A multiattribute decision time theory

In this study, we analyze choice in the presence of some conflict that affects the decision time (response time), a subject that has been documented in the literature. We axiomatize a multiattribute decision time (MDT) representation, which is a dynamic extension of the classic multiattribute expected utility theory that allows potentially incomplete preferences. Under this framework, one alternative is preferred to another in a certain period if and only if the weighted sum of the attribute-dependent expected utility induced by the former alternative is larger than that induced by the latter for all attribute weights in a closed and convex set. MDT uniquely determines the decision time as the earliest period at which the ranking between alternatives becomes decisive. The comparative statics result indicates that the decision time provides useful information to locate indifference curves in a specific setting. MDT also explains various empirical findings in economics and other relevant fields.     

What can multiple price lists really tell us about risk preferences?

Multiple price lists have emerged as a simple and popular method for eliciting risk preferences. Despite their popularity, a key downside of multiple price lists has not been widely recognized — namely that the approach is unlikely to generate sufficient information to accurately identify different dimensions of risk preferences. The most popular theories of decision making under risk posit that preferences for risk are driven by a combination of two factors: the curvature of the utility function and the extent to which probabilities are weighted non-linearly. In this paper, we show that the widely used multiple price list introduced by Holt and Laury (The American Economic Review 92(5) 1644–1655 2002) is likely more accurate at eliciting the shape of the probability weighting function, and we construct a different multiple price list that is likely more accurate at eliciting the shape of the utility function. We show that by combining information from different multiple price lists, greater predictive performance can be achieved.     

Subgame perfect equilibrium in a bargaining model with deterministic procedures

Two players, A and B, bargain to divide a perfectly divisible pie. In a bargaining model with constant discount factors, \(\delta _A\) and \(\delta _B\), we extend Rubinstein (Econometrica 50:97–110, 1982)’s alternating offers procedure to more general deterministic procedures, so that any player in any period can be the proposer. We show that each bargaining game with a deterministic procedure has a unique subgame perfect equilibrium (SPE) payoff outcome, which is efficient. Conversely, each efficient division of the pie can be supported as an SPE outcome by some procedure if \(\delta _A+\delta _B\ge 1\), while almost no division can ever be supported in SPE if \(\delta _A+\delta _B < 1\).     

Conditional expected utility

Let \({\mathcal {E}}\) be a class of events. Conditionally Expected Utility decision makers are decision makers whose conditional preferences \(\succsim _{E}\), \(E\in {\mathcal {E}}\), satisfy the axioms of Subjective Expected Utility (SEU) theory. We extend the notion of unconditional preference that is conditionally EU to unconditional preferences that are not necessarily SEU. We study a subclass of these preferences, namely those that satisfy dynamic consistency. We give a representation theorem, and show that these preferences are Invariant Bi-separable in the sense of Ghirardato et al. (Journal of Economic Theory 118:133–173, 2004). We also show that these preferences have only a trivial overlap with the class of Choquet Expected Utility preferences, but there are plenty of preferences of the \(\alpha \)-Maxmin Expected Utility type that satisfy our assumptions. We identify several concrete settings where our results could be applied. Finally, we consider the special case where the unconditional preference is itself SEU, and compare our results with those of Fishburn (Econometrica 41:1–25, 1973).     

Resolute majority rules

We investigate resolute voting rules that always rank two alternatives strictly and avoid social indecision. Resolute majority rules differ from the standard majority rule in that whenever both alternatives win the same number of votes, a tie-breaking function is used to determine the outcome. We provide axiomatic characterizations of resolute majority rules or resolute majority rules with a quorum. Resoluteness axiom is used in all these results. The other axioms are weaker than those considered in the characterization of the majority rule by May (1952 Econometrica, 20:680–684). In particular, instead of May’s positive responsiveness, we consider a much weaker monotonicity axiom.     

An additive representation on the product of complete,continuous extensive structures

This article develops an axiom system to justify an additive representation for a preference relation \({\succsim}\) on the product \({\prod_{i=1}^{n}A_{i}}\) of extensive structures. The axiom system is basically similar to the n-component (n ≥ 3) additive conjoint structure, but the independence axiom is weakened in the system. That is, the axiom exclusively requires the independence of the order for each of single factors from fixed levels of the other factors. The introduction of a concatenation operation on each factor A _i makes it possible to yield a special type of restricted solvability, i.e., additive solvability and the usual cancellation on \({\prod_{i=1}^{n}A_{i}}\). In addition, the assumption of continuity and completeness for A _i implies a stronger type of solvability on A _i . The additive solvability, cancellation, and stronger solvability axioms allow the weakened independence to be effective enough in constructing the additive representation.     

Which Scoring Rule Maximizes Condorcet Efficiency Under Iac?

