Stability and Efficiency of Partitions in Matching Problems

We define two versions of stability and efficiency of partitions and analyze their relationships for some matching rules. The stability and efficiency of a partition depends on the matching rule φ. The results are stated under various membership property rights axioms. It is shown that in a world where agents can freely exit from and enter coalitions, whenever the matching rule is individually rational and Pareto optimal, the set of φ-stable and φ-efficient partitions coincide and it is unique: the grand coalition. Then we define a weaker version of stability and efficiency, namely specific to a given preference profile and find some negative results for stable matching rules.     

Preferences and the price of stability in matching markets

This paper studies welfare tradeoffs in two-sided, one-to-one matching markets. We begin by providing theoretical upper bounds on a utilitarian price of stability, and show that these bounds vary with the composition of participants’ ordinal preference lists. We then turn to simulation experiments to describe how changes in basic characteristics of agents’ preferences can increase or decrease the average price of stability as measured by both utilitarian and Rawlsian welfare criteria. Our results indicate that markets featuring moderate degrees of correlation and positive intercorrelation in the preferences of participants exhibit the steepest tradeoffs between stability and utilitarian welfare and between stability and Rawlsian welfare.     

Informational Asymmetries and Observational Learning in Search

As economics modeling moves from super rational decision makers to considering boundedly rational agents, some economic problems deserve a second look. This paper studies the effects of learning on the efficiency of search. Once learning is taken into account, the structure of information flow becomes important. In particular, I highlight the truncated information structure in the search problem. Agents stop searching once a sufficiently attractive price is found. Therefore, they observe the performance of shorter searches, but do not directly observe the performance of longer searches. I design and conduct an experiment to test the hypothesis that this asymmetric flow of information leads agents to search too little. I find strong evidence in its favor. This suggests that in the presence of learning, the provision of a more symmetric information structure will make search more efficient.JEL Classification: C91, D83     

The Search For Stability and Permanence: Modelling the Pathways of Long-stay Looked After Children

This paper presents findings from a study of children lookedafter by 24 local authorities. It combines analysis of statisticaldata with analysis of qualitative and quantitative data froma questionnaire survey of a targeted sub-sample of childrenwho had been looked after for 4 years or more. The paper highlightsa complex picture of continuity and discontinuity in attemptsto achieve stability and permanence in a range of birth family,foster care, adoption, residential and leaving care placementsfor long-stay children. Some long-stay children are moving smoothlyand in a planned way towards a family for life, while some experiencelong periods in stable but temporary placements or have a numberof moves prior to finding stability and a sense of belonging.A further group of children experience stability or moves whilelooked after, without having a family to belong to when theymove into adult life. The paper discusses the difficulty withthe Government’s current long-stay performance measurein capturing the difference between stability in placement andplanned permanence for children and families.     

Equitable Selection in Bilateral Matching Markets

This paper presents a procedure to select equitable stable allocations in two-sided matching markets without side payments. The Equitable set is computed using the Equitable algorithm. The algorithm limits the set of options available for each agent throughout the procedure. The stable matchings selected are generally not extreme, form a lattice and satisfy the condition of being “Ralwsian” in each partition of the market. The Equitable algorithm can also be used to select a particular matching from the Equitable Set favoring particular agents independent of the side of the market to which they belong.     

Twice chosen: Spouse matching and earnings among women in first and second unions

This study examines spouse matching for females in second order marriages or cohabitating relationships. It is based on detailed data from longitudinal Swedish population registers. We follow women who marry, divorce, and subsequently remarry compared to women who marry and remain married over the course of the study interval. The earnings of both groups, along with the earnings of their respective husbands, are modeled on the basis of data in the year prior to their marriages. From the regressions we obtain spouse-to-be pairs of earnings residuals and measure the correlation between spouses within each marital regime. Overall, we find significant positive residual correlations for both sample partitions. The correlation is smaller for the first of two marriages for women who divorce than for women who marry and remain married. For the second of successive marriages, however, the correlation is larger than that for women who marry but once. Also for twice-married women, we find evidence of matching between successive husbands. Women who marry men with unmeasured positive earnings capacities, in the event of divorce, tend to select and match in a similar fashion the second time around.     

Matching with contracts: calculation of the complete set of stable allocations

Theory and Decision - For a many-to-many matching model with contracts, where all the agents have substitutable preferences, we provide an algorithm to compute the full set of stable allocations....     

