Components of a Dialogue

Note from the editors of Literaturnoe obozrenie: As we know, readers in our country, including readers of criticism, are extraordinarily diverse. In your work do you aim at a particular type of reader rather informed in the field of literature, or at one who still has to be presented fundamentals? At the youthful reader, or one with a certain experience of life and spirit? At an individual with particular predilections, enthusiasms, interests; at one who fundamentally shares your convictions or, on the contrary, at a person differing from you, but whom you would like to "convert"? What qualities (not merely as a reader) would you like to "cultivate" in your reader?     

Hopes and Fears: the Conflicting Effects of Risk Ambiguity

The Ellsberg Paradox documented the aversion to ambiguity in the probability of winning a prize. Using an original sample of 266 business owners and managers facing risks from climate change, this paper documents the presence of departures from rationality in both directions. Both ambiguity-seeking behavior and ambiguity-averse behavior are evident. People exhibit fear effects of ambiguity for small probabilities of suffering a loss and hope effects for large probabilities. Estimates of the crossover point from ambiguity aversion (fear) to ambiguity seeking (hope) place this value between 0.3 and 0.7 for the risk per decade lotteries considered, with empirical estimates indicating a crossover mean risk of about 0.5. Attitudes toward the degree of ambiguity also reverse at the crossover point.     

Signed orders in linear and nonlinear utility theory

Self-reflecting signed orders on a set A and its anti-set A ^* were introduced previously as a way to account for negative as well as positive feelings about the inclusion of items in A in potential subsets of choice. The present paper extends the notion of signed orders to lotteries on A A ^*, describes reflection axioms for the lottery context, and shows how these axioms simplify utility representations for preference between lotteries. The simplified representations are then used to guide procedures for extending preferences from A A ^* and its lotteries to preferences between subsets of items.     

Precautionary behavior and willingness to pay for a mortality risk reduction: Searching for the expected relationship

This paper examines within-sample correlation between six different precautionary behaviors and stated willingness to pay for a mortality risk reduction. The paper also shows estimates of the value of a statistical life based on seat belt and bicycle helmet use as well as based on the stated willingness to pay for a risk reduction in traffic mortality. Contrary to the theoretical expectations, no correlation is found between precautionary behavior and stated willingness to pay. One major explanation is that females and the elderly take more precaution, but state a lower WTP for a risk reduction. The estimates of VSL from the different approaches are $11.0 million, $5.0 million and $2.8 million from stated WTP, bicycle helmet use and seat belt use, respectively.

When an Event Makes a Difference

For (S, Σ) a measurable space, let and be convex, weak^* closed sets of probability measures on Σ. We show that if ∪ satisfies the Lyapunov property , then there exists a set A ∈ Σ such that min_μ1∈ μ₁(A) > max_μ2 ∈ (A). We give applications to Maxmin Expected Utility (MEU) and to the core of a lower probability.     

An Answer to B. Firsanov

The editors of Komsomolskaya Pravda have turned over your letter to me, Comrade Firsanov, and asked that I answer you.     

East-West Correspondence

I have read your article in the December issue criticizing non-objective art ["Beauty and Distortion," by V. S. Kemenov; the soviet review, December 1961; translated from Sovetskaya Kultura, Sept. 5, 1961]. Your thoughts interest me because I am both a painter and secondary school instructor in crafts. There are many people in both our cultures who would agree with your premise. I happen to be one who does not and consequently am taking this opportunity to communicate with you.     

Is There a “Pessimistic” Bias in Individual Beliefs? Evidence from a Simple Survey

It is an important issue for economic and finance applications to determine whether individuals exhibit a behavioral bias toward pessimism in their beliefs, in a lottery or more generally in an investment opportunities framework. In this paper, we analyze the answers of a sample of 1,540 individuals to the following question “Imagine that a coin will be flipped 10 times. Each time, if heads, you win $10\texttt{C}\!\!\!\rule[2.3pt]{.4em}{.3pt}\!\!\rule[3.3pt]{.4em}{.3pt}It is an important issue for economic and finance applications to determine whether individuals exhibit a behavioral bias toward pessimism in their beliefs, in a lottery or more generally in an investment opportunities framework. In this paper, we analyze the answers of a sample of 1,540 individuals to the following question “Imagine that a coin will be flipped 10 times. Each time, if heads, you win . How many times do you think that you will win?” The average answer is surprisingly about 3.9 which is below the average 5, and we interpret this as a pessimistic bias. We find that women are more “pessimistic” than men, as are old people relative to young. We also analyze how our notion of pessimism is related to more general notions of pessimism previously introduced in psychology.     

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.     