Consider an election in which each of the n voters casts a vote consisting of a strict preference ranking of the three candidates A, B, and C. In the limit as n→∞, which scoring rule maximizes, under the assumption of Impartial Anonymous Culture (uniform probability distribution over profiles), the probability that the Condorcet candidate wins the election, given that a Condorcet candidate exists? We produce an analytic solution, which is not the Borda Count. Our result agrees with recent numerical results from two independent studies, and contradicts a published result of Van Newenhizen (Economic Theory 2, 69–83. (1992)).     

Experimental evidence on valuation with multiple priors

Popular models for decision making under ambiguity assume that people use not one but multiple priors. This paper is a first attempt to experimentally elicit the min and the max of multiple priors directly. In an ambiguous scenario we measure a participant’s single prior, her min and max of multiple priors, and the valuation of an ambiguous asset with the same underlying states as the ambiguous scenario. We use the min and the max of multiple priors to directly test two popular multiple priors models: the maxmin model and the α maxmin model. We find more support for the α maxmin model: although people put about twice the weight on the minimum of multiple priors, they also consider the maximum. Furthermore, we indirectly elicit confidence weights over the whole set of multiple priors and test two additional models: variational preferences and the smooth model of ambiguity. Two particular versions of the variational preferences model explain less than the α maxmin but more than the maxmin model. Overall, the smooth model of ambiguity performs best among all models tested.     

Violations of betweenness and choice shifts in groups

In decision theory, the betweenness axiom postulates that a decision maker who chooses an alternative A over another alternative B must also choose any probability mixture of A and B over B itself and can never choose a probability mixture of A and B over A itself. The betweenness axiom is a weaker version of the independence axiom of expected utility theory. Numerous empirical studies documented systematic violations of the betweenness axiom in revealed individual choice under uncertainty. This paper shows that these systematic violations can be linked to another behavioral regularity—choice shifts in a group decision making. Choice shifts are observed if an individual faces the same decision problem but makes a different choice when deciding alone and in a group.     

A note on the Condorcet jury theorem for couples

A jury and two valid options are given. Each agent of the jury picks exactly one of these options. The option with the most votes will be chosen by the jury. In the N-couple model of Althöfer and Thiele (Theory and Decision 81:1–15, 2016), the jury consisted of 2N agents. These agents form N independent couples, with dependencies within the couples. The authors assumed that the agents who form a couple have the same competence level. In this note, we relax this assumption by allowing different competence levels within the couples. We show that the theoretical results of Althöfer and Thiele remain valid under this relaxation.     

Comparing uncertainty aversion towards different sources

In this article, we discuss some aspects of Eliaz and Ok ’s (Games Econ Behav 56:61–86, 2006) choice theoretical foundations of incomplete preferences. Our aim is to clarify some aspects of their regularity condition for preorders, showing that, as far as rationalization of a choice correspondence alone is concerned, no further restriction is imposed by requiring the preorder to be regular. However, if one is also interested in capturing other observable aspects of the individual’s choice procedure, such as Eliaz and Ok’s notion of c-incomparability or the notion of behavioral indifference introduced in this paper, then the only option is to use a regular preorder. We also argue that their weak axiom of revealed non-inferiority (WARNI) is too strong a property if our aim is to characterize the rationalizability of a choice correspondence by a (possibly incomplete) preorder. Finally, as we have mentioned above, we introduce the notion of behavioral indifference and argue, not only that Eliaz and Ok’s notion of c-incomparability (observable incomparability) can be derived from it, but also that it has a wider range of applicability than their notion of observable incomparability.     

Elicitation of preferences under ambiguity

This paper is about behaviour under ambiguity—that is, a situation in which probabilities either do not exist or are not known. Our objective is to find the most empirically valid of the increasingly large number of theories attempting to explain such behaviour. We use experimentally-generated data to compare and contrast the theories. The incentivised experimental task we employed was that of allocation: in a series of problems we gave the subjects an amount of money and asked them to allocate the money over three accounts, the payoffs to them being contingent on a ‘state of the world’ with the occurrence of the states being ambiguous. We reproduced ambiguity in the laboratory using a Bingo Blower. We fitted the most popular and apparently empirically valid preference functionals [Subjective Expected Utility (SEU), MaxMin Expected Utility (MEU) and α-MEU], as well as Mean-Variance (MV) and a heuristic rule, Safety First (SF). We found that SEU fits better than MV and SF and only slightly worse than MEU and α-MEU.     