A Tack in the Shoe: Neutralizing and Resisting the New Surveillance

Eleven behavioral techniques of neutralization intended to subvert the collection of personal information are discussed: discovery moves, avoidance moves, piggybacking moves, switching moves, distorting moves, blocking moves, masking moves, breaking moves, refusal moves, cooperative moves and counter-surveillance moves. In Western liberal democracies the advantages of technological and other strategic surveillance developments are often short-lived and contain ironic vulnerabilities. The logistical and economic limits on total monitoring, the interpretive and contextual nature of many human situations, system complexity, and interconnectedness and the vulnerability of those engaged in surveillance to be compromised, provide ample room for resistance. Neutralization is a dynamic adversarial social dance involving strategic moves and counter-moves and should be studied as a conflict interaction process .     

Perspectives on a Pair of Envelopes

The two envelopes problem has generated a significant number of publications (I have benefitted from reading many of them, only some of which I cite; see the epilogue for a historical note). Part of my purpose here is to provide a review of previous results (with somewhat simpler demonstrations). In addition, I hope to clear up what I see as some misconceptions concerning the problem. Within a countably additive probability framework, the problem illustrates a breakdown of dominance with respect to infinite partitions in circumstances of infinite expected utility. Within a probability framework that is only finitely additive, there are failures of dominance with respect to infinite partitions in circumstances of bounded utility with finitely many consequences (see the epilogue).     

Children's accounts of moving to a foster home

Little is known about how children themselves understand their moves to and between foster homes. The data presented in this paper come from a study that sought children's views on becoming and being a foster child. A key finding of that study was how children's accounts of being fostered illustrated a high level of anxiety and concern about their moving to live with a foster family. This paper firstly explores the key issues about looked‐after children's moves. It then describes the research study undertaken, before exploring the data generated from children's accounts of their moves to a new foster home. Lastly, there is a discussion of the implications for social work practice in this area.     

On the coase theorem and coalitional stability: the principle of equal relative concession

The Coase theorem is argued to be incompatible with bargaining set stability due to a tension between the grand coalition and sub-coalitions. We provide a counter-intuitive argument to demonstrate that the Coase theorem may be in complete consonance with bargaining set stability. We establish that an uncertainty concerning the formation of sub-coalitions will explain such compatibility: each agent fears that others may `gang up' against him and this fear forces the agents to negotiate. The grand coalition emerges from the negotiations if each agent uses the principle of equal relative sacrifice to determine the actual allocation. We also establish the rational basis for the choice of the principle of equal relative concession by the negotiating agents. Hence we argue that the Coase theorem will be valid even if there are stable sub-coalitions.     

The Relation Between Probability and Evidence Judgment: An Extension of Support Theory

We propose a theory that relates perceived evidence to numerical probability judgment. The most successful prior account of this relation is Support Theory, advanced in Tversky and Koehler (1994). Support Theory, however, implies additive probability estimates for binary partitions. In contrast, superadditivity has been documented in Macchi, Osherson, and Krantz (1999), and both sub- and superadditivity appear in the experiments reported here. Nonadditivity suggests asymmetry in the processing of focal and nonfocal hypotheses, even within binary partitions. We extend Support Theory by revising its basic equation to allow such asymmetry, and compare the two equations' ability to predict numerical assessments of probability from scaled estimates of evidence for and against a given proposition. Both between- and within-subject experimental designs are employed for this purpose. We find that the revised equation is more accurate than the original Support Theory equation. The implications of asymmetric processing on qualitative assessments of chance are also briefly discussed.     

Using concurrent planning to establish permanency for looked after young children

Many looked after children spend lengthy periods in impermanent care, and their frequent moves probably contribute to subsequent disturbed behaviour. Concurrent planning aims to reduce the number of moves and the length of time before placement in a permanent family. In this study 24 young children in three concurrent planning (CP) projects and 44 from two ‘traditional’ adoption teams were followed for 12–15 months. Records were obtained of the number of moves between households and the dates of key events before the child's permanent family placement was confirmed by the courts. The CP children moved into permanent families significantly faster and with significantly fewer previous moves than the two comparison groups. Unexpectedly, the CP children were significantly younger than the children following ‘traditional’ adoption programmes, making direct comparison impossible. Among those birth parents who were interviewed, the majority saw advantages in the CP approach. Concurrent planning carers reported high levels of personal anxiety but positive views of the advantages for the children. We conclude that CP can be used to achieve earlier permanence and fewer moves between carers for young children from selected birth families. The success of a CP team is dependent on the support of other professionals involved in determining permanent placements, based on a shared acknowledgement of the damaging effects of delay for the looked after child.     