Valuing a homeland security policy: Countermeasures for the threats from shoulder mounted missiles

This paper reports estimates for the ex ante tradeoffs for three specific homeland security policies that all address a terrorist attack on commercial aircraft with shoulder mounted missiles. Our analysis focuses on the willingness to pay for anti-missile laser jamming countermeasures mounted on commercial aircraft compared with two other policies as well as the prospect of remaining with the status quo. Our findings are based a stated preference conjoint survey conducted in 2006 and administered to a sample from Knowledge Networks’ national internet panel. The estimates range from $100 to $220 annually per household. Von Winterfeldt and O’Sullivan’s (2006) analysis of the same laser jamming plan suggests that the countermeasures would be preferred if economic losses are above $74 billion, the probability of attack is larger than 0.37 in 10 years, and if the cost of the measures is less than about $14 billion. Our results imply that, using the most conservative of our estimates, a program with a cost consistent with their thresholds would yield significant aggregate net benefits.

Reasonable beliefs

The theory of inductive inference developed by I. Levi in Gambling with Truth has two important limitations. In the first place, it makes acceptability of hypotheses question-dependent: any statement of the form It is reasonable to believe a hypothesis h on evidence e has to be expanded so as to include a reference to some specific question which h is supposed to answer, or, alternatively, to a set of possible answers which is associated with that question. Secondly, Levi's account is insensitive to modal distinctions: no difference is made between what is merely reasonable to believe and what is unreasonable not to believe. The aim of this paper is to construct a theory which utilizes Levi's main proposals and, at the same time, avoids the above-mentioned limitations.     

On the intensity of downside risk aversion

The degree of downside risk aversion (or equivalently prudence) is so far usually measured by . We propose here another measure, , which has specific and interesting local and global properties. Some of these properties are to a wide extent similar to those of the classical measure of absolute risk aversion, which is not always the case for . It also appears that the two measures are not mutually exclusive. Instead, they seem to be rather complementary as shown through an economic application dealing with a simple general equilibrium model of savings.

Convex stochastic dominance with finite consequence sets

Stochastic dominance is a notion in expected-utility decision theory which has been developed to facilitate the analysis of risky or uncertain decision alternatives when the full form of the decision maker's von Neumann-Morgenstern utility function on the consequence space X is not completely specified. For example, if f and g are probability functions on X which correspond to two risky alternatives, then f first-degree stochastically dominates g if, for every consequence x in X, the chance of getting a consequence that is preferred to x is as great under f as under g. When this is true, the expected utility of f must be as great as the expected utility of g.Most work in stochastic dominance has been based on increasing utility functions on X with X an interval on the real line. The present paper, following [1], formulates appropriate notions of first-degree and second-degree stochastic dominance when X is an arbitrary finite set. The only structure imposed on X arises from the decision maker's preferences. It is shown how typical analyses with stochastic dominance can be enriched by applying the notion to convex combinations of probability functions. The potential applications of convex stochastic dominance include analyses of simple-majority voting on risky alternatives when voters have similar preference orders on the consequences.     

How Many Balance Functions Does it Take to Determine a Utility Function?

Call b your balance function at wealth W if you are indifferent between W and a 50–50 lottery with outcomes x and b(x). Given one b, u is arbitrary on one side of W but then determined on the other. Given two b‘s, u is arbitrary between the two W′ s but then determined elsewhere. Additional properties of u restrict the b’s but do not ordinarily make u unique. Contradictions can occur. Given three b′ s, an algorithm is developed using minimal domains of definition that determines the relative utility of the W’s. If it is irrational, then the set S generated by applying all combinations of b’s to W′ s is dense and u is determined. If finitely many b’s are rationally related, then S is discrete, a further algorithm determines it, the values of u on S are equally spaced, and u is arbitrary between any two adjacent points of S but then determined elsewhere. Infinitely many balance functions determine u unless they are rationally related in a uniform way.JEL Classification: D81     

Utilities for distributive justice

This paper falls within the field of Distributive Justice and (as the title indicates) addresses itself specifically to the meshing problem. Briefly stated, the meshing problem is the difficulty encountered when one tries to aggregate the two parameters of beneficence and equity in a way that results in determining which of two or more alternative utility distributions is most just. A solution to this problem, in the form of a formal welfare measure, is presented in the paper. This formula incorporates the notions of equity and beneficence (which are defined earlier by the author) and weighs them against each other to compute a numerical value which represents the degree of justice a given distribution possesses. This value can in turn be used comparatively to select which utility scheme, of those being considered, is best.Three fundamental adequacy requirements, which any acceptable welfare measuring method must satisfy, are presented and subsequently demonstrated to be formally deducible as theorems of the author's system. A practical application of the method is then considered as well as a comparison of it with Nicholas Rescher's method (found in his book, Distributive Justice). The conclusion reached is that Rescher's system is unacceptable, since it computes counter-intuitive results. Objections to the author's welfare measure are considered and answered. Finally, a suggestion for expanding the system to cover cases it was not originally designed to handle (i.e. situations where two alternative utility distributions vary with regard to the number of individuals they contain) is made. The conclusion reached at the close of the paper is that an acceptable solution to the meshing problem has been established.I would like to gratefully acknowledge the assistance of Michael Tooley whose positive suggestions and critical comments were invaluable in the writting of this paper.     

