A note on identification in discrete choice models with partial observability

This note establishes a new identification result for additive random utility discrete choice models. A decision-maker associates a random utility \(U_{j}+m_{j}\) to each alternative in a finite set \(j\in \left\{ 1,\ldots ,J\right\} \), where \(\mathbf {U}=\left\{ U_{1},\ldots ,U_{J}\right\} \) is unobserved by the researcher and random with an unknown joint distribution, while the perturbation \(\mathbf {m}=\left( m_{1},\ldots ,m_{J}\right) \) is observed. The decision-maker chooses the alternative that yields the maximum random utility, which leads to a choice probability system \(\mathbf { m\rightarrow }\left( \Pr \left( 1|\mathbf {m}\right) ,\ldots ,\Pr \left( J| \mathbf {m}\right) \right) \). Previous research has shown that the choice probability system is identified from the observation of the relationship \( \mathbf {m}\rightarrow \Pr \left( 1|\mathbf {m}\right) \). We show that the complete choice probability system is identified from observation of a relationship \(\mathbf {m}\rightarrow \sum _{j=1}^{s}\Pr \left( j|\mathbf {m} \right) \), for any \(s<J\). That is, it is sufficient to observe the aggregate probability of a group of alternatives as it depends on \(\mathbf {m}\). This is relevant for applications where choices are observed aggregated into groups while prices and attributes vary at the level of individual alternatives.     

Characterization of the existence of semicontinuous weak utilities for binary relations

We characterize the existence of semicontinuous weak utilities in a general framework, where the axioms of transitivity and acyclicity are relaxed to that of consistency in the sense of Suzumura (Economica 43:381?C390, 1976). This kind of representations allow us to transfer the problem of the existence of the ${{\mathcal{G}}{\mathcal{O}}{\mathcal{C}}{\mathcal{H}}{\mathcal{A}}}$ set of a binary relation to the easier problem of getting maxima of a real function. Finally, we show that the maxima of these representations correspond to the different levels of satiation that each of individual has (an individual reaches his or her level of satiation when an increase of consuming an alternative product/service brings no increase in utility).     

On recursive solutions to simple allocation problems

We propose and axiomatically analyze a class of rational solutions to simple allocation problems where a policy-maker allocates an endowment $E$ among $n$ agents described by a characteristic vector c. We propose a class of recursive rules which mimic a decision process where the policy-maker initially starts with a reference allocation of $E$ in mind and then uses the data of the problem to recursively adjust his previous allocation decisions. We show that recursive rules uniquely satisfy rationality, c-continuity, and other-c monotonicity. We also show that a well-known member of this class, the Equal Gains rule, uniquely satisfies rationality, c-continuity, and equal treatment of equals.     

Recall searching with and without recall

We revisit the sequential search problem by Hey (J Econ Behav Organ 8:137–144, 1987). In a 2 \(\times \) 2 factorial design, varying fixed and random cost treatments with and without recall, we address open research questions that were originally stated by Hey (1987). Our results provide clear evidence for Hey’s (1987) conjecture that recall negatively affects performance in sequential search. With experience, however, search behavior with and without recall converges toward the optimal reservation rule. We further find that the utilization of optimal reservation rules is independent from the stochastic nature of the search cost.     

A geometric approach to revealed preference via Hamiltonian cycles

It is shown that a fundamental question of revealed preference theory, namely whether the weak axiom of revealed preference (WARP) implies the strong axiom of revealed preference (SARP), can be reduced to a Hamiltonian cycle problem: A set of bundles allows a preference cycle of irreducible length if and only if the convex monotonic hull of these bundles admits a Hamiltonian cycle. This leads to a new proof to show that preference cycles can be of arbitrary length for more than two but not for two commodities. For this, it is shown that a set of bundles satisfying the given condition exists if and only if the dimension of the commodity space is at least three. Preference cycles can be constructed by embedding a cyclic $(L-1)$ -polytope into a facet of a convex monotonic hull in $L$ -space, because cyclic polytopes always admit Hamiltonian cycles. An immediate corollary is that WARP only implies SARP for two commodities. The proof is intuitively appealing as this gives a geometric interpretation of preference cycles.     

