# Contextual Probability and Operational Minimality in Tug-of-War Decision Making

arXiv: https://arxiv.org/abs/2601.10034 · HTML: https://mlsanity.com/paper/2601.10034/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 15 Jan 2026.

## Builds on (most cited first, 5 of 5)

- [Ultrafast photonic reinforcement learning based on laser chaos](https://mlsanity.com/paper/1704.04379/) (2017)
- [Efficient Decision-Making by Volume-Conserving Physical Object](https://mlsanity.com/paper/1412.6141/) (2014)
- [Decision Maker based on Atomic Switches](https://mlsanity.com/paper/1507.05895/) (2015)
- [A Balance for Fairness: Fair Distribution Utilising Physics in Games of Characteristic Function Form](https://mlsanity.com/paper/2101.11496/) (2021)
- [Resource allocation method using tug-of-war-based synchronization](https://mlsanity.com/paper/2108.11979/) (2021)

## Built on by (most cited first, 3 of 3)

- [Contextual Information Allocation in Shared-State Cognitive Models: An Information-Theoretic Bound](https://mlsanity.com/paper/2602.16716/) (2026)
- [Contextual Control without Memory Growth in a Context-Switching Task](https://mlsanity.com/paper/2604.03479/) (2026)
- [Spacetime Formation under Requirements: Contextual Realization and Form-Dependent Probability](https://mlsanity.com/paper/2605.23943/) (2026)

## Abstract (arXiv)

What connects minimal decision-making to contextual probability? We address this question through the Tug-of-War (TOW) principle, a resource-coupled mechanism for multi-armed bandit decision-making. Starting from classical probability, we show that when reward-learning functionality and specified information requirements are fixed, minimizing the necessary relaxation of common event semantics can lead to nonclassical probability. We derive the exact minimum semantic repair and identify the conditions under which information efficiency, calibration, and compositional consistency select contextual statistics. We then construct a single quantum Tug-of-War (QTOW) instrument in which the same decision--reward process both improves stationary decision performance and drives the unconditional learned state beyond the Klyachko--Can--Biniciouglu--Shumovsky (KCBS) noncontextuality bound. A finite diagnostic based on the instrument's recovery operations also yields a corrected contextuality witness. These results connect minimal decision-making, operational economy, and the emergence of contextual probability.