Metatickles and the dynamics of deliberation

The traditional or orthodox decision rule of maximizing conditional expected utility has recently come under attack by critics who advance alternative causal decision theories. The traditional theory has, however, been defended. And these defenses have in turn been criticized. Here, I examine two objections to such defenses and advance a theory about the dynamics of deliberation (a diachronic theory about the process of deliberation) within the framework of which both objections to the defenses of the traditional theory fail.     

Payoff Kinks in Preferences over Lotteries

This paper identifies two distinct types of payoff kinks that can be exhibited by preference functions over monetary lotteries—locally separable vs. locally nonseparable—and illustrates their relationship to the payoff and probability derivatives of such functions. Expected utility and Fréchet differentiable preference functions are found to be incapable of exhibiting locally nonseparable payoff kinks; rank-dependent preference functions are incapable of avoiding them.     

On the foundations of mean-variance analyses

Let (, ) and (, ) be mean-standard deviation pairs of two probability distributions on the real line. Mean-variance analyses presume that the preferred distribution depends solely on these pairs, with primary preference given to larger mean and smaller variance. This presumption, in conjunction with the assumption that one distribution is better than a second distribution if the mass of the first is completely to the right of the mass of the second, implies that (, ) is preferred to (, ) if and only if either > or ( = and < ), provided that the set of distributions is sufficiently rich. The latter provision fails if the outcomes of all distributions lie in a finite interval, but then it is still possible to arrive at more liberal dominance conclusions between (, ) and (, ).This research was supported by the Office of Naval Research.     

Majority vote of even and odd experts in a polychotomous choice situation

The performance of majority vote by an odd number of voters in a dichotomous situation is a much-studied subject. In this paper, we study the performance of group consensus in a situation of polychotomous choice. The differences in majority vote behaviour between even and odd numbers of expert panellists are examined, and the effects of adding new members are derived. Unlike the dichotomous model, optimality in the present context may not be uniquely defined, so the probabilities of the consensus being correct or erroneous are both considered as the number of experts is increased.     

Avoiding the voter's paradox democratically

This paper is concerned with selecting an appropriate perspective from which to understand and evaluate social-decision procedures. Distinguishing between agentrationality and option-rationality, the author argues that a rational agent may choose a social-decision procedure that is not itself agent-rational (but merely option-rational). The argument puts the voter's paradox in a context allowing evaluation of (a) its general import and (b) practical proposals for avoiding it in particular cases. Arrow's four conditions for a social-decision procedure are shown to have little relevance to the understanding or evaluation of constitutions. The author concludes that the more fruitful perspective for discussing social-decision procedures is that of option-rationality rather than (as Arrow, Wolff, and others have supposed) that of agent-rationality.     

Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence

Choices between gambles show systematic violations of stochastic dominance. For example, most people choose ($6, .05; $91, .03; $99, .92) over ($6, .02; $8, .03; $99, .95), violating dominance. Choices also violate two cumulative independence conditions: (1) If S = (z, r; x, p; y, q) R = (z, r; x, p; y, q) then S = (x, r; y, p + q) R = (x, r + p; y, q). (2) If S = (x, p; y, q; z, r) R = (x, p; y, q; z, r) then S = (x, p + q; y, r) R = (x, p; y, q + r), where 0 < z < x < x < y < y < y < z.Violations contradict any utility theory satisfying transivity, outcome monotonicity, coalescing, and comonotonic independence. Because rank-and sign-dependent utility theories, including cumulative prospect theory (CPT), satisfy these properties, they cannot explain these results.However, the configural weight model of Birnbaum and McIntosh (1996) predicted the observed violations of stochastic dominance, cumulative independence, and branch independence. This model assumes the utility of a gamble is a weighted average of outcomes\' utilities, where each configural weight is a function of the rank order of the outcome\'s value among distinct values and that outcome\'s probability. The configural weight, TAX model with the same number of parameters as CPT fit the data of most individuals better than the model of CPT.     

Predictive superiority of the beta-characteristic function in cooperative non-sidepayment N-person games

This article reports an experimental study of decision-making outcomes in cooperative non-sidepayment games. The objective of this test was to determine which characteristic function, V (S) or V (S), provides the most accurate basis for payoff predictions from solution concepts. The experiment tested three solution concepts (core, stable set, imputation set) in the context of 5-person, 2-strategy non-sidepayment games. Predictions from each of the three solution concepts were computed on the basis of both V (S) and V (S), making a total of six predictive theories under test. Consistent with earlier studies (Michener et al., 1984a; Michener et al., 1985), two basic findings emerged. First, the data show that for each of the solutions tested, the prediction from any solution concept computed from V(S) was more accurate than the prediction from the same solution concept computed from V (S). Second, the -core was the most accurate of the six theories tested. Overall, these results support the view that V (S) is superior to V (S) as a basis for payoff predictions in cooperative non-sidepayment games.     