Policy Stable States in the Graph Model for Conflict Resolution

A new approach to policy analysis is formulated within the framework of the graph model for conflict resolution. A policy is defined as a plan of action for a decision maker (DM) that specifies the DM’s intended action starting at every possible state in a graph model of a conflict. Given a profile of policies, a Policy Stable State (PSS) is a state that no DM moves away from (according to its policy), and such that no DM would prefer to change its policy given the policies of the other DMs. The profile of policies associated to a PSS is called a Policy Equilibrium. Properties of PSSs are developed, and a refinement is suggested that restricts DMs to policies that are credible in that they are in the DM’s immediate interest. Relationships with existing stability definitions in the graph model for conflict resolution are then explored.     

Social organizations and matching theory

We generalize the Gale-Shapley matching theory to the formation of social units consisting of more than two individuals and each individual having more than one role.We show how social preferences and social structure could conflict with freedom. In the absence of such a conflict, we define stability and show that this could conflict with social preferences and social structure. Next, we define Rawlsian justice in case of stability and show how social preferences and social structure can conflict with justice. Thus, it is the social preferences and social-structure which decide whether our concepts of freedom, stability, and justice are achievable or not.     

Quasi stable outcomes in the assignment game

There is a great deal of literature on matching, theoretical, and empirical, concerning stable assignments and mechanisms that achieve them. The starting point of this study is an interesting question about assignment procedures: given a situation where some agents (the senior workers) on one side have a priority status, which changes the classical theory. The core of game may not be stable. We prove the existence of a quasi stable constrained core. This constrained core may not be a lattice but it is a finite and disjoint union of complete lattices that check the properties of the core’s classical assignment game. We study the manipulability questions that derive.     

A macroeconomic potential describing structural change of the economy

For the purpose of describing change in an economy's structure, and addressing issues of transformation, the notion of a time-dependent macroeconomic potential function is introduced. It penalizes deviations from equilibrium (entrepreneurial error) and induces moves toward equilibrium. Thus, from the concept of a potential function is derived the concept of short-term and long-term change forces. We focus here on the long-term structural changes of an economy as distinct from short-term cyclical variations, and we represent economic transformations as phase-transitions between monostable and ambiguous bistable states of the economy. One important feature of the potential function approach is that the parameter of the potential can be determined from empirical data. In particular, the parameters can be regressed for input variables. Hence, a relationship has been established between the structural change force and a set of input variables, some of which are controlled in part by either public or private sector agents. The method has been applied to West German and United States industry data for 1950–1980.     

The influence of governance on public sector efficiency: A cross-country analysis

This paper examines whether governance quality affects public sector efficiency in the policy areas of administration, education, infrastructure, and stability. Using cross-country evidence, we find that a country's measures of governance quality are positively and significantly associated with public sector efficiency in the policy areas of administration, infrastructure, and stability. However, regression results suggest that a country's governance quality cannot affect efficiency in the policy area of education, even after controlling for some explanatory variables.     

“Nothing goes as planned”: Practitioners reflect on matching children and foster families

Matching children with foster carers is an important step in every nonkinship family foster care placement. Although guidelines for matching are provided in several studies, the case‐specific context of the decision can influence the practitioners' ability to adhere to these guidelines. Therefore, this study answers the following question: “How does the case‐specific context influence the practitioners' decision‐making process regarding matching in family foster care?” Using a qualitative design, 20 semistructured interviews were conducted with practitioners matching children with foster families. Three themes emerged representing different layers of practitioners' everyday decision‐making: matching as planned, matching being tailored, and matching being compromised. The results show that exceptions are part of practitioners' daily work, either due to the belief that it might benefit those involved or because of obstacles presented during the decision‐making process. When the decision is compromised, matching practitioners lower their standards, while at the same time safeguarding the quality of the match. This proves that matching in practice is more than choosing a family, and guidelines are needed to determine what “good‐enough” matching should entail.     

`Sex-Equal' Stable Matchings

The paper defines a measure on the set of stable matchings in the marriage problem. This measure is based on the minimization of the envy difference between the sets of men and women, while preserving stability and selects stable matchings with the least conflict of interest between both groups of agents. The solution concept proposed is called Sex-equal Matching (SEM) and the paper also provides an algorithm to compute the set of SEM.