一、评价依据:为何不转载既有宜居排名
There are a few authoritative rankings in the field of global livability, and their results are often widely cited by media and policy. However, their methodology has three limitations: first, the dimensions are concentrated in "stability, healthcare, education, infrastructure, and environment," with insufficient coverage of the accessibility of public services for ordinary citizens (housing, transport, green space); second, they rely mainly on expert scoring and surveys, giving low weight to objective underlying data; and third, their rankings are long-frozen and cannot reflect real changes such as air quality improvement or housing policy adjustments.
全球宜居排名领域存在少数权威榜单,其结果常被媒体与政策广泛引用。但其方法论存在三点局限:其一,维度集中于"稳定性、医疗、教育、基建、环境",对普通市民的公共服务可及性(住房、交通、绿地)覆盖不足;其二,以专家打分与调查为主,客观底层数据权重偏低;其三,排名常年固化,难以反映空气质量改善、住房政策调整等真实变化。
CPPPS adheres to the principle of "not copying rankings, but computing from underlying data": it directly collects underlying data on air quality, public security, healthcare, education, infrastructure, housing prices, public transport, culture and green space, and smart-city level, and independently designs weights and models to produce a reproducible and auditable independent ranking.
CPPPS 坚持"不摘抄名次、用底层数据自算":直接采集空气质量、治安、医疗、教育、基建、房价、公共交通、文化绿地、智慧化等底层数据,自行设计权重与模型,产出可复现、可审计的独立排名。
二、数学结构:四维指标体系
All indicators are first standardized and mapped to [0,1]: quantitative indicators (population, GDP, PM2.5, house-price-to-income ratio) use range standardization (large-span scale indicators are first log-transformed to avoid megacities crushing small and medium-sized cities by size); rating-type indicators (safety, healthcare, education, infrastructure, smart city, public transport, culture and green space—all rated 0-100) are normalized directly against a full score of 100, to avoid amplifying noise by range-standardizing within the narrow band of elite cities. Negative indicators (PM2.5, house-price-to-income ratio) are inverted.
全部指标先做标准化映射到 [0,1]:数量型指标(人口、GDP、PM2.5、房价收入比)采用极差标准化(规模类大跨度指标先取对数,避免超大城市体量对中小城市的碾压);评分型指标(安全、医疗、教育、基建、智慧城市、公共交通、文化绿地,均为 0-100 评级)以满分 100 直接归一,避免在精英城市窄区间内做极差标准化导致噪声放大。反向指标(PM2.5、房价收入比)取反向。
规模 S = 0.40·log(人口)′ + 0.60·log(城市GDP)′
Scale captures the objective size of a city, serving as the "base" of evaluation. But scale itself is not the goal of livability—small cities are often more livable—so it carries the lowest weight (10%) in the composite score.
规模刻画城市的客观体量,作为评价的"底座"。但规模本身并非宜居目标——小城市往往更宜居——故在综合分中权重最低(10%)。
质量 Q = (空气′ × 安全′ × 医疗′ × 教育′ × 基础设施′)1/5
Quality is the core of livability, accounting for 50% of the composite score. The five items use geometric mean rather than arithmetic mean, reflecting the "barrel effect": any shortcoming (such as poor air or weak public security) will significantly drag down overall quality—livability is not "one strength covering all flaws," but "every element indispensable." After standardization, air quality is floored at 0.10 to prevent a single zero item from collapsing the whole to zero.
质量是宜居的核心,占综合分 50%。五项取几何平均而非算术平均,体现"木桶效应":任一短板(如空气差、治安弱)都会显著压低整体质量——宜居不是"一好遮百丑",而是"缺一不可"。空气质量标准化后取 0.10 下限,防止单项为零导致整体塌缩为零。
创新 I = 智慧城市′
Innovation uses the "smart city" index to measure a city's digital governance, digital infrastructure, and innovation-driven capability, accounting for 15% of the composite score.