Implementing equal division with an ultimatum threat

We modify the payment rule of the standard divide the dollar (DD) game by introducing a second stage and thereby resolve the multiplicity problem and implement equal division of the dollar in equilibrium. In the standard DD game, if the sum of players’ demands is less than or equal to a dollar, each player receives what he demanded; if the sum of demands is greater than a dollar, all players receive zero. We modify this second part, which involves a harsh punishment. In the modified game \((D\!D^{\prime })\) , if the demands are incompatible, then players have one more chance. In particular, they play an ultimatum game to avoid the excess. In the two-player version of this game, there is a unique subgame perfect Nash equilibrium in which players demand (and receive) an equal share of the dollar. We also provide an \(n\) -player extension of our mechanism. Finally, the mechanism we propose eliminates not only all pure strategy equilibria involving unequal divisions of the dollar, but also all equilibria where players mix over different demands in the first stage.     

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).     

Games with a local permission structure: separation of authority and value generation

It is known that peer group games are a special class of games with a permission structure. However, peer group games are also a special class of (weighted) digraph games. To be specific, they are digraph games in which the digraph is the transitive closure of a rooted tree. In this paper we first argue that some known results on solutions for peer group games hold more general for digraph games. Second, we generalize both digraph games as well as games with a permission structure into a model called games with a local permission structure, where every player needs permission from its predecessors only to generate worth, but does not need its predecessors to give permission to its own successors. We introduce and axiomatize a Shapley value-type solution for these games, generalizing the conjunctive permission value for games with a permission structure and the $\beta $ -measure for weighted digraphs.     

Hold or roll: reaching the goal in jeopardy race games

We consider a class of dynamic tournaments in which two contestants are faced with a choice between two courses of action. The first is a riskless option (“hold”) of maintaining the resources the contestant already has accumulated in her turn and ceding the initiative to her rival. The second is the bolder option (“roll”) of taking the initiative of accumulating additional resources, and thereby moving ahead of her rival, while at the same time sustaining a risk of temporary setback. We study this tournament in the context of a jeopardy race game (JRG), extend the JRG to $N > 2$ contestants, and construct its equilibrium solution. Compared to the equilibrium solution, the results of three experiments reveal a dysfunctional bias in favor of the riskless option. This bias is substantially mitigated when the contestants are required to commit in advance how long to pursue the risky course of action.     

Prudence and extensionality in theories of preference and value

Luce's axiom governing probabilities of choice is formulated as a principle governing metalinguistic probabilities. IfX, Y, W are sets of options, and δ(X), δ(Y), δ(W) are sentences asserting that choice is made from these sets, then the axiom is $$\begin{gathered} If \pi [\delta (X)] \ne 0 and \pi [\delta (X \cap Y)] \ne 0, then \hfill \\ \pi _{\delta (X)} [\delta (Y \cap W)] = \pi _{\delta (X \cap Y)} [\delta (W)]\pi _{\delta (X)} [\delta (Y)] \hfill \\ \end{gathered} $$ where π is a probability on sentences. The axiom is then entailed by extensionality of the probability π in company with a simple condition on probabilities of truth-functions. Conditions are also given under which the probability π is uniquely represented by a probability on the sets of options. What look to be logical constraints on the metalanguage entail a normative or prudential constraint. Debreu's well-known counterinstance to the axiom as a principle governing probability of choice is examined and a novel and consistent interpretation of the axiom is proposed.     

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.     

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.     

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 \(\delta _A+\delta _B < 1\).     

Metrizing social preference

In his Introduction to Value Theory N. Rescher suggests a procedure by which individual valuations can be combined to yield meaningful and accurate social valuation measures. A social valuation is the effective average m ^* of individual valuations, such that: $$m^ * = m - \tfrac{1}{2}\sigma $$ , where m is the mean of individual valuations and σ the standard deviation of individual valuations from m. Rescher's employment of this concept of effective average has the following unacceptable features: (1) the effective average is undefined for the situation by which Rescher chooses to introduce the concept; (2) negative effective averages, which are calculable for many situations, are given no interpretation by Rescher; (3) some effective averages are lower than each individual valuation which figures in their computation, and as a consequence use of the concept of effective average to pinpoint social valuations favors conformity of individual valuations to an unjustifiable extent. Rescher doubts whether a conception of social welfare (or value) can be distilled from individual preferences (or valuations). His doubts are justified, for such a move would require a prior weighting of individual preferences in such a manner that social welfare measures could be arrived at solely by attending to the preferences of qualified individuals, making computation of a welfare measure from the set of individuals' preferences gratuitous.     

The influence of fear in decisions: Experimental evidence

This article studies decisions made under conditions of fear, when a catastrophic outcome is introduced in a lottery. It reports on experimental results and seeks to compare the predictions of the expected utility (EU) framework with those of a new axiomatic treatment of choice under uncertainty that takes explicit account of emotions such as fear (Chichilnisky 1996, 2000, 2002, 2009). Results provide evidence that fear influences the cognitive process of decision-making by leading some subjects to focus excessively on catastrophic events. Such heterogeneity in subjects’ behavior, while not consistent with EU-based functions, is fully consistent with the new type of utility function implied by the new axioms.     