Loss aversion leading to advantageous selection

Some insurance markets are characterized by “advantageous selection”, that is, ex-post risk and coverage are negatively correlated. We show that expectation-based loss aversion as in K?szegi and Rabin (Quarterly Journal of Economics, 121(4), 1133–1165, 2006; The American Economic Review, 97(4), 1047–1073, 2007) provides a natural explanation for this phenomenon in environments in which risk aversion models do not, e.g., when agents face modest-scale risks and/or in absence of moral hazard. More exposure to risk has two competing effects on an agent’s willingness to pay for insurance: a positive effect, as in standard expected utility models; and a negative one, due to a reference effect. We determine conditions under which an insurance provider optimally sets a high price at which only low risk agents buy.     

Gender differences in ambiguity aversion under different outcome correlation structures

This paper studies the impact of different outcome correlation structures on gender differences in ambiguity aversion. We conducted an investment game with two separate treatments. In the uncorrelated treatment, the outcomes of the investment game were determined individually. In the correlated treatment, the outcomes of the investment game were determined collectively within a reference group. From an evolutionary perspective, men should be more concerned about relative outcomes, because their reproductive success mainly depended on their relative standing within society. Women, by contrast, should be more concerned about absolute outcomes, because their reproductive success was mainly linked to their access to resources for themselves and their children. Therefore, we predict that the type of outcome correlation structure has a larger impact on men than on women. In particular, we hypothesize that men are less ambiguity averse under an uncorrelated outcome structure. In this situation, the ambiguous alternative should be more attractive, because it potentially reduces inequality and thereby improves men’s relative standing within society. Women’s choices should not be significantly affected by different outcome correlation structures. Both hypotheses are supported by evidence from laboratory experiments.     

Implementing egalitarianism in a class of Nash demand games

We add a stage to Nash’s demand game by allowing the greedier player to revise his demand if the demands are not jointly feasible. If he decides to stick to his initial demand, then the game ends and no one receives anything. If he decides to revise it down to \(1-x\), where x is his initial demand, the revised demand is implemented with certainty. The implementation probability changes linearly between these two extreme cases. We derive a condition on the feasible set under which the two-stage game has a unique subgame perfect equilibrium. In this equilibrium, there is first-stage agreement on the egalitarian demands. We also study two n-player versions of the game. In either version, if the underlying bargaining problem is “divide-the-dollar,” then equal division is sustainable in a subgame perfect equilibrium if and only if the number of players is at most four.     

When and how to satisfice: an experimental investigation

This paper is about satisficing behaviour. Rather tautologically, this is when decision-makers are satisfied with achieving some objective, rather than in obtaining the best outcome. The term was coined by Simon (Q J Econ 69:99–118, 1955), and has stimulated many discussions and theories. Prominent amongst these theories are models of incomplete preferences, models of behaviour under ambiguity, theories of rational inattention, and search theories. Most of these, however, seem to lack an answer to at least one of two key questions: when should the decision-maker (DM) satisfice; and how should the DM satisfice. In a sense, search models answer the latter question (in that the theory tells the DM when to stop searching), but not the former; moreover, usually the question as to whether any search at all is justified is left to a footnote. A recent paper by Manski (Theory Decis. doi: 10.1007/s11238-017-9592-1, 2017) fills the gaps in the literature and answers the questions: when and how to satisfice? He achieves this by setting the decision problem in an ambiguous situation (so that probabilities do not exist, and many preference functionals can therefore not be applied) and by using the Minimax Regret criterion as the preference functional. The results are simple and intuitive. This paper reports on an experimental test of his theory. The results show that some of his propositions (those relating to the ‘how’) appear to be empirically valid while others (those relating to the ‘when’) are less so.     

Piecewise linear rank-dependent utility

Choice under risk is modelled using a piecewise linear version of rank-dependent utility. This model can be considered a continuous version of NEO-expected utility (Chateauneuf et al., J Econ Theory 137:538–567, 2007). In a framework of objective probabilities, a preference foundation is given, without requiring a rich structure on the outcome set. The key axiom is called complementary additivity.     

Prospect theory and the “forgotten” fourfold pattern of risk preferences

Markowitz (Journal of Political Economy 60:151–158, 1952) identified a fourfold pattern of risk preferences in outcome magnitude: When outcomes are large, people are risk averse in gains and risk seeking in losses, but risk preferences reverse when the outcomes are small, with people exhibiting risk seeking in gains and risk aversion in losses. This fourfold pattern was not addressed by either version of prospect theory (Kahneman and Tversky Econometrica 47:363–391, 1979; Tversky and Kahneman Journal of Risk and Uncertainty 5:297–323, 1992). We show how prospect theory can accommodate the pattern by combining an overweighting of low probabilities with a decreasingly elastic value function. We then examine the performance of prospect theory with two decreasingly elastic value functions: Prospect theory performs better, both quantitatively and qualitatively, with a normalized logarithmic value function than with a normalized exponential value function. We discuss several issues, and speculate about why Tversky and Kahneman did not address Markowitz’s fourfold pattern.