用物理模型优化爱尔兰选区划分，平衡比例代表与紧凑性。
Constituency Optimisation Through Hamiltonian Representation Of Mandates (COTHROM): Algorithmic Redistricting of Irish Election Boundaries
- 将宪法目标建模为庞茨哈密顿量，用蒙特卡洛方法搜索最优边界
- 在科克郡测试中，新方案在多种权重下均优于现行边界
- 适合关注选举公平性与算法治理的研究者和政策制定者
爱尔兰比例代表单可转移投票制（PR-STV）的选区重划面临从海量可能配置中选出最能体现宪法目标的边界组合的挑战，而这些目标常相互冲突。本文提出首个针对爱尔兰选区重划的计算框架，系统优化多重宪法要求，并使权衡关系显式且可量化。问题通过统计物理解析：将宪法目标视为庞茨哈密顿量中的项，利用马尔可夫链蒙特卡洛（MCMC）和模拟退火最小化该目标函数，耦合常数作为目标权重的代理。进一步采用多准则决策分析（MCDA）和帕累托最优性解决权重选择的模糊性。在科克郡评估中，无论何种权重设置，COTHROM方案在比例代表与紧凑性方面均持续优于现行法律边界。
原文摘要 · Abstract (English)
Electoral redistricting in Ireland's Proportional Representation Single Transferable Vote (PR-STV) system faces the challenge of selecting an optimally representative set of electoral boundaries from an enormous set of possible configurations, and where ``representative'' is a delicate balance of constitutional objectives that are often in tension with one another. We present the first computational framework for Irish electoral redistricting that systematically optimises across multiple constitutional requirements while making trade-offs explicit and quantifiable. The electoral redistricting problem is parsed using statistical physics, where constitutional objectives are considered as terms in a Potts Hamiltonian. Markov Chain Monte Carlo (MCMC) methods and simulated annealing are employed to minimise this objective function, systematically exploring this configuration space, with coupling constants as proxies for objective weightings. Multi Criterion Decision Analysis (MCDA) and Pareto Optimality is then utilised to remedy the ambiguity in choosing a certain objective weighting combination over others. With respect to proportional representation and compactness objectives evaluated in County Cork, COTHROM consistently improves on the existing legal constituency boundaries for a range of objective weightings.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。