Theory of Acyclic Nested Sets: Relation Nesting, Emergence, and Feedback in Complex Social Systems

• In Event: Social Theory and Complexity Science: New Research Directions (Co-sponsored by Mathematical Sociology Section)

Abstract

This paper introduces the Theory of Acyclic Nested Sets (TANS) as a relational framework for analysing emergence and feedback in complex social systems. Sociology has long recognised that higher-level structures such as organisations, fields, and institutions emerge from patterned interaction while simultaneously shaping future interaction. Complexity science provides formal concepts of cross-scale dynamics, yet sociology lacks an explicit relational framework linking micro-level interaction and macro-level social structure.

TANS addresses this gap by conceptualising relation nesting as a higher-order relational property. Social relations may be nested within shared organisational or institutional contexts, co-nested across multiple contexts, or remain non-nested across boundaries. These differences are theoretically consequential: they shape whether interactions accumulate into stabilised collective actors and how higher-level structures feed back into ongoing interaction.

The framework reconceptualises society as a system of acyclically nested sets of relations, in which lower-level relations can be embedded within higher-level relations but not the reverse. This acyclicity analytically distinguishes mechanisms of bottom-up emergence from processes of top-down feedback and explains why identical micro-level interaction patterns may generate divergent macro-level outcomes depending on their structural location.

By formalising relation nesting, TANS connects central insights of grand social theory—including institutionalisation, structuration, and field formation—with complexity-oriented accounts of self-organisation. The theory provides a unified vocabulary for analysing how higher-level entities arise from relational configurations and how feedback across levels stabilises or transforms social organisation.

The paper concludes by outlining strategies for operationalising nested relational structures using extensions of statistical network models, including Nested Exponential Random Graph Models and Generalised Relational Hyperevent Models.

Authors

• Nikita Basov, The University of Manchester

• Philip Leifeld, University of Manchester

• Jürgen Lerner, University of Konstanz