Cognitive resource allocation determines the organization of personal networks.

The typical human personal social network contains about 150 relationships including kin, friends, and acquaintances, organized into a set of hierarchically inclusive layers of increasing size but decreasing emotional intensity. Data from a number of different sources reveal that these inclusive layers exhibit a constant scaling ratio of [Formula: see text] While the overall size of the networks has been connected to our cognitive capacity, no mechanism explaining why the networks present a layered structure with a consistent scaling has been proposed. Here we show that the existence of a heterogeneous cost to relationships (in terms of time or cognitive investment), together with a limitation in the total capacity an individual has to invest in them, can naturally explain the existence of layers and, when the cost function is linear, explain the scaling between them. We develop a one-parameter Bayesian model that fits the empirical data remarkably well. In addition, the model predicts the existence of a contrasting regime in the case of small communities, such that the layers have an inverted structure (increasing size with increasing emotional intensity). We test the model with five communities and provide clear evidence of the existence of the two predicted regimes. Our model explains, based on first principles, the emergence of structure in the organization of personal networks and allows us to predict a rare phenomenon whose existence we confirm empirically.

Beyond Dunbar circles: a continuous description of social relationships and resource allocation.

We discuss the structure of human relationship patterns in terms of a new formalism that allows to study resource allocation problems where the cost of the resource may take continuous values. This is in contrast with the main focus of previous studies where relationships were classified in a few, discrete layers (known as Dunbar's circles) with the cost being the same within each layer. We show that with our continuum approach we can identify a parameter [Formula: see text] that is the equivalent of the ratio of relationships between adjacent circles in the discrete case, with a value [Formula: see text]. We confirm this prediction using three different datasets coming from phone records, face-to-face contacts, and interactions in Facebook. As the sample size increases, the distributions of estimated parameters smooth around the predicted value of [Formula: see text]. The existence of a characteristic value of the parameter at the population level indicates that the model is capturing a seemingly universal feature on how humans manage relationships. Our analyses also confirm earlier results showing the existence of social signatures arising from having to allocate finite resources into different relationships, and that the structure of online personal networks mirrors those in the off-line world.

Social capital as a network measure provides new insights on economic growth.

Unveiling the main drivers of economic growth is of paramount importance. Previous research recognizes the critical role played by the factors of production: capital and labor. However, the exact mechanisms that underpin Total Factor Productivity (TFP) are not fully understood. An increasing number of studies suggests that the creation and transmission of knowledge, factor supply and economic integration are indeed crucial. Yet, the need for a systematic and unifying framework still exists. Nowadays capital and labor are embedded into a complex network structure through global supply chains and international migration. Recent research has established a link between network centralities and different types of social capital. In this work we employ the OECD's Multi-Regional Input-Output and International Migration datasets to build the network representation for capital and labor of 63 economies during 10 years. We then examine the role of social capital measures as drivers of the TFP adopting an extended Cobb-Douglass production function and addressing potential issues such as multicollinearity, reverse causality and non-linear effects. Our results indicate that social capital in the factors of production networks can significantly drive economic outputs through TFP.

Structural measures of personal networks predict migrants' cultural backgrounds: an explanation from Grid/Group theory.

Culture and social structure are not separated analytical domains but intertwined phenomena observable in personal networks. Drawing on a personal networks dataset of migrants in the United States and Spain, we show that the country of origin, a proxy for diverse languages and cultural institutions, and religion may be predicted by specific combinations of personal network structural measures (closeness, clustering, betweenness, average degree, etc). We obtain similar results applying three different methods (a multinomial logistic regression, a Random Forest algorithm, and an artificial neural network). This finding is explained within the framework of the Grid/Group theory that has long posed the interdependence of social structural and cultural features of human groups.

Nonverbal Auditory Cues Allow Relationship Quality to be Inferred During Conversations.

