Social hierarchies and social networks in humans

Across species, social hierarchies are often governed by dominance relations. In humans, where there are multiple culturally valued axes of distinction, social hierarchies can take a variety of forms and need not rest on dominance relations. Consequently, humans navigate multiple domains of status, i.e. relative standing. Importantly, while these hierarchies may be constructed from dyadic interactions, they are often more fundamentally guided by subjective peer evaluations and group perceptions. Researchers have typically focused on the distinct elements that shape individuals’ relative standing, with some emphasizing individual-level attributes and others outlining emergent macro-level structural outcomes. Here, we synthesize work across the social sciences to suggest that the dynamic interplay between individual-level and meso-level properties of the social networks in which individuals are embedded are crucial for understanding the diverse processes of status differentiation across groups. More specifically, we observe that humans not only navigate multiple social hierarchies at any given time but also simultaneously operate within multiple, overlapping social networks. There are important dynamic feedbacks between social hierarchies and the characteristics of social networks, as the types of social relationships, their structural properties, and the relative position of individuals within them both influence and are influenced by status differentiation. This article is part of the theme issue ‘The centennial of the pecking order: current state and future prospects for the study of dominance hierarchies’.

Unleveraged Portfolios and Pure Allocation Return

In asset management, the portfolio leverage affects performance, and can be subject to constraints and operational limitations. Due to the possible leverage aversion of the investors, the comparison between portfolio performances can be incomplete or misleading. We propose a procedure to unleverage the mean-variance efficient portfolios to satisfy a leverage requirement. We obtain a class of unleveraged portfolios that are homogeneous in terms of leverage, so therefore properly comparable. The proposed unleverage procedure permits isolating the pure allocation return, i.e., the return component, due to the qualitative choice of portfolio allocation, from the return component due to the portfolio leverage. Theoretical analysis and empirical evidence on actual data show that efficient mean-variance portfolios, once unleveraged, uncover mean-variance dominance relations hidden by the leverage contribution to portfolio return. Our approach may be useful to practitioners proposing to take long positions on “short assets” (e.g. inverse ETF), thereby considering short positions as active investment choices, in contrast with the usual interpretation where are used to overweight long positions.

Social Hierarchy and Social Networks in Humans

Across species, social hierarchies are often governed by dominance relations. In humans, where there are multiple culturally-valued axes of distinction, social hierarchies can take a variety of forms and need not rest on dominance relations. Consequently, humans navigate multiple domains of status, i.e., relative standing. Importantly, while these hierarchies may be constructed from dyadic interactions, they are often more fundamentally guided by subjective peer evaluations and group perceptions. Researchers have typically focused on the distinct elements that shape individuals’ relative standing, with some emphasising individual-level attributes and others outlining emergent macro-level structural outcomes. Here, we synthesise work across the social sciences to suggest that the dynamic interplay between individual-level and meso-level properties of the social networks in which individuals are embedded are crucial for understanding the diverse processes of status differentiation across groups. More specifically, we observe that humans not only navigate multiple social hierarchies at any given time, but also simultaneously operate within multiple, overlapping social networks. There are important dynamic feedbacks between social hierarchies and the characteristics of social networks, as the types of social relationships, their structural properties, and the relative position of individuals within them both influence and are influenced by status differentiation.

An unexpected characteristic of tournament predictive power

A tournament is a series of games (matches) among competitors for an overall prize. Beyond sporting events, tournament structure can relate to elections, applicants competing for an employment position, etc. Tournament structure also exists within certain species of birds and mammals where dominance relations develop, forming a tournament-like pecking structure [1]. The format of the tournament depends on the tournament’s objective giving consideration to time, financial, geographical, and other constraints. The two most common formats where players compete pairwise are the single elimination (knockout, sudden death) tournament and the round robin tournament. Our discussion includes both. A third popular format is that of a contest, where all players perform simultaneously only once. Examples of this type include most golf tournaments as well as track and field athletic events. A detailed analysis of contests as they relate to topics discussed here is given in [2].

Emergence of hierarchy in networked endorsement dynamics

Many social and biological systems are characterized by enduring hierarchies, including those organized around prestige in academia, dominance in animal groups, and desirability in online dating. Despite their ubiquity, the general mechanisms that explain the creation and endurance of such hierarchies are not well understood. We introduce a generative model for the dynamics of hierarchies using time-varying networks, in which new links are formed based on the preferences of nodes in the current network and old links are forgotten over time. The model produces a range of hierarchical structures, ranging from egalitarianism to bistable hierarchies, and we derive critical points that separate these regimes in the limit of long system memory. Importantly, our model supports statistical inference, allowing for a principled comparison of generative mechanisms using data. We apply the model to study hierarchical structures in empirical data on hiring patterns among mathematicians, dominance relations among parakeets, and friendships among members of a fraternity, observing several persistent patterns as well as interpretable differences in the generative mechanisms favored by each. Our work contributes to the growing literature on statistically grounded models of time-varying networks.

Extension of Monotonic Functions and Representation of Preferences

Consider a dominance relation (a preorder) ≿ on a topological space X, such as the greater than or equal to relation on a function space or a stochastic dominance relation on a space of probability measures. Given a compact set K ⊆ X, we study when a continuous real function on K that is strictly monotonic with respect to ≿ can be extended to X without violating the continuity and monotonicity conditions. We show that such extensions exist for translation invariant dominance relations on a large class of topological vector spaces. Translation invariance or a vector structure are no longer needed when X is locally compact and second countable. In decision theoretic exercises, our extension theorems help construct monotonic utility functions on the universal space X starting from compact subsets. To illustrate, we prove several representation theorems for revealed or exogenously given preferences that are monotonic with respect to a dominance relation.

Approximate extrema of a bounded family of intervals

Устанавливаются связи между экстремальными множествами для ``приближенных'' отношений доминирования для произвольного ограниченного семейства интервалов вещественных чисел. Connections are established between extremal sets for ``approximate'' dominance relations for an arbitrary bounded family of intervals of real numbers.