一、宜居的多维定义与理论依据
This algorithm does not presuppose a single definition of "livability," but instead synthesizes internationally authoritative evaluation systems and local human-settlements concepts and maps them onto three levels of the model:
本算法不预设单一的"宜居"定义，而是综合国际权威评价体系与本土人居环境理念，将其映射到模型的三个层次：
- 人居环境科学（吴良镛《人居环境科学导论》）：人居环境是人类聚居的空间，宜居城市是"人、自然、社会"和谐共生的统一体——为本模型的"环境—生活—公共服务"三层结构提供本土理论依据。
- 《经济学人》智库（EIU）全球宜居指数：以稳定性、医疗保健、文化与环境、教育、基础设施五大维度评价城市宜居度——为本模型"公共服务（医疗+教育）与环境并重"提供参照。
- 美世（Mercer）生活质量调查：涵盖政治、经济、社会文化、医疗、教育、公共服务、娱乐、消费品、住房、自然环境十项——为"生活便利（住房可负担、出行）+ 公共服务"的细分提供依据。
- 联合国人居署（UN-Habitat）：可持续城市与宜居性强调居者有其屋、基本公共服务均等化与绿色公共空间——为"房价收入比、绿化覆盖"指标提供依据。
- 田园城市理论（埃比尼泽·霍华德《明日的田园城市》）：城市与乡村、人工与自然的平衡——为"环境系数"作为硬门槛提供思想源头。
- 世界卫生组织（WHO）健康城市：健康是宜居的前提，清洁空气、洁净水源是健康城市的基石——为"空气质量、空气含氧量"指标提供依据。
- 生态文明思想（"绿水青山就是金山银山"）：良好生态环境是最普惠的民生福祉，是宜居的硬约束——为"环境短板效应"的乘法结构提供价值依据。
二、模型的数学结构
The livability index does not use simple linear weighting, but a nonlinear combination with the environment coefficient as a multiplier and living convenience and public services as weighted terms:
宜居指数不采用简单线性加权，而是以环境系数为乘数、生活便利与公共服务为加权的非线性组合：
The four environmental factors are geometrically averaged: any single environmental shortcoming (poor air, high-altitude hypoxia, harsh climate, insufficient greenery) will drag down the whole, reflecting the "barrel effect" — the ecological environment is a hard threshold for livability (a multiplicative relationship in which none can be missing).
环境四要素取几何平均：任何一个环境短板（空气差、高原低氧、气候恶劣、绿化不足）都会把整体压低，体现"木桶效应"——生态环境是宜居的硬门槛（乘法关系，缺一不可）。
Living convenience depicts "affordable to live, smooth to travel": both traffic congestion and the housing-price-to-income ratio are inverse indicators (the lower, the more convenient), with traffic weighted slightly higher than housing because commuting is a high-frequency daily necessity.
生活便利刻画"住得起、行得畅"：交通拥堵与房价收入比均为反向指标（越低越便利），交通权重略高于房价，因通勤是每日高频刚需。
Public services measure the accessibility of healthcare and education by the number of Grade-A tertiary hospitals and the number of universities, weighted equally, reflecting "medical care for the sick and schooling for the young."
公共服务以三甲医院数与高校数衡量医疗与教育的可及性，二者等权，体现"病有所医、学有所教"。
The environment coefficient E acts as a multiplier (the environment is a hard threshold, so a poor environment discounts the whole); living convenience L and public services P are added (able to compensate each other); living convenience (0.55) is weighted slightly higher than public services (0.45), reflecting that "daily living" affects residential experience more directly than "long-cycle services."