The claim that nonverbal cues provide more information than the linguistic content of a conversational exchange (the Mehrabian Conjecture) has been widely cited and equally widely disputed, mainly on methodological grounds. Most studies that have tested the Conjecture have used individual words or short phrases spoken by actors imitating emotions. While cue recognition is certainly important, speech evolved to manage interactions and relationships rather than simple information exchange. In a cross-cultural design, we tested participants' ability to identify the quality of the interaction (rapport) in naturalistic third party conversations in their own and a less familiar language, using full auditory content versus audio clips whose verbal content has been digitally altered to differing extents. We found that, using nonverbal content alone, people are 75-90% as accurate as they are with full audio cues in identifying positive vs negative relationships, and 45-53% as accurate in identifying eight different relationship types. The results broadly support Mehrabian's claim that a significant amount of information about others' social relationships is conveyed in the nonverbal component of speech. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s10919-021-00386-y.

Hierarchical clustering of bipartite data sets based on the statistical significance of coincidences.

When some 'entities' are related by the 'features' they share they are amenable to a bipartite network representation. Plant-pollinator ecological communities, co-authorship of scientific papers, customers and purchases, or answers in a poll, are but a few examples. Analyzing clustering of such entities in the network is a useful tool with applications in many fields, like internet technology, recommender systems, or detection of diseases. The algorithms most widely applied to find clusters in bipartite networks are variants of modularity optimization. Here, we provide a hierarchical clustering algorithm based on a dissimilarity between entities that quantifies the probability that the features shared by two entities are due to mere chance. The algorithm performance is O(n^{2}) when applied to a set of n entities, and its outcome is a dendrogram exhibiting the connections of those entities. Through the introduction of a 'susceptibility' measure we can provide an 'optimal' choice for the clustering as well as quantify its quality. The dendrogram reveals further useful structural information though-like the existence of subclusters within clusters or of nodes that do not fit in any cluster. We illustrate the algorithm by applying it first to a set of synthetic networks, and then to a selection of examples. We also illustrate how to transform our algorithm into a valid alternative for one-mode networks as well, and show that it performs at least as well as the standard, modularity-based algorithms-with a higher numerical performance. We provide an implementation of the algorithm in python freely accessible from GitHub.

Large scale and information effects on cooperation in public good games.

The problem of public good provision is central in economics and touches upon many challenging societal issues, ranging from climate change mitigation to vaccination schemes. However, results which are supposed to be applied to a societal scale have only been obtained with small groups of people, with a maximum group size of 100 being reported in the literature. This work takes this research to a new level by carrying out and analysing experiments on public good games with up to 1000 simultaneous players. The experiments are carried out via an online protocol involving daily decisions for extended periods. Our results show that within those limits, participants' behaviour and collective outcomes in very large groups are qualitatively like those in smaller ones. On the other hand, large groups imply the difficulty of conveying information on others' choices to the participants. We thus consider different information conditions and show that they have a drastic effect on subjects' contributions. We also classify the individual decisions and find that they can be described by a moderate number of types. Our findings allow to extend the conclusions of smaller experiments to larger settings and are therefore a relevant step forward towards the understanding of human behaviour and the organisation of our society.

Emotions and Strategic Behaviour: The Case of the Ultimatum Game.

Human behaviour in economic interactions has attracted an increasing amount of attention over the last decades. The economic assumption that people would behave focusing on their own material self-interest was proved incomplete, once the empirical evidence consistently showed that many other motives may influence such behaviour. Therefore, models that can incorporate rational decision process as well as other intervening factors are a key issue to both understand the observations from economic experiments and to apply the lessons learned from them. In this paper, we incorporate the influence of emotions to the utility function in an explicit manner, using the Ultimatum Game as a case study. Our model is amenable to analytical study, and is connected with the Circumplex model of emotions and with Kahneman's two-system theory. The simplicity of the model allows to obtain predictions for the offers and acceptance thresholds. We study two specific examples, when the model parameters are distributed uniformly or normally, and show that in the latter case the results are already qualitatively correct. Although this work can be considered as a first approach, it includes what we believe are the main stylized facts, is able to qualitatively reproduce experimental results in a very simple manner, and can be straightforwardly extended to other games.