Two envelopes

“You have been given either envelopeA orB. B contains either one-half or twice the money inA. Do you want to switch? Now you open your envelope? Are you still happy to stand pat?” Answers depend on whether you think there is an upper bound to the money inA. You should no longer be indifferent if you think there is not an upper bound, but, if you think there is a certain upper boundU, you should want to switch or not depending on whether your envelope holds less thanU. Expected monetary values are extended to acts with infinitely many equally possible monetary values. It is maintained that though strong dominance under infinite partitions does not in the absence of an upper bound for values imply greater expected value, ‘univocal strong dominance’ is even then properly decisive for choice.     

A formulation of the determinism hypothesis

The author tries to formulate what a determinist believes to be true. The formulation is based on some concepts defined in a systems-theoretical manner, mainly on the concept of an experiment over the sets A ^m (a set of m-tuples of input values) and B ⁿ (a set of n-tuples of output values) in the time interval (t ₁, ..., t _k ) (symbolically E[t ₁,..., t _k , A ^m , B ⁿ ]), on the concept of a behavior of the system S ^m,n (=(A ^m , B ⁿ )) on the basis of the experiment E[t ₁, ..., t _k , A ^m , B ⁿ ] and, indeed, on the concept of deterministic behavior .... The resulting formulation of the deterministic hypothesis shows that this hypothesis expresses a belief that we always could find some hidden parameters.     

Domination structures and multicriteria problems in n-person games

Multiple criteria decision problems with one decision maker have been recognized and discussed in the recent literature in optimization theory, operations research and management science. The corresponding concept with n-decision makers, namely multicriteria n-person games, has not yet been extensively explored.In this paper we first demonstrate that existing solution concepts for single criterion n-person games in both normal form and characteristic function form induce domination structures (similar to those defined and studied by Yu [39] for multicriteria single decision maker problems) in various spaces, including the payoff space, the imputation space and the coalition space. This discussion provides an understanding of some underlying assumptions of the solution concepts and provides a basis for generalizing and generating new solution concepts not yet defined. Also we illustrate that domination structures may be regarded as a measure of power held by the players.We then illustrate that a multicriteria problem can naturally arise in decision situations involving (partial) conflict among n-persons. Using our discussion of solution concepts for single criterion games as a basis, various approaches for resolving both normal form and characteristic function form multicriteria n-person games are proposed. For multicriteria games in characteristic function form, we define a multicriteria core and show that there exists a single game point whose core is equal to the multicriteria core. If we reduce a multicriteria game to a single criterion game, domination structures which are more general than classical ones must be considered, otherwise some crucial information in the game may be lost. Finally, we discuss a parametrization process which, for a given multicriteria game, associates a single criterion game to each point in a parametric space. This parametrization provides a basis for the discussion of solution concepts in multicriteria n-person games.     

Sophisticated Voting Under the Sequential Voting by Veto1

The research reported here was the first empirical examination of strategic voting under the Sequential Voting by Veto (SVV) voting procedure, proposed by Mueller (1978). According to this procedure, a sequence of n voters must select s out of s+m alternatives (mn2; s>0). Hence, the number of alternatives exceeds the number of participants by one (n+1). When the ith voter casts her vote, she vetoes the alternative against which a veto has not yet been cast, and the s remaining non-vetoed alternatives are elected. The SVV procedure invokes the minority principle, and it has advantages over all majoritarian procedures; this makes SVV a very desirable means for relatively small groups to make collective decisions. Felsenthal and Machover (1992) pointed out three models of voting under SVV: sincere, optimal, and canonical. The current research investigated, through laboratory experiments, which cognitive model better accounts for the voters' observed behavior and the likelihood of obtaining the optimal outcome as a function of the size of n (when s=1). The findings suggest that while voters under SVV use all three models, their choice is conditioned by group size. In the small groups (n=3), the canonical mode was a better predictor than the sincere model. In the larger groups (n=5), the sincere model was a better predictor than the canonical model. There is also evidence of players' learning during the experiment.     

Strategic ambiguity and decision-making: an experimental study

We conducted a set of experiments to compare the effect of ambiguity in single-person decisions and games. Our results suggest that ambiguity has a bigger impact in games than in ball and urn problems. We find that ambiguity has the opposite effect in games of strategic substitutes and complements. This confirms a theoretical prediction made by Eichberger and Kelsey (J Econ Theory 106:436–466, 2002). In addition, we note that subjects’ ambiguity attitudes appear to be context dependent: ambiguity loving in single-person decisions and ambiguity averse in games. This is consistent with the findings of Kelsey and le Roux (Theory Decis 79:667–688, 2015).