Equitable public land partitioning in community agriculture: A Hilbert space framework comparing mechanism design and stochastic-geometric Markov models
DOI:
https://doi.org/10.21839/jaar.2026.v11.10053Keywords:
Community agriculture, Equitable land allocation, Fair division, Land governance, Markov models, Rural development, Spectral operator theoryAbstract
Equitable access to public land is not only a technical allocation problem; it also shapes production opportunities, perceived justice, cooperation and the sustainability of community agriculture. This study develops a unified Hilbert-space framework for comparing two approaches to public-land allocation: mechanism-design procedures based on fair division and stochastic-geometric Markov models. The land domain is represented as a probability space and community members’ heterogeneous valuations are treated as vector fields. Within this common framework, mechanism design seeks allocations that satisfy fairness constraints while protecting social welfare, whereas the stochastic approach describes allocation as a dynamic process whose long-run behavior is governed by a Markov semigroup. The comparison highlights a practical trade-off. Mechanism design responds more directly and stably to localized valuation bias and is computationally attractive when communities are large and preferences can be elicited reliably. Stochastic-geometric methods are better able to absorb global spatial distortions through ergodic averaging, which may be useful where land quality and spatial conditions are highly heterogeneous. A spectral hybrid operator is therefore proposed to combine the strengths of both approaches. Beyond its mathematical contribution, the framework provides a decision-support perspective for community land governance by linking fairness, robustness and computational feasibility to the characteristics of beneficiaries and agricultural space. It offers a theoretical basis for choosing allocation procedures that can support transparent, equitable and context-sensitive management of public agricultural land.
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