strictly dominated by the score for some probabilistically consistent forecast. Recently, this result has been extended to non-additive continuous scoring rules. In this paper, a condition weaker than continuity is given that suffices for the result, and the condition is proved to be optimal. (shrink)

Decision theory aims at a general account of rationality covering humans but to begin makes idealizations about decision problems and agents' resources and circumstances. It treats inerrant agents with unlimited cognitive power facing tractable decision problems. This book systematically rolls back idealizations and without loss of precision treats errant agents with limited cognitive abilities facing decision problems without a stable top option. It recommends choices that maximize utility using quantizations of beliefs and desires in cases where probabilities and utilities are (...) indeterminate and using higher-order utility analysis in cases of limited access to probabilities and utilities. For agents burdened with mistakes, it advocates reasonable attempts to correct unacceptable mistakes before deciding. In decision problems without a stable top option, a topic of game theory, it proposes maximizing self-conditional utility among self-supporting options. In games of strategy, the new principles lead to solutions that are Pareto optimal among equilibria composed of jointly self-supporting strategies. Offering an account of bounded rationality, the bookmakes large strides toward realism in decision theory. (shrink)

Preferences for options that do not secure optimal outcomes, like the ones catalogued by Sunstein, derive from two sources: cognitive heuristics and deontological rules. Although rules may stem from automatic affective reactions, they are deliberately maintained. Because strongly held convictions have important behavioral implications, it may be useful to regard cognitive heuristics and deontological rules as separate sources of nonconsequential judgment in the moral domain.

In this study I analyse the performance of a democratic decision-making rule: the weighted majority rule. It assigns to each voter a number of votes that is proportional to her stakes in the decision. It has been shown that, for collective decisions with two options, the weighted majority rule in combination with self-interested voters maximises the common good when the latter is understood in terms of either the sum-total or prioritarian sum of the voters’ well-being. The main (...) result of my study is that this argument for the weighted majority rule — that it maximises the common good — can be improved along the following three main lines. (1) The argument can be adapted to other criteria of the common good, such as sufficientarian, maximin, leximin or non-welfarist criteria. I propose a generic argument for the collective optimality of the weighted majority rule that works for all of these criteria. (2) The assumption of self-interested voters can be relaxed. First, common-interest voters can be accommodated. Second, even if voters are less than fully competent in judging their self-interest or the common interest, the weighted majority rule is weakly collectively optimal, that is, it almost certainly maximises the common good given large numbers of voters. Third, even for smaller groups of voters, the weighted majority rule still has some attractive features. (3) The scope of the argument can be extended to decisions with more than two options. I state the conditions under which the weighted majority rule maximises the common good even in multi-option contexts. I also analyse the possibility and the detrimental effects of strategic voting. Furthermore, I argue that self-interested voters have reason to accept the weighted majority rule. (shrink)

A Millian response is presented to Sen's celebrated Paretian liberal impossibility theorem. It is argued that Millian Paretian liberalism is possible, if the application of Paretian norms is restricted to the selection of an optimal code of liberal justice and rights, as well as to individual choices made in compliance with the rules of the code. Key steps in outlining the Millian response include suitably modifying Sen's social choice formulation of the idea of claim-right to personal liberty, and incorporating (...) within social choice theory the distinction between a right and its direction of exercise. The Millian response is illustrated in the context of Sen's original example of the ‘prude’ and the ‘lewd’. If the argument is successful, coherent and appealing liberal versions of Pareto-inclusive philosophies such as utilitarianism, contractualism and neo-republicanism are feasible in principle. (Published Online February 16 2006). (shrink)

This inquiry critically assesses previous research utilizing a game theory framework to understand Hume’s account of convention as the tangible expression of justice for the purpose of regulating possessions. In so doing, this research offers an alternative understanding of Humean convention that first clearly lays out the rules and main assumptions of the game, as presented in A Treatise of Human Nature, and then proceeds to analyze the implied optimal strategy and outcome. Rejecting commonly held views considering Humean convention (...) in terms of the Nash equilibrium and pure contractarianism, this research offers a novel middle approach—a “Third Way” between self-interest and sympathy, between cooperation versus non-cooperation, and ultimately between contractarianism versus utilitarianism. This “Third Way”conceives of Hume’s account of convention as a cooperative game with binding threats that necessarily always rests on the Pareto optimal strategy, and seeks a resulting Pareto optimal outcome. (shrink)

What is the optimal size of a democratic society? While not taking an explicit stand on this issue, Hélène Landemore's model of democracy in Democratic Reason suggests that democracies ought to be small, certainly smaller than many existing states. If, as Landemore argues, we must rely on the random selection of representatives, then we should be concerned about both the size of the population and the way cognitive diversity is distributed within it. Given the realities of party politics and (...) media framing, this means that smaller political societies will yield wiser decisions than very large ones. (shrink)