创新以"智慧城市"指数衡量城市的数字治理、数字基础设施与创新驱动能力,占综合分 15%。
贡献 C = 0.40·住房可负担′ + 0.30·公共交通′ + 0.30·文化绿地′
Contribution is a distinctive CPPPS dimension, accounting for 25% of the composite score, measuring public services that benefit ordinary citizens: the house-price-to-income ratio (inverted; the lower, the more affordable) carries the highest weight, with public transport and culture/green space equally weighted—these directly relate to the fairness and well-being of citizens' daily lives, rather than the city's fame or financial resources.
贡献是 CPPPS 特色维度,占综合分 25%,衡量惠及普通市民的公共服务:房价收入比(反向,越低越可负担)权重最高,公共交通与文化绿地并重——这些直接关系市民日常生活的公平与福祉,而非城市的名气或财力。
宜居指数 = 100 × ( 0.10·S + 0.50·Q + 0.15·I + 0.25·C )
三、指标与权重依据
| 维度 | 指标 | 方向 | 权重 | 依据 |
| 规模 | 都市圈人口(取对数) | 正向 | 0.40 | 城市体量底座;对数防头部垄断 |
| 规模 | 城市 GDP(取对数) | 正向 | 0.60 | 经济底座;对数防头部垄断 |
| 质量 | 空气质量(PM2.5) | 反向 | 几何 | 健康城市;清洁空气是宜居基石 |
| 质量 | 治安/安全 | 正向 | 几何 | 居住安全感 |
| 质量 | 医疗水平 | 正向 | 几何 | 病有所医;健康寿命 |
| 质量 | 教育水平 | 正向 | 几何 | 学有所教;人力资本 |
| 质量 | 基础设施 | 正向 | 几何 | 水电气网、市政设施 |
| 创新 | 智慧城市指数 | 正向 | 1.00 | 数字治理与创新驱动 |
| 贡献 | 房价收入比 | 反向 | 0.40 | 居者有其屋;住房可负担 |
| 贡献 | 公共交通 | 正向 | 0.30 | 通勤与出行普惠 |
| 贡献 | 文化绿地 | 正向 | 0.30 | 公园绿地与文化设施普惠 |
四、质量短板效应(为何用几何平均)
The Quality dimension uses geometric mean rather than arithmetic mean: arithmetic mean allows "one strength to cover all flaws"—a city with excellent air but very poor public security could still obtain a high average score—whereas geometric mean reflects "the weakest link determines the whole," so a serious deficiency in any quality element significantly lowers the quality score. This is consistent with the view that "livability is a hard constraint where every element is indispensable": if any one of air quality, safety, healthcare, education, or infrastructure is substandard, citizens' living experience is discounted.
质量维度采用几何平均而非算术平均:算术平均允许"一好遮百丑"——空气极佳但治安很差的城市仍可能获得高平均分;几何平均则体现"短板决定整体",任一质量要素的严重缺陷都会显著压低质量分。这与"宜居是缺一不可的硬约束"一致:空气质量、安全、医疗、教育、基建五者,任何一项不合格,都会让市民的居住体验打折。
五、数据来源与局限性
Population, GDP, air quality (annual average PM2.5), and house-price-to-income ratio use approximate values from publicly available common knowledge, while public security, healthcare, education, infrastructure, smart city, public transport, and culture/green space use approximate subjective scores, all marked "subject to official figures"—please refer to the official statistics of each country/city for specific values. This model focuses on the objective supply side and the accessibility of public services, and does not include climate disaster risk, subjective satisfaction, and other dimensions that are hard to quantify; approximate values also contain errors, so the ranking is for research and reference only.
人口、GDP、空气质量(PM2.5 年均值)、房价收入比等采用公开常识近似值,治安、医疗、教育、基础设施、智慧城市、公共交通、文化绿地等为主观评分近似值,均标注"以官方为准",具体数值请以各国/城市官方统计为准。本模型聚焦客观供给端与公共服务可及性,不包含气候灾害风险、主观满意度等难以量化的维度,且近似值存在误差,排名仅供研究与参考。
六、参考文献
- Economist Intelligence Unit(EIU):The Global Liveability Index(方法参照,非名次转载)。
- Mercer:Quality of Living City Ranking(方法参照,非名次转载)。
- 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)。
- 世界银行、国际货币基金组织:城市经济与人口数据。
- 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)。