Correlated strategies as Institutions

Two institutions that are often implicit or overlooked in noncooperative games are the assumption of Nash behavior to solve a game, and the ability to correlate strategies. We consider two behavioral paradoxes; one in which maximin behavior rules out all Nash equilibria (Chicken), and another in which minimax supergame behavior leads to an inefficient outcome in comparison to the unique stage game equilibrium (asymmetric Deadlock). Nash outcomes are achieved in both paradoxes by allowing for correlated strategies, even when individual behavior remains minimax or maximin. However, the interpretation of correlation as a public institution differs for each case.     

Objective knowledge out of ignorance: Popper on body,mind, and the third world

In the fifties, Popper defended an interactionistic version of body-mind dualism. It distinguished between the world of physical bodies and states and the world of mental states. Later he added a third world of objective thought contents. He claims the assumption that there is the third world is a necessary presupposition of problem-solving in general and of his philosophy of science in particular. The present article contains separate reasonings to the effect that this presupposition is neither necessary nor even possible. It is further argued that postulating the existence of entities makes sense only relative to a criterion of ontological commitment, which Popper does not mention and obviously does not have, and that in addition it presupposes a theory, which is tentatively accepted as true and which according to the criterion implies the existence of the entities. But as yet there is no testable theory involving terms like mind, intention etc., which made the notion that itself or its terms are essentially different from what is already known in the empirical sciences at least plausible. Therefore the body-mind controversy is still pointless. Popper's stand on it seems to be but a reflex of his anti-behavioristic and anti-psychologistic attitude.     

A strategic foundation for the cooperator's advantage

Orbell and Dawes develop a non-game theoretic heuristic that yields a cooperator's advantage by allowing players to project their own cooperate-defect choices onto potential partners (1991, p. 515). With appropriate parameter values their heuristic yields a cooperative environment, but the cooperation depends, simply, on optimism about others' behavior (1991, p. 526). In earlier work, Dawes (1989) established a statistical foundation for such optimism. In this paper, I adapt some of the concerns of Dawes (1989) and develop a game theoretic model based on a modification of the Harsanyi structure of games with incomplete information (1967–1968). I show that the commonly made conjecture that strategic play is incompatible with cooperation and the cooperator's advantage is false.     

Independent social choice correspondences

A fixed agenda social choice correspondence on outcome set X maps each profile of individual preferences into a nonempty subset of X. If satisfies an analogue of Arrow's independence of irrelevant alternatives condition, then either the range of contains exactly two alternatives, or else there is at most one individual whose preferences have any bearing on . This is the case even if is not defined for any proper subset of X.     

A μ-σ-Risk Aversion Paradox and Wealth Dependent Utility

We report a surprising property of --preferences: the assumption of nonincreasing relative risk aversion implies the optimal portfolio being riskless. We discuss a solution of that paradox using wealth dependent utility functions in detail. Using the revealed preference theory we show that (general, i.e. not necessary -) wealth dependent utility functions can be characterized by Wald's axiom.     

A Note on the Computation of the Mean Random Consistency Index of the Analytic Hierarchy Process (Ahp)

In this paper, we use Saaty's Eigenvector Method and the Power Method as well as =1, 2, , 9, 1/2, 1/3, , 1/9} and -={1,2, ,9,1, 1/2, ,1/9} as the sets from which the pairwise comparison judgments are assigned at random to examine the variation in the values determined for the mean random consistency index. By extensive simulation analysis, we found that both methods produce the same values for the mean random consistency random index. Also, we found that the reason for producing two different sets of values is the use of vs. - and not the selection of the Power Method vs. Saaty's Eigenvector Method.     

Mean variance preferences and the heat equation

Chipman (1979) proves that for an expected utility maximizer choosing from a domain of normal distributions with mean and variance ² the induced preference functionV(, ) satisfies a differential equation known as the heat equation. The purpose of this note is to provide a generalization and simple proof of this result which does not depend on the normality assumption.     

Substitution of indifferent options at choice nodes and admissibility: a reply to Rabinowicz

Tiebreak rules are necessary for revealing indifference in non- sequential decisions. I focus on a preference relation that satisfies Ordering and fails Independence in the following way. Lotteries a and b are indifferent but the compound lottery 0.5f, 0.5b is strictly preferred to the compound lottery 0.5f, 0.5a. Using tiebreak rules the following is shown here: In sequential decisions when backward induction is applied, a preference like the one just described must alter the preference relation between a and b at certain choice nodes, i.e., indifference between a and b is not stable. Using this result, I answer a question posed by Rabinowicz (1997) concerning admissibility in sequential decisions when indifferent options are substituted at choice nodes.     

