Additive representation of separable preferences over infinite products

Let \(\mathcal{X }\) be a set of outcomes, and let \(\mathcal{I }\) be an infinite indexing set. This paper shows that any separable, permutation-invariant preference order \((\succcurlyeq )\) on \(\mathcal{X }^\mathcal{I }\) admits an additive representation. That is: there exists a linearly ordered abelian group \(\mathcal{R }\) and a ‘utility function’ \(u:\mathcal{X }{{\longrightarrow }}\mathcal{R }\) such that, for any \(\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }\) which differ in only finitely many coordinates, we have \(\mathbf{x}\succcurlyeq \mathbf{y}\) if and only if \(\sum _{i\in \mathcal{I }} \left[u(x_i)-u(y_i)\right]\ge 0\) . Importantly, and unlike almost all previous work on additive representations, this result does not require any Archimedean or continuity condition. If \((\succcurlyeq )\) also satisfies a weak continuity condition, then the paper shows that, for any \(\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }\) , we have \(\mathbf{x}\succcurlyeq \mathbf{y}\) if and only if \({}^*\!\sum _{i\in \mathcal{I }} u(x_i)\ge {}^*\!\sum _{i\in \mathcal{I }}u(y_i)\) . Here, \({}^*\!\sum _{i\in \mathcal{I }} u(x_i)\) represents a nonstandard sum, taking values in a linearly ordered abelian group \({}^*\!\mathcal{R }\) , which is an ultrapower extension of \(\mathcal{R }\) . The paper also discusses several applications of these results, including infinite-horizon intertemporal choice, choice under uncertainty, variable-population social choice and games with infinite strategy spaces.     

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).     

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 \(\delta _A+\delta _B < 1\).     

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.     

Who should cast the casting vote? Using sequential voting to amalgamate information

In this study, we are concerned with how agents can best amalgamate their private information about a binary state of Nature. The agents are heterogeneous in their “ability”, the quality of their private information. The agents cannot directly communicate their private information but instead can only vote between the two states (say “Innocent” or “Guilty” on a criminal jury). We first describe possible methods of sequential majority voting, and then we analyze a particular one: the first \(n-1\) jurors vote simultaneously and, in the case of a tie, the remaining juror has the casting vote. We prove that when \(n=3\) (a common situation for a tribunal of three judges), the probability of a correct verdict is maximized when the agent of median ability has the casting vote.     

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.     

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.     

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.     

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.     

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.     

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.

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.     

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.     

Stepwise Psychosocial Palliative Care: A New Approach to the Treatment of Posttraumatic Stress Disorder at the End of Life

Although evidence-based therapies for Posttraumatic Stress Disorder (PTSD) exist for physically healthy populations, these often do not adequately address PTSD in dying patients. Particularly because these interventions require 8–16 weekly sessions, and the median stay in U.S. hospices is 17.5 days (National Hospice and Palliative Care Organization [NHPCO], 2015 National Hospice &; Palliative Care Organization (NHPCO). (2015). NHPCO Facts and figures: Hospice care in America. Retrieved from http://www.nhpco.org/sites/default/files/public/Statistics_Research/2015_Facts_Figures.pdf. [Google Scholar]), there is a potentially serious timing mismatch. Moreover, these treatments may temporarily increase trauma symptoms (Nishith, Resick, &; Griffin, 2002 Nishith, P., Resick, P. A., &; Griffin, M. G. (2002). Pattern of change in prolonged exposure and cognitive-processing therapy for female rape victims with posttraumatic stress disorder. Journal of Consulting and Clinical Psychology, 70, 880–886. doi:10.1037//0022-006x.70.4.880[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), resulting in some patients dying in greater distress than had they not received care. The Stepwise Psychosocial Palliative Care (SPPC) model presented in this article compensates for these difficulties by embracing a palliative care approach to PTSD. Although it utilizes techniques drawn from existing PTSD interventions, these are re-ordered and utilized in a time-responsive, patient-centered manner that takes into account prognosis, fatigue, and logistical concerns. The SPPC approach is further considered with respect to existing social work palliative care competencies (Gwyther et al., 2005 Gwyther, L. P., Altilio, T., Blacker, S., Christ, G., Csikai, E. L., Hooyman, N., … Howe, J. (2005). Social work competencies in palliative and end-of-life care. Journal of Social Work in End-of-Life &; Palliative Care, 1, 87–120. doi:10.1300/j457v01n01_06[Taylor &; Francis Online] , [Google Scholar]) and a case study is used to demonstrate its application.     

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.     