Katarzyna de Lazari-Radek and Peter Singer’s wonderful book, The Point of View of the Universe: Sidgwick and Contemporary Ethics, contains a wealth of intriguing arguments and compelling ideas. The present paper focuses on areas of continuing dispute. The paper first attacks LazariRadek’s and Singer’s evolutionary debunking arguments against both egoism and parts of common-sense morality. The paper then addresses their discussion of the role of rules in utilitarianism. De Lazari-Radek and Singer concede that rules should constitute our moral decision procedure (...) and our public morality. This paper argues that, if no one should be blamed for complying with the optimal decision procedure and optimal public rules, there are strong reasons to accept that these same rules determine what is morally permissible from what is morally wrong. (shrink)

Katarzyna de Lazari-Radek and Peter Singer’s wonderful book, The Point of View of the Universe: Sidgwick and Contemporary Ethics, contains a wealth of intriguing arguments and compelling ideas. The present paper focuses on areas of continuing dispute. The paper first attacks LazariRadek’s and Singer’s evolutionary debunking arguments against both egoism and parts of common-sense morality. The paper then addresses their discussion of the role of rules in utilitarianism. De Lazari-Radek and Singer concede that rules should constitute our moral decision procedure (...) and our public morality. This paper argues that, if no one should be blamed for complying with the optimal decision procedure and optimal public rules, there are strong reasons to accept that these same rules determine what is morally permissible from what is morally wrong. (shrink)

Estimation and evaluation of individualized treatment rules have been studied extensively, but real-world treatment resource constraints have received limited attention in existing methods. We investigate a setting in which treatment is intervened upon based on covariates to optimize the mean counterfactual outcome under treatment cost constraints when the treatment cost is random. In a particularly interesting special case, an instrumental variable corresponding to encouragement to treatment is intervened upon with constraints on the proportion receiving treatment. For such settings, we first (...) develop a method to estimate optimal individualized treatment rules. We further construct an asymptotically efficient plug-in estimator of the corresponding average treatment effect relative to a given reference rule. (shrink)

Animals depleting one patch of resources must decide when to leave and switch to a fresh patch. Foraging theory has predicted various decision mechanisms; which is best depends on environmental variation in patch quality. Previously we tested whether these mechanisms underlie human decision making when foraging for external resources; here we test whether humans behave similarly in a cognitive task seeking internally generated solutions. Subjects searched for meaningful words made from random letter sequences, and as their success rate declined, they (...) could opt to switch to a fresh sequence. As in the external foraging context, time since the previous success and the interval preceding it had a major influence on when subjects switched. Subjects also used the commonness of sequence letters as a proximal cue to patch quality that influenced when to switch. Contrary to optimality predictions, switching decisions were independent of whether sequences differed little or widely in quality. (shrink)

Compensation rules for patent infringement greatly affect patent quality, which is closely related to R & D investments. In this study, A duopoly game model was developed to analyze innovative factories’ R&D investment and patent licensing behavior, as well as the strategic choices of potential infringers under different compensation rules for patent infringement. Furthermore, a comparative analysis was conducted to analyze the patent quality under different scenarios, ultimately finalizing an optimal sequence rule for patent infringement compensation. The results (...) show that patent quality is influenced by the invention height of patent and R&D efficiency, while the amount of patent infringement compensation has a great effect on potential infringement behavior. Patent quality can be effectively improved if the court adopts a proper sequence rule for patent infringement compensation according to the market circumstances. (shrink)

We focus on the dichotomous choice model, which goes back as far as Condorcet (1785; Essai sur l'application de l'analyse a la probabilité des décisions rendues a la pluralité des voix, Paris). A group of experts is required to select one of two alternatives, of which exactly one is regarded as correct. The alternatives may be related to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision. A decision (...) class='Hi'>rule is optimal if it maximizes the probability of the group to make a correct choice. In this paper we assume the correctness probabilities of the experts to be independent random variables, selected from some given distribution. Moreover, the ranking of the members in the team is (at least partly) known. Thus, one can follow rules based on this ranking. The polar different rules are the expert and the majority rules. The probabilities of the two polar rules being optimal were compared in a series of papers. The main purpose of this paper is to outline the results, providing exact formulas or estimates for these probabilities. We consider a variety of distributions and show that for all of these distributions the asymptotic behaviour of the probabilities of the two polar rules follows the same patterns. (shrink)

The paper introduces the concept of polar decision rules and establishes that majority rules are polar rules. We identify second best rules and penultimate rules in cases that majority rules are optimal or the most inferior, respectively. We especially specify the almost expert rule and the almost majority rule as the secondary rules of the expert and majority rules, respectively.

