Enrollment management under deep uncertainty: an entropy-driven Bayesian decision architecture for UK higher education: preprint

UK universities face compounded enrollment uncertainty from demographic plateau, volatile international postgraduate taught demand, and a frozen domestic fee cap, while capital commitments and programme restructuring are largely irreversible within a planning horizon. We introduce an entropy-driven Bayesian Decision Theory (BDT) architecture, formalised as a partially observable Markov decision process (POMDP), for annual enrollment-driven financial management in Research Intensive higher education institutions (HEIs). The architecture uses the Shannon entropy of the posterior demand-regime belief as an automatic caution regulator: under high regime uncertainty the system hedges toward prior expectations and favours reversible strategic postures; as Higher Education Statistics Agency (HESA) evidence accumulates and entropy collapses, it progressively commits to the posterior-optimal strategy. A satisficing gate imposes a hard viability constraint that prevents catastrophic over-commitment when Low-regime probability is elevated, and an option-value mechanism penalises irreversible decisions before regime identity has been established. Empirical calibration uses HESA student and finance data from four Russell Group universities (Warwick, Exeter, Leeds, Bristol) over 2014/15--2024/25. Monte Carlo simulation ($n = 500$) shows that the architecture achieves risk-adjusted Pareto dominance over five comparators: statistically equivalent expected reward to the best comparator strategy (mean 349.2 vs.\ 360.7, $p = 0.986$) with 0.9 percentage points lower distress probability---approximately 4--5 fewer financial-crisis paths per 500 simulations. Entropy collapse following Bayesian belief updating alone explains 17--30\,\% of the reward premium over non-belief strategies. The architecture produces zero distress across all five initial belief scenarios tested, including a pessimistic 50\,\% prior on the Low regime. The calibration pipeline uses only HESA and Office for National Statistics (ONS) open data and is designed for annual redeployment.