Fair student placement

We revisit the concept of fairness in the Student Placement framework. We declare an allocation as \(\upalpha \)-equitable if no agent can propose an alternative allocation that nobody else might argue to be inequitable. It turns out that \(\upalpha \)-equity is compatible with efficiency. Our analysis fills a gap in the literature by giving normative support to the allocations improving, in terms of efficiency, the Student Optimal Stable allocation.     

Risk preferences of Australian academics: where retirement funds are invested tells the story

Risk preferences of Australian academics are elicited by analyzing the aggregate distribution of their retirement funds (superannuation) across available investment options. Not more than 10 % of retirement funds are invested as if their owners maximize expected utility under the assumption of constant relative risk aversion with an empirically plausible level of risk aversion. An implausibly high level of risk aversion is required to rationalize any investment into bonds when stocks are available. Not more than 36.54 % of all investments can be rationalized by a model of loss averse preferences. Moreover, the levels of loss aversion typically reported in the experimental studies imply overinvestment in bonds, which is not observed in the data. Up to 67.18 % of all investments can be rationalized by rank-dependent utility or Yaari’s (Econometrica 55:95–115 1987) dual model with empirically plausible parameters. A median Australian academic behaves as if maximizing rank-dependent utility with parameter \(\gamma \in [0.76, 0.79]\) in a Tversky and Kahneman (J Risk Uncertain 5:297–323 1992) probability weighting function.     

Randomized dictatorship and the Kalai–Smorodinsky bargaining solution

“Randomized dictatorship,” one of the simplest ways to solve bargaining situations, works as follows: a fair coin toss determines the “dictator”—the player to be given his first-best payoff. The two major bargaining solutions, that of Nash (Econometrica 18:155–162, 1950) and that of Kalai and Smorodinsky (Econometrica, 43:513–518, 1975), Pareto-dominate this process (in the ex ante sense). However, whereas the existing literature offers axiomatizations of the Nash solution in which this ex ante domination plays a central role (Moulin, Le choix social utilitariste, Ecole Polytechnique Discussion Paper, 1983 ; de Clippel, Social Choice and Welfare, 29:201–210, 2007), it does not provide an analogous result for Kalai–Smorodinsky. This paper fills in this gap: a characterization of the latter is obtained by combining the aforementioned domination with three additional axioms: Pareto optimality, individual monotonicity, and a weakened version of the Perles–Maschler (International Journal of Game Theory, 10:163–193, 1981) super additivity axiom.     

Grief and Trauma Group Therapy for Children After Hurricane Katrina

Theoretical and evidence-based group therapy models that address the interplay of grief and trauma are needed for children postdisaster. This article describes a theoretically informed 10-week grief and trauma group model that was evaluated with children in schools after Hurricane Katrina. The foundation of the grief and trauma intervention includes utilizing developmentally specific methods, an ecological perspective, and culturally relevant approaches. The theoretical ordering of themes addressed occurs within three overlapping phases: (1) resilience and safety, (2) restorative retelling, (3) and reconnecting (Herman, 1997 Herman, J. L. 1997. Trauma and recovery, New York: Basic Books.  [Google Scholar]; Rynearson, 2001 Rynearson, R. 2001. Retelling violent death, Philadelphia: Brunner-Routledge.  [Google Scholar]). Techniques from cognitive behavioral therapy and narrative therapy are combined to address loss and trauma.     

Fostering Integrity in Postgraduate Research: An Evidence-Based Policy and Support Framework

Postgraduate research students have a unique position in the debate on integrity in research as students and novice researchers. To assess how far policies for integrity in postgraduate research meet the needs of students as “research trainees,” we reviewed online policies for integrity in postgraduate research at nine particular Australian universities against the Australian Code for Responsible Conduct of Research (the Code) and the five core elements of exemplary academic integrity policy identified by Bretag et al. (2011 Bretag, T., Mahmud, S., Wallace, M., Walker, R., Green, M., East, J., James, C., McGowan, U. and Partridge, L. 2011. Core elements of exemplary academic integrity policy in Australian higher education. International Journal for Educational Integrity, 7: 3–12.  [Google Scholar]), i.e., access, approach, responsibility, detail, and support. We found inconsistency with the Code in the definition of research misconduct and a lack of adequate detail and support. Based on our analysis, previous research, and the literature, we propose a framework for policy and support for postgraduate research that encompasses a consistent and educative approach to integrity maintained across the university at all levels of scholarship and for all stakeholders.