A theoretical framework for the reinforcement learning of aesthetic biases was recently proposed based on brain circuitries revealed by neuroimaging. A model grounded on that framework accounted for interesting features of human aesthetic biases. These features included individuality, cultural predispositions, stochastic dynamics of learning and aesthetic biases, and the peak-shift effect. However, despite the success in explaining these features, a potential weakness was the linearity of the value function used to predict reward. This linearity meant that the learning process employed (...) a value function that assumed a linear relationship between reward and sensory stimuli. Linearity is common in reinforcement learning in neuroscience. However, linearity can be problematic because neural mechanisms and the dependence of reward on sensory stimuli were typically nonlinear. Here, we analyze the learning performance with models including optimal nonlinear value functions. We also compare updating the free parameters of the value functions with the delta rule, which neuroscience models use frequently, vs. updating with a new Phi rule that considers the structure of the nonlinearities. Our computer simulations showed that optimal nonlinear value functions resulted in improvements of learning errors when the reward models were nonlinear. Similarly, the new Phi rule led to improvements in these errors. These improvements were accompanied by the straightening of the trajectories of the vector of free parameters in its phase space. This straightening meant that the process became more efficient in learning the prediction of reward. Surprisingly, however, this improved efficiency had a complex relationship with the rate of learning. Finally, the stochasticity arising from the probabilistic sampling of sensory stimuli, rewards, and motivations helped the learning process narrow the range of free parameters to nearly optimal outcomes. Therefore, we suggest that value functions and update rules optimized for social and ecological constraints are ideal for learning aesthetic biases. (shrink)

Florida International University, USA edwardj{at}fiu.edu ' + u + '@ ' + d + ' '/ /- -> Several authors have analyzed the optimal k -majority rule based on a variety of criteria. Buchanan and Tullock argued that, in constitutional settings, the criterion should be that all changes meet the Pareto criterion; otherwise the status quo should be preferred. They then asserted that unanimity rule would be the preferred voting rule in this setting. In parliamentary settings, (...) they claimed that a near majority rule would be preferred because it minimizes the sum of decision costs and external costs. This article investigates both claims in an N -voter, two-alternative setting. We show the conditions under which unanimity rule is less likely to select BT preferred alternatives than other k -majority rules and prove that the difference in performance can be negligible when N is large and certain weak conditions are met. Furthermore, if we define external costs as the expected number of losers from a BT-inferior vote, then external costs become negligible for a range of supermajority rules. This implies that unanimity rule and a range of supermajority rules should be equally preferred when decision costs are added. Finally, we show that the external cost function can actually increase for certain populations. Many of the broader conclusions should also hold for multiple alternatives. Key Words: constitutional design • Pareto criterion • external costs • social contract. (shrink)

We characterize seniority rules, also known as lexical dictatorships, under weak consistency constraints on the group’s choice function. These constraints are base triple-acyclicity in the case of binary choices and rationalizability (although not rationality) in the case of choices between an arbitrary number of alternatives. Existing results on these weakened constraints remain silent on the treatment of the group’s most junior individuals and therefore do not yield a complete characterization of seniority rules. We also impose a universal domain, binary strict (...) Pareto optimality, binary Pareto indifference, binary independence of irrelevant alternatives, and the newly introduced condition of conflict resolution. The latter condition requires a social choice rules not to remain indecisive between alternatives for which individuals have conflicting preferences. (shrink)

Over the last few years, a new methodology to address the P versus NP problem has been developed, based on searching for borderlines between the nonefficiency of computing models and the presumed efficiency. These borderlines can be seen as frontiers of efficiency, which are crucial in this methodology. “Translating,” in some sense, an efficient solution in a presumably efficient model to an efficient solution in a nonefficient model would give an affirmative answer to problem P versus NP. In the framework (...) of Membrane Computing, the key of this approach is to detect the syntactic or semantic ingredients that are needed to pass from a nonefficient class of membrane systems to a presumably efficient one. This paper deals with tissue P systems with communication rules of type symport/antiport allowing the evolution of the objects triggering the rules. In previous works, frontiers of efficiency were found in these kinds of membrane systems both with division rules and with separation rules. However, since they were not optimal, it is interesting to refine these frontiers. In this work, optimal frontiers of the efficiency are obtained in terms of the total number of objects involved in the communication rules used for that kind of membrane systems. These optimizations could be easier to translate, if possible, to efficient solutions in a nonefficient model. (shrink)