We propose mechanisms for a mathematical social-choice game that is designed to mediate decision-making processes for city planning, urban area redevelopment, and architectural design (massing) of urban housing complexes. The proposed game is effectively a multi-player generative configurator equipped with automated appraisal/scoring mechanisms for revealing the aggregate impact of alternatives; featuring a participatory digital process to support transparent and inclusive decision-making processes in spatial design for ensuring an equitable balance of sustainable development goals. As such, the game effectively empowers a group of decision-makers to reach a fair consensus by mathematically simulating many rounds of trade-offs between their decisions, with different levels of interest or control over various types of investments. Our proposed gamified design process encompasses decision-making about the most idiosyncratic aspects of a site related to its heritage status and cultural significance to the physical aspects such as balancing access to sunlight and the right to sunlight of the neighbours of the site, ensuring coherence of the entire configuration with regards to a network of desired closeness ratings, the satisfaction of a programme of requirements, and intricately balancing individual development goals in conjunction with communal goals and environmental design codes. The game is developed fully based on an algebraic computational process on our own digital twinning platform, using open geospatial data and open-source computational tools such as NumPy. The mathematical process consists of a Markovian design machine for balancing the decisions of actors, a massing configurator equipped with Fuzzy Logic and Multi-Criteria Decision Analysis, algebraic graph-theoretical accessibility evaluators, and automated solar-climatic evaluators using geospatial computational geometry.

翻译：摘要：我们提出了一种基于数学社会选择理论的游戏机制，旨在调解城市规划、城区再开发以及城市住宅综合体建筑体量设计中的决策过程。该游戏本质上是一个多玩家生成式配置器，配备自动评估/评分机制以揭示各方案的总体影响；其通过参与式数字流程，支持空间设计中透明且包容的决策过程，以确保可持续发展目标的公平平衡。该游戏通过数学模拟多轮关于不同投资维度中利益或控制权差异的权衡决策，有效赋能决策群体达成公平共识。所提出的游戏化设计流程涵盖场地特殊属性的决策，包括遗产地位与文化意义，以及物理层面（如平衡场地及其邻里的日照获取权与日照权），同时确保整体配置符合期望邻近度网络、满足项目需求规划，并精细协调个体发展目标、社区目标与环境设计规范。该游戏完全基于我们自有数字孪生平台上的代数计算流程开发，使用开放地理空间数据及NumPy等开源计算工具。其数学过程包括：用于平衡参与者决策的马尔可夫设计引擎、配备模糊逻辑与多准则决策分析的体量配置器、基于代数图论的可达性评估器，以及利用地理空间计算几何的自动太阳能气候评估器。