Illusory correlation, group size and memory

Two studies were conducted to test the predictions of a multi-component model of distinctiveness-based illusory correlation (IC) regarding the use of episodic and evaluative information in the production of the phenomenon. Extending on the standard paradigm, participants were presented with 4 groups decreasing in size, but all exhibiting the same ratio of positive to negative behaviours. Study 1 (N = 75) specifically tested the role of group size and distinctiveness, by including a zero-frequency cell in the design. Consistent with predictions drawn from the proposed model, with decreasing group size, the magnitude of the IC effect showed a linear in- crease in judgments thought to be based on evaluative information. In Study 2 (N = 43), a number of changes were introduced to a group assignment task (double presentation, inclusion of decoys) that allowed a more rig- orous test of the predicted item-specific memory effects. In addition, a new multilevel, mixed logistic regression approach to signal-detection type analysis was used, providing a more flexible and reliable analysis than previ- ously. Again, with decreasing group size, IC effects showed the predicted monotonic increase on the measures (group assignment frequencies, likability ratings) thought to be dependent on evaluative information. At the same time, measures thought to be based on episodic information (free recall and group assignment accuracy) partly revealed the predicted enhanced episodic memory for smaller groups and negative items, while also supporting a distinctiveness-based approach. Additional analysis revealed that the pattern of results for judg- ments though to be based on evaluative information was independent of interpersonal variation in behavioral memory, as predicted by the multi-component model, and in contrast to predictions of the competing models. The results are discussed in terms of the implications of the findings for the proposed mechanisms of illusory correlation

Informal Insurance with Endogenous Group Size

We present a theory of endogenous formation of insurance groups which combines heterogeneity on agents' risk aversion under asymmetric information and lack of enforceability of contracts. Income sharing inside the group is decided by majority voting and the size of the group adjusts to this decision through participation constraints. At equilibrium, all group members agree on the same imperfect level of income sharing, which yields a constrained-efficient equilibrium. Comparative statics on the risk faced by the community provide interesting results. A mean preserving spread of income implies more income sharing and a larger group size. New members, and possibly even old members may be better o¤, while non-members are worse-o¤. These results have relevant policy implications.

Group Testing with Pools of Fixed Size

In the classical combinatorial (adaptive) group testing problem, one is given two integers $d$ and $n$, where $0\le d\le n$, and a population of $n$ items, exactly $d$ of which are known to be defective. The question is to devise an optimal sequential algorithm that, at each step, tests a subset of the population and determines whether such subset is contaminated (i.e. contains defective items) or otherwise. The problem is solved only when the $d$ defective items are identified. The minimum number of steps that an optimal sequential algorithm takes in general (i.e. in the worst case) to solve the problem is denoted by $M(d, n)$. The computation of $M(d, n)$ appears to be very difficult and a general formula is known only for $d = 1$. We consider here a variant of the original problem, where the size of the subsets to be tested is restricted to be a fixed positive integer $k$. The corresponding minimum number of tests by a sequential optimal algorithm is denoted by $M^{\lbrack k\rbrack}(d, n)$. In this paper we start the investigation of the function $M^{\lbrack k\rbrack}(d, n)$

Synergy and Group Size in Microbial Cooperation

Microbes produce many molecules that are important for their growth and development, and the consumption of these secretions by nonproducers has recently become an important paradigm in microbial social evolution. Though the production of these public goods molecules has been studied intensely, little is known of how the benefits accrued and costs incurred depend on the quantity of public good molecules produced. We focus here on the relationship between the shape of the benefit curve and cellular density with a model assuming three types of benefit functions: diminishing, accelerating, and sigmoidal (accelerating then diminishing). We classify the latter two as being synergistic and argue that sigmoidal curves are common in microbial systems. Synergistic benefit curves interact with group sizes to give very different expected evolutionary dynamics. In particular, we show that whether or not and to what extent microbes evolve to produce public goods depends strongly on group size. We show that synergy can create an “evolutionary trap” which can stymie the establishment and maintenance of cooperation. By allowing density dependent regulation of production (quorum sensing), we show how this trap may be avoided. We discuss the implications of our results for experimental design

Group lending with endogenous group size

This paper focuses on the size of the borrower group in group lending. We show that, when social ties in a community enhance borrowers' incentives to exert effort, a profit-maximizing financier chooses a group of limited size. Borrowers that would be fundable under moral hazard but have insufficient social ties do not receive funding. The result arises because there is a trade-off between raising profits through increased group size and providing incentives for borrowers with less social ties. The result may explain why many micro-lending institutions and rural credit cooperatives lend to groups of small size.Group Lending; Moral Hazard; Social Capital

