Condorcet Cycles, Contextuality, and the Emergence of Quantum-like Collective States.

Abstract

The Condorcet paradox is traditionally viewed as a macro-level phenomenon of collective decision-making, showing that individually rational agents with coherent and transitive preferences may nevertheless generate socially intransitive majority outcomes. This interpretation assumes that cyclicity emerges exclusively through aggregation. In this study, we distinguish between micro-Condorcet dynamics, arising from contextual interactions within individual decision processes, and macro-Condorcet dynamics, emerging through majority aggregation. To investigate the relationship between these two levels, we introduce a minimal contextual model in which pairwise decisions are generated sequentially and linked through a contextual coupling mechanism. Although individual agents remain locally coherent and entirely classical at the microscopic level, each decision modifies the context of subsequent comparisons. Simulation results show that increasing contextuality progressively increases the probability of both micro- and macro-level Condorcet cycles. The transition between the two levels is strongly influenced by heterogeneity in decision thresholds, particularly those governing intermediate and closing comparisons. Rather than being driven primarily by initial preference relations, collective cycles emerge from heterogeneous evaluations of intermediate alternatives, which amplify contextual effects and facilitate cycle closure. A critical contextuality threshold is observed beyond which classical representability breaks down and no probability distribution over transitive preference rankings can reproduce the observed pairwise preference probabilities. These findings suggest that quantum-like probabilistic structures may emerge naturally as higher-level representations of contextual collective decision systems.