环境系数 E 作为乘数（环境是硬门槛，环境差则整体打折）；生活便利 L 与公共服务 P 相加（可互补补偿）；生活便利权重（0.55）略高于公共服务（0.45），体现"日常起居"比"长周期服务"更直接影响居住体验。
三、指标与权重依据
| 指标 | 方向 | 权重 | 所属层 | 依据 |
|---|
| 空气质量 | 正向 | 环境·几何 | 环境 | WHO 健康城市；生态环境部空气质量 |
| 空气含氧量 | 正向 | 环境·几何 | 环境 | 高原低氧与宜居相悖的地域修正 |
| 气候舒适度 | 正向 | 环境·几何 | 环境 | 温湿度与四季宜人；EIU 气候维度 |
| 绿化覆盖率 | 正向 | 环境·几何 | 环境 | UN-Habitat 绿色公共空间；田园城市 |
| 交通拥堵 | 反向 | 生活 0.55 | 便利 | 通勤质量；EIU 基础设施维度 |
| 房价收入比 | 反向 | 生活 0.45 | 便利 | 居者有其屋；Mercer 住房维度 |
| 三甲医院数 | 正向 | 公共 0.5 | 服务 | EIU 医疗保健；Mercer 医疗维度 |
| 高校数 | 正向 | 公共 0.5 | 服务 | EIU 教育；Mercer 教育维度 |
四、环境短板效应（为何用几何平均）
The environment coefficient uses the geometric mean rather than the arithmetic mean: the arithmetic mean allows "one strength to cover a hundred flaws" — a city with excellent air but a bitterly cold climate could still earn a high environment score; the geometric mean, by contrast, embodies "the short board determines the whole," so any severe deficiency in a single environmental factor significantly lowers the environment coefficient. This is consistent with the ecological-civilization philosophy that "lucid waters and lush mountains are invaluable assets": the ecological environment is an irreplaceable, non-tradable hard constraint, in which air, oxygen, climate, and greenery are all indispensable.
环境系数采用几何平均而非算术平均：算术平均允许"一好遮百丑"——空气极佳但气候严寒的城市仍可能获得高环境分；几何平均则体现"短板决定整体"，任一环境要素的严重缺陷都会显著压低环境系数。这与"绿水青山就是金山银山"的生态文明理念一致：生态环境是不可替代、不可交易的硬约束，空气、含氧、气候、绿化缺一不可。
At the same time, because the environment coefficient is a multiplier (rather than an addend) in the overall model, a city with a poor environment will have its livability index discounted even if its living convenience and public services are strong — the environment is the precondition of "being eligible to talk about livability," not an optional "icing on the cake."
同时，环境系数作为整体模型的乘数（而非加数），意味着环境差的城市即便生活便利、公共服务再强，宜居指数也会被打折——环境是"有没有资格谈宜居"的前提，而非"锦上添花"的可选项。
五、数据来源与局限性
Air quality, air-oxygen content, traffic congestion, and housing-price-to-income ratio reuse the existing data standards of the existing city happiness index; climate comfort, green coverage, the number of Grade-A tertiary hospitals, and the number of universities are approximate values from public knowledge, marked "subject to official sources." This model focuses on the objective supply side (environment, convenience, public services) and does not include subjective satisfaction or dimensions that are hard to quantify such as urban safety and disaster risk; moreover, the approximate values carry errors. The ranking is for research and reference only.
空气质量、空气含氧量、交通拥堵、房价收入比复用既有城市幸福指数的既有数据口径；气候舒适度、绿化覆盖率、三甲医院数、高校数为公开知识近似值，标注"以官方为准"。本模型聚焦客观供给端（环境、便利、公共服务），不包含主观满意度与城市安全、灾害风险等难以量化的维度，且近似值存在误差，排名仅供研究与参考。
六、参考文献
- 吴良镛：《人居环境科学导论》，中国建筑工业出版社。
- 埃比尼泽·霍华德：《明日的田园城市》（Garden Cities of To-morrow）。
- Economist Intelligence Unit（EIU）：The Global Liveability Index。
- Mercer：Quality of Living City Ranking。
- United Nations Human Settlements Programme（UN-Habitat）：可持续城市与宜居性报告。
- 世界卫生组织（WHO）：健康城市倡议（Healthy Cities）。
- 生态环境部：全国城市空气质量报告。
- 国家统计局：年度国民经济与社会发展统计公报。