Finite-Size Scaling from the non-perturbative Renormalization Group

The phase diagram of QCD at finite temperature and density and the existence of a critical point are currently very actively researched topics. Although tremendous progress has been made, in the case of two light quark flavors even the order of the phase transition at zero density is still under discussion. Finite-size scaling is a powerful method for the analysis of phase transitions in lattice QCD simulations. From the scaling behavior, critical exponents can be tested and the order as well as the universality class of a phase transition can be established. This requires knowledge of the critical exponents and the scaling behavior. We use a non-perturbative Renormalization Group method to obtain critical exponents and the finite-size scaling functions for the O(4) universality class in three dimensions. These results are useful for a comparison to the actual scaling behavior in lattice QCD simulations with two flavors, as well as for an estimate of the size of the scaling region and the deviations from the expected scaling behavior.Comment: contribution to the proceedings of the workshop QCD@work 2007, Martina Franca (Italy), June 2007, proceedings to be published by AIP, 6 pages, 6 figures (scaled down from published version

Free Riding on Altruism and Group Size

It is shown that altruism does not affect the equilibrium provision of public goods although altruism takes the form of unconditional commitment to contribute. The reason is that altruistic contributions completely crowd out selfish contributions. That is, egoists free ride on altruism. It is also shown that public goods are less likely to be provided in larger groups.Free Riding, Public good, Altruism

Group Size and Social Ties in Microfinance Institutions

Microfinance programmes provide poor people with small loans given to jointly liable self-selected groups. Follow-up loans provide incentives to repay. In an experiment we investigate the influence of those features on strategic default. Each group member invests in an individual risky project, whose outcome is known only to the individual investor. Subjects decide, whether to contribute to group repayment or not. Only those with successful projects can contribute. The experiment ends if too few repay. We investigate group size and social ties effects. We observe high repayments rates, which are robust across treatment. Group lending outperforms individual lending. Self-selected groups show a high but less stable willingness to contribute.microcredits, group lending, public goods, laboratory experiments, development economics

On the Size and Structure of Group Cooperation

This paper examines characteristics of cooperative behavior in a repeated, n-person, continuous action generalization of a Prisoner’s Dilemma game. When time preferences are heterogeneous and bounded away from one, how “much” cooperation can be achieved by an ongoing group? How does group cooperation vary with the group’s size and structure? For an arbitrary distribution of discount factors, we characterize the maximal average co-operation (MAC) likelihood of this game. The MAC likelihood is the highest average level of cooperation, over all stationary subgame perfect equilibrium paths, that the group can achieve. The MAC likelihood is shown to be increasing in monotone shifts, and decreasing in mean preserving spreads, of the distribution of discount factors. The latter suggests that more heterogeneous groups are less cooperative on average. Finally, we establish weak conditions under which the MAC likelihood exhibits increasing returns to scale when discounting is heterogeneous. That is, larger groups are more cooperative, on average, than smaller ones. By contrast, when the group has a common discount factor, the MAC likelihood is invariant to group size.Repeated games, Maximal average Cooperation likelihood, Heterogeneous discount factors, Returns to scale

On the Size and Structure of Group Cooperation

This paper examines characteristics of cooperative behavior in a repeated, n-person, continuous action generalization of a Prisoner’s Dilemma game. When time preferences are heterogeneous and bounded away from one, how “much” cooperation can be achieved by an ongoing group? How does group cooperation vary with the group’s size and structure? For an arbitrary distribution of discount factors, we characterize the maximal average cooperation (MAC) likelihood of this game. The MAC likelihood is the highest average level of cooperation, over all stationary subgame perfect equilibrium paths, that the group can achieve. The MAC likelihood is shown to be increasing in monotone shifts, and decreasing in mean preserving spreads, of the distribution of discount factors. The latter suggests that more heterogeneous groups are less cooperative on average. Finally, we establish weak conditions under which the MAC likelihood exhibits increasing returns to scale when discounting is heterogeneous. That is, larger groups are more cooperative, on average, than smaller ones. By contrast, when the group has a common discount factor, the MAC likelihood is invariant to group size.Repeated games ; maximal average cooperation likelihood ; heterogeneous discount factors ; returns to scale JEL Classification: C7 ; D62 ; D7