Preference reversal in quantum decision theory

We consider the psychological effect of preference reversal and show that it finds a natural explanation in the frame of quantum decision theory. When people choose between lotteries with non-negative payoffs, they prefer a more certain lottery because of uncertainty aversion. But when people evaluate lottery prices, e.g. for selling to others the right to play them, they do this more rationally, being less subject to behavioral biases. This difference can be explained by the presence of the attraction factors entering the expression of quantum probabilities. Only the existence of attraction factors can explain why, considering two lotteries with close utility factors, a decision maker prefers one of them when choosing, but evaluates higher the other one when pricing. We derive a general quantitative criterion for the preference reversal to occur that relates the utilities of the two lotteries to the attraction factors under choosing versus pricing and test successfully its application on experiments by Tversky et al. We also show that the planning paradox can be treated as a kind of preference reversal.Comment: Latex file, 15 page

Lottery Qualities

The aim of this paper is to propose a model of decision-making for lotteries. Lottery qualities are the key concepts of the theory. Qualities allow the derivation of optimal decision-making processes and are taken explicitly into account for lottery evaluation. Our contribution explains the major violations of the expected utility theory for decisions on two-point lotteries and shows the necessity of giving explicit consideration to lottery qualities. Judged certainty equivalent and choice certainty equivalent concepts are discussed in detail along with the comparison of lotteries. Examples are provided by using different test results in the literature.Lottery choice, common ratio, preference reversal, pricing, lottery test, cognitive process, certainty equivalent

Lotteries and Lindahl Prices in Public Good Provision

Lotteries are traditional instruments for fundraising in general. Morgan has shown that they can also be very effective in the provision of a public good. However, a fair lottery can only enhance provision but never result in the efficient amount. Franke and Leininger show how—by borrowing from optimal contest theory—biased lotteries can provide the efficient amount of the public good. This paper aligns this result with standard public good theory, in particular the classic notion of Lindahl pricing. It shows that biased lotteries can—implicitly—implement Lindahl pricing of the public good in noncooperative Nash equilibrium.</p

Perception of the fairness of pricing

Regulation by means of price in order to remove excess demand is generally perceived as being unfair. This paper empirically tests different principles of regulation including lotteries, rationing, a moral rule and compensation.We start from the postulate that the perception of the fairness of a urban road pricing policy is important for a successful implementation. This perception is analysed through the results of an attitudinal survey held in Lyons area in 2003 (N 400). We confirm that peak-period pricing as a means of limiting demand is overwhelmingly rejected. Administrative allocation and lotteries are also rejected. The reference transaction can also lead to rejection of waiting line. Price compensation is overwhelmingly considered to be fair and the right to this is demanded both from public or private sector monopoly: it is possible therefore to reinstate pricing in the form of compensation.Those surveyed express rather definite preferences for some principles of regulation (moral rule, compensation) to the detriment of pricing or even the administrative or traditional regulation (queuing). Ways of unfreezing the situation are identified, who could be exploited in order to form coalitions likely to support this kind of policy. Finally, certain dimensions of the equity are revealed through the analysis of the survey.Principles of justice ; fairness ; transport pricing ; perception ; Lyon

On the Necessity of Using Lottery Qualities

The aim of this paper is to propose a model of decision-making for lotteries. The key element of the theory is the use of lottery qualities. Qualities allow the derivation of optimal decision-making processes and are taken explicitly into account for lottery evaluation. Our contribution explains the major violations of the expected utility theory for decisions on two-point lotteries and shows the necessity of giving explicit consideration to the lottery qualities.Lottery choice, common ratio, preference reversal, pricing, lottery test, cognitive process, certainty equivalent, lottery quality

Lottery pricing equilibria

We extend the notion of Combinatorial Walrasian Equilibrium, as defined by Feldman et al. [2013], to settings with budgets. When agents have budgets, the maximum social welfare as traditionally defined is not a suitable benchmark since it is overly optimistic. This motivated the liquid welfare of [Dobzinski and Paes Leme 2014] as an alternative. Observing that no combinatorial Walrasian equilibrium guarantees a non-zero fraction of the maximum liquid welfare in the absence of randomization, we instead work with randomized allocations and extend the notions of liquid welfare and Combinatorial Walrasian Equilibrium accordingly. Our generalization of the Combinatorial Walrasian Equilibrium prices lotteries over bundles of items rather than bundles, and we term it a lottery pricing equilibrium. Our results are two-fold. First, we exhibit an efficient algorithm which turns a randomized allocation with liquid expected welfare W into a lottery pricing equilibrium with liquid expected welfare 3-√5/2 W (≈ 0.3819-W). Next, given access to a demand oracle and an α-approximate oblivious rounding algorithm for the configuration linear program for the welfare maximization problem, we show how to efficiently compute a randomized allocation which is (a) supported on polynomially-many deterministic allocations and (b) obtains [nearly] an α fraction of the optimal liquid expected welfare. In the case of subadditive valuations, combining both results yields an efficient algorithm which computes a lottery pricing equilibrium obtaining a constant fraction of the optimal liquid expected welfare. © Copyright 2016 ACM

An Experimental Investigation of Alternatives to Expected Utility Using Pricing Data

Experimental research on decision making under risk has until now always employed choice data in order to evaluate the empirical performance of expected utility and the alternative non-expected utility theories. The present paper performs a similar analysis which relies on pricing data instead of choice data. Since pricing data lead in many cases to a different ordering of lotteries than choices (e.g. the preference reversal phenomenon) our analysis may have fundamental different results than preceding investigations. We elicit three different types of pricing data: willingness-to-pay, willingness-to-accept and certainty equivalents under the Becker-DeGroot-Marschak (BDM) incentive mechanism. One of our main result shows that the comparative performance of the single theories differs significantly under these three types of pricing data.experiments

Explaining the Favorite-Longshot Bias: Is it Risk-Love or Misperceptions?

The favorite–long shot bias describes the long-standing empirical regularity that betting odds provide biased estimates of the probability of a horse winning: long shots are overbet whereas favorites are underbet. Neoclassical explanations of this phenomenon focus on rational gamblers who overbet long shots because of risk-love. The competing behavioral explanations emphasize the role of misperceptions of probabilities. We provide novel empirical tests that can discriminate between these competing theories by assessing whether the models that explain gamblers’ choices in one part of their choice set (betting to win) can also rationalize decisions over a wider choice set, including compound bets in the exacta, quinella, or trifecta pools. Using a new, large-scale data set ideally suited to implement these tests, we find evidence in favor of the view that misperceptions of probability drive the favorite–long shot bias, as suggested by prospect theory