The Psychotherapeutic Dimensions of Clinical Case Management with a Combat Veteran

This article addresses the overlapping dimensions of clinical case management and psychotherapy. The theoretical framework that is used as the basis of analysis is drawn from the work of D. W. and Clare Winnicott. Kanter has more than adequately demonstrated that these two authors were extremely knowledgeable about clinical case management and psychotherapy. The conclusion of the paper agrees with D. W. Winnicott (1961 Winnicott, D. W. 1961. “Varieties of psychotherapy.”. In Home is where we start from: Essays by a psychoanalyst, Edited by: Winnicott, C, Shepherd, R and Davis, M. 101–111. New York: Norton.  [Google Scholar]) who defined clinical case management as a variety of psychotherapy. The shared psychotherapeutic dimensions of clinical case management are identified as a focus on human development, the importance of the facilitating/holding environment and issues related to transference and countertransference.     

Mixed-Status Families and Immigration Interior Enforcement Policies: Effects on Clinical Practice and the Intraethnic Therapeutic Dyad

ABSTRACT

This article explores the sociopolitical and intersubjective enactments that unfolded when working with a mixed-status immigrant family facing parental deportation. Through the integration of a sociopolitical and intersubjective conceptualization, dynamics pertaining to inclusion, exclusion, domination, and subjugation are examined. The psychological exploration of the clinical treatment is guided by Altman’s (2010 Altman, N. (2010). The analyst in the inner city: Race, class and culture through a psychoanalytic lens (2nd ed.). New York, NY: Routledge. [Google Scholar]) three-person psychology and Stolorow’s (1991 Stolorow, R. D. (1991). The intersubjective context of intrapsychic experience: A decade of psychoanalytic inquiry. Psychoanalytic Inquiry, 11, 171–184. doi:10.1080/07351699109533850[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], 1993 Stolorow, R. D. (1993). Chapter 3 thoughts on the nature and therapeutic action of psychoanalytic interpretation. Progress in Self-Psychology, 9, 31–43. [Google Scholar]) theory of intersubjectivity. The analysis also incorporates dynamics pertaining to the ethnocultural transference and countertranference (Comas-Díaz & Jacobsen, 1991 Comas-Díaz, L., & Jacobsen, F. M. (1991). Ethnocultural transference and countertransference in the therapeutic dyad. American Journal of Orthopsychiatry, 61(3), 392–402. doi:10.1037/h0079267[Crossref], [PubMed], [Web of Science ®] , [Google Scholar], 1995 Comas-Díaz, L., & Jacobsen, F. M. (1995). The therapist of color and the white patient dyad: Contradictions and recognitions. Cultural Diversity and Mental Health, 1(2), 93–106. doi:10.1037/1099-9809.1.2.93[Crossref], [PubMed] , [Google Scholar]) and to associative identification processes (Shonfeld-Ringer, 2000 Shonfeld-Ringer, S. (2000). Close encounters: Exclusion and marginalization as an intersubjective experience. Smith College Studies in Social Work, 71(1), 51–59.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The case illustrates how dynamics of racialization, embedded within an increasingly White Nativist, ideological deportation immigration context, infiltrated the intraethnic, therapeutic relational encounter. The therapist took part in an intragroup, racialized reenactment that could have led to the therapist becoming part of the oppressive structure, but the therapist avoided doing so, explaining her internal process for rectifying the situation.     

An Exploration of Mental Health Literacy Among African American Clergy

ABSTRACT

The purpose of this qualitative study was to explore African American clergy's mental health literacy with older congregants 60 years of age and older. Using a grounded theory approach, we recruited a purposive sample of 9 African American clergy representing diverse ages, denominations, locales, and educational levels. Data was coded and classified according to Kevin's (1976) Kevin, R. C. 1976. Factors influencing the judgment and referral of mental health presenting problems by clergymen and psychologists, Unpublished doctoral dissertation: University of Texas, Austin.  [Google Scholar] typology of pastoral counseling and Jorm et al.'s (1997) Jorm, A. F., Korten, A. E., Jacomb, P. A., Christensen, H., Rodgers, B. and Pollitt, P. 1997. “Mental health literacy”: A survey of the public's ability to recognize mental disorders and their beliefs about the effectiveness of treatment. Medical Journal of Australia, 166: 182–186. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar] conceptual model of mental health literacy. Findings from data analysis revealed study respondents were adherents of Kevin's Religious–Community (R–C) model. Additionally, the following themes emerged: loss of cognitive functioning, psychosocial stressors, religiosity, and appreciation for professional assistance, cultural barriers, and key informants/familiarity with formal mental health providers which partially maps onto Jorm et al.'s conceptual model of mental health literacy.