Dynamical system model predicts when social learners impair collective performance.

A key question concerning collective decisions is whether a social system can settle on the best available option when some members learn from others instead of evaluating the options on their own. This question is challenging to study, and previous research has reached mixed conclusions, because collective decision outcomes depend on the insufficiently understood complex system of cognitive strategies, task properties, and social influence processes. This study integrates these complex interactions together in one general yet partially analytically tractable mathematical framework using a dynamical system model. In particular, it investigates how the interplay of the proportion of social learners, the relative merit of options, and the type of conformity response affect collective decision outcomes in a binary choice. The model predicts that, when the proportion of social learners exceeds a critical threshold, a bistable state appears in which the majority can end up favoring either the higher- or lower-merit option, depending on fluctuations and initial conditions. Below this threshold, the high-merit option is chosen by the majority. The critical threshold is determined by the conformity response function and the relative merits of the two options. The study helps reconcile disagreements about the effect of social learners on collective performance and proposes a mathematical framework that can be readily adapted to extensions investigating a wider variety of dynamics.

Falling through the cracks: Modeling the formation of social category boundaries.

Social categorizations divide people into "us" and "them", often along continuous attributes such as political ideology or skin color. This division results in both positive consequences, such as a sense of community, and negative ones, such as group conflict. Further, individuals in the middle of the spectrum can fall through the cracks of this categorization process and are seen as out-group by individuals on either side of the spectrum, becoming inbetweeners. Here, we propose a quantitative, dynamical-system model that studies the joint influence of cognitive and social processes. We model where two social groups draw the boundaries between "us" and 'them" on a continuous attribute. Our model predicts that both groups tend to draw a more restrictive boundary than the middle of the spectrum. As a result, each group sees the individuals in the middle of the attribute space as an out-group. We test this prediction using U.S. political survey data on how political independents are perceived by registered party members as well as existing experiments on the perception of racially ambiguous faces, and find support.

Scaling of urban income inequality in the USA.

Urban scaling analysis, the study of how aggregated urban features vary with the population of an urban area, provides a promising framework for discovering commonalities across cities and uncovering dynamics shared by cities across time and space. Here, we use the urban scaling framework to study an important, but under-explored feature in this community-income inequality. We propose a new method to study the scaling of income distributions by analysing total income scaling in population percentiles. We show that income in the least wealthy decile (10%) scales close to linearly with city population, while income in the most wealthy decile scale with a significantly superlinear exponent. In contrast to the superlinear scaling of total income with city population, this decile scaling illustrates that the benefits of larger cities are increasingly unequally distributed. For the poorest income deciles, cities have no positive effect over the null expectation of a linear increase. We repeat our analysis after adjusting income by housing cost, and find similar results. We then further analyse the shapes of income distributions. First, we find that mean, variance, skewness and kurtosis of income distributions all increase with city size. Second, the Kullback-Leibler divergence between a city's income distribution and that of the largest city decreases with city population, suggesting the overall shape of income distribution shifts with city population. As most urban scaling theories consider densifying interactions within cities as the fundamental process leading to the superlinear increase of many features, our results suggest this effect is only seen in the upper deciles of the cities. Our finding encourages future work to consider heterogeneous models of interactions to form a more coherent understanding of urban scaling.

The interpretation of urban scaling analysis in time.

Scaling is a general analytical framework used by many disciplines-from physics to biology and the social sciences-to characterize how population-averaged properties of a collective vary with its size. The observation of scale invariance over some range identifies general system types, be they ideal gases, ecosystems or cities. The use of scaling in the analysis of cities quantifies many of their arguably fundamental general characteristics, especially their capacity to create interrelated economies of scale in infrastructure and increasing returns to scale in socio-economic activities. However, the measurement of these effects, and the relationship of observable parameters to theory, hinge on how scaling analysis is used empirically. Here, we show how two equivalent approaches to urban scaling-cross-sectional and temporal-lead to the measurement of different mixtures of the same fundamental parameters describing pure scale and pure temporal phenomena. Specifically, temporal exponents are sensitive to the intensive growth of urban quantities and to circumstances when population growth vanishes, leading to instabilities and infinite divergences. These spurious effects are avoided in cross-sectional scaling, which is more common and closer to theory in terms of quantitative testable expectations for its parameters.