Rational preference: Decision theory as a theory of practical rationality

In general, the technical apparatus of decision theory is well developed. It has loads of theorems, and they can be proved from axioms. Many of the theorems are interesting, and useful both from a philosophical and a practical perspective. But decision theory does not have a well agreed upon interpretation. Its technical terms, in particular, utility and preference do not have a single clear and uncontroversial meaning.How to interpret these terms depends, of course, on what purposes in pursuit of which one wants to put decision theory to use. One might want to use it as a model of economic decision-making, in order to predict the behavior of corporations or of the stock market. In that case, it might be useful to interpret the technical term utility as meaning money profit. Decision theory would then be an empirical theory. I want to look into the question of what utility could mean, if we want decision theory to function as a theory of practical rationality. I want to know whether it makes good sense to think of practical rationality as fully or even partly accounted for by decision theory. I shall lay my cards on the table: I hope it does make good sense to think of it that way. For, I think, if Humeans are right about practical rationality, then decision theory must play a very large part in their account. And I think Humeanism has very strong attractions.     

An axiomatic basis of accounting: A structuralist reconstruction

Set-theoretic axiomatizations are given for a model of accounting with double classification, and a general core-model for accounting. The empirical status, and representational role of systems of accounts, as well as the problem of how to assign correct values to the goods accounted, are analyzed in precise terms. A net of special laws based on the core-model is described.     

Utility theory and the Bayesian paradigm

In this paper, a problem for utility theory - that it would have an agent who was compelled to play Russian Roulette with one revolver or another, to pay as much to have a six-shooter with four bullets relieved of one bullet before playing with it, as he would be willing to pay to have a six-shooter with two bullets emptied - is reviewed. A less demanding Bayesian theory is described, that would have an agent maximize expected values of possible total consequence of his actions. And utility theory is located within that theory as valid for agents who satisfy certain formal conditions, that is, for agents who are, in terms of that more general theory, indifferent to certain dimensions of risk. Raiffa- and Savage-style arguments for its more general validity are then resisted. Addenda are concerned with implications for game theory, and relations between utilities and values.     

Fairness,Public Good,and Emotional Aspects of Punishment Behavior

We report an experiment on two treatments of an ultimatum minigame. In one treatment, responders reactions are hidden to proposers. We observe high rejection rates reflecting responders intrinsic resistance to unfairness. In the second treatment, proposers are informed, allowing for dynamic effects over eight rounds of play. The higher rejection rates can be attributed to responders provision of a public good: Punishment creates a group reputation for being tough and effectively educate proposers. Since rejection rates with informed proposers drop to the level of the treatment with non-informed proposers, the hypothesis of responders enjoyment of overt punishment is not supported.     

Simulation methodology

Operational researchers, management scientists, and industrial engineers have been asked by Russell Ackoff to become systems scientists, yet he stated that Systems Science is not a science. (TIMS Interfaces, 2 (4), 41). A. C. Fabergé (Science 184, 1330) notes that the original intent of operational researchers was that they be scientists, trained to observe. Hugh J. Miser (Operations Research 22, 903), views operations research as a science, noting that its progress indeed is of a cyclic nature.The present paper delineates explicitly the attributes of simulation methodology. Simulation is shown to be both an art and a science; its methodology, properly used, is founded both on confirmed (validated) observation and scrutinised (verified) art work.The paper delineates the existing procedures by which computer-directed models can be cyclically scrutinised and confirmed and therefore deemed credible. The complexities of the phenomena observed by social scientists are amenable to human understanding by properly applied simulation; the methodology of the scientist of systems (the systemic scientist).

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Résumé Russell Ackoff propose à ceux qui s'occupent de recherches opérationnelle, industrielle, et de gestion, d'agir en systems scientists, et pourtant il affirme que systems science n'est pas une science (TIMS Interfaces 2 (4), 41). A. C. Fabergé (Science 184, 1330) remarque, qu'à l'origine, le but de ceux qui s'occupaient de recherche opérationnelle était d'agir en hommes de science instruits à observer. Hugh J. Miser (Operational Research 22, 903) considère la recherche opérationnelle comme science, notant que ses progrès sont en effet de nature cyclique.La présente étude délimite explicitement les attributs de la méthode de la simulation. Il est démontré que la simulation est à la fois un art et une science; sa méthode, lorsqu'utilisée correctement, repose sur l'observation validée et le modèle vérifié.L'étude délimite les moyens actuels dont nous disposons pour vérifier et valider cycliquement les modèles bâtis à l'aide d'ordinateurs, établissant ainsi leur crédibilité. La nature complexe des phénomènes étudiés par les sciences sociales peut être comprise à l'aide de la simulation: la méthode dont se servent les hommes de science qui étudient les systèmes (les scientistes systémiques).