一、评价依据:为何不转载既有生活质量排名
In the field of urban quality of living there exist a few authoritative annual lists whose results are widely cited in policy and research. But their methodologies have three limitations: first, the dimensions over-weight "stability, medical care, education, infrastructure, and environment" while under-capturing income purchasing power and cultural provision; second, they rely mainly on expert scoring and surveys, with objective underlying data under-weighted; third, ranks remain entrenched over the years, making it hard to reflect real changes such as improvements in air quality and adjustments in housing policy.
城市生活质量领域存在少数权威年度榜单,其结果常被政策与研究广泛引用。但其方法论存在三点局限:其一,维度偏重"稳定性、医疗、教育、基建、环境",对收入购买力与文化供给的刻画不足;其二,以专家打分与调查为主,客观底层数据权重偏低;其三,名次常年固化,难以反映空气质量改善、住房政策调整等真实变化。
CPPPS adheres to "not copying ranks, but computing from underlying data itself": it directly collects underlying data on medical care, education, safety, environment, housing prices, income, infrastructure, culture, and smart-city development, designs its own weights and model, and produces a reproducible, auditable independent ranking.
CPPPS 坚持"不摘抄名次、用底层数据自算":直接采集医疗、教育、安全、环境、房价、收入、基础设施、文化、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 to [0,1]: scale indicators (population, GDP) are log-transformed and then min-max normalized to avoid megacity scale crushing small and medium cities; environment, housing prices, and income use reference-anchored standardization—air quality anchored to the WHO PM2.5 guideline (5 μg/m³ as excellent, 40 μg/m³ as poor), house-price-to-income ratio anchored to affordability references (3 as very affordable, 30 as severely unaffordable), and income log-transformed and anchored (US$15,000–100,000) to reflect the diminishing marginal contribution of income to quality of living (the Easterlin paradox). Score-type indicators (safety, medical care, education, infrastructure, culture, smart city—all 0–100 ratings) are normalized directly against a perfect score of 100, avoiding noise amplification from min-max normalization within the narrow band of elite cities. Inverse indicators are inverted, and air quality is given a lower floor of 0.10 after standardization.
全部指标先做标准化映射到 [0,1]:规模类指标(人口、GDP)先取对数再极差标准化,避免超大都市体量对中小城市的碾压;环境、房价、收入采用参考锚定标准化——空气质量锚定世界卫生组织 PM2.5 指南(5μg/m³为优、40μg/m³为差),房价收入比锚定可负担性参考(3 为很可负担、30 为严重不可负担),收入取对数后锚定(1.5万–10万美元)以体现收入对生活质量的边际递减(Easterlin 悖论)。评分型指标(安全、医疗、教育、基础设施、文化、智慧城市,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。反向指标取反向,空气质量标准化后取 0.10 下限。
规模 S = 0.50·log(人口)′ + 0.50·log(城市GDP)′
Scale characterizes a city's objective size, serving as the "base" of the evaluation. But scale itself is not the goal of quality of living—megacities tend to be congested, high-cost, and socially distant—so it carries the lowest weight in the composite score (8%).
规模刻画城市的客观体量,作为评价的"底座"。但规模本身并非生活质量目标——超大城市往往拥堵、高成本、人际关系疏离——故在综合分中权重最低(8%)。
质量 Q = (环境′)0.25·(安全′)0.25·(医疗′)0.20·(教育′)0.15·(基础设施′)0.15
Quality is the core of quality of living, accounting for 52% of the composite score. The five items use a weighted geometric mean rather than an arithmetic mean, reflecting the "bucket effect": any shortfall (such as poor air, weak public safety, or backward medical care) markedly lowers overall quality. Safety and environment carry the highest weights (25% each) because they are the hard bottom lines of quality of living—quality of living is not "one merit covering a hundred flaws", but "nothing can be missing".
质量是生活质量的核心,占综合分 52%。五项取加权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、医疗落后)都会显著压低整体质量。其中安全与环境权重最高(各 25%),因它们为生活质量的硬底线——生活质量不是"一好遮百丑",而是"缺一不可"。
创新 I = 智慧城市指数′
Innovation is measured by a "smart city / digital services" index of a city's digital governance, digital infrastructure, and digital service capability, accounting for 10% of the composite score—digitalization is becoming a new dimension of contemporary quality of living (online government services, smart mobility, telemedicine).
创新以"智慧城市/数字服务"指数衡量城市的数字治理、数字基础设施与数字服务能力,占综合分 10%——数字化正在成为当代生活质量的新维度(在线政务、智慧出行、远程医疗)。
贡献 C = 0.40·住房可负担′ + 0.30·收入购买力′ + 0.30·文化设施′
Contribution is a CPPPS signature dimension, accounting for 30% of the composite score, measuring the accessibility of public services that benefit ordinary citizens: the house-price-to-income ratio (inverted, the lower the more affordable) carries the highest weight, with per-capita income (purchasing power, log-transformed to reflect diminishing returns) and the inclusiveness of cultural facilities equally emphasized—these bear directly on whether ordinary citizens can "afford housing, afford to buy, and live a fulfilling life", rather than on a city's fame or financial strength.
贡献是 CPPPS 特色维度,占综合分 30%,衡量惠及普通市民的公共服务可及性:房价收入比(反向,越低越可负担)权重最高,人均收入(购买力,取对数体现边际递减)与文化设施普惠并重——这些直接关系普通市民"住得起、买得起、过得有滋有味",而非城市的名气或财力。
生活质量指数 = 100 × ( 0.08·S + 0.52·Q + 0.10·I + 0.30·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 | 0.50 | 城市体量底座;对数防头部垄断 |
| 规模 | 城市 GDP(取对数) | 正向 | 0.50 | 经济底座;对数防头部垄断 |
| 质量 | 空气质量(PM2.5) | 反向 | 几何 0.25 | 清洁空气是健康生活的基石 |
| 质量 | 治安/安全 | 正向 | 几何 0.25 | 居住安全感(硬底线) |
| 质量 | 医疗水平 | 正向 | 几何 0.20 | 病有所医;健康寿命 |
| 质量 | 教育水平 | 正向 | 几何 0.15 | 学有所教;人力资本 |
| 质量 | 基础设施 | 正向 | 几何 0.15 | 水电气网、市政与交通设施 |
| 创新 | 智慧城市/数字服务 | 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 | 人均收入(购买力,取对数) | 正向 | 0.30 | 物质生活水平;边际递减 |
| 贡献 | 文化设施 | 正向 | 0.30 | 精神生活与公共文化普惠 |
四、质量短板效应(为何用加权几何平均)
The Quality dimension uses a weighted geometric mean rather than an arithmetic mean: an arithmetic mean allows "one merit to cover a hundred flaws"—a city with excellent air but very poor public safety could still get a high average score; the geometric mean embodies "the shortest board determines the whole", where a serious deficiency in any quality element markedly lowers the quality score. Moreover, safety and environment carry the highest weights (25% each), further emphasizing that "safety and air are the hard bottom lines of quality of living": among environment, safety, medical care, education, and infrastructure, if any single item fails, citizens' daily experience is discounted.
质量维度采用加权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。且安全与环境权重最高(各 25%),进一步强调"安全与空气是生活质量的硬底线":环境、安全、医疗、教育、基建五者,任何一项不合格,都会让市民的日常体验打折。
五、数据来源与局限性
Population, GDP, air quality (annual average PM2.5), per-capita income, and house-price-to-income ratio use approximations of public common knowledge, while public safety, medical care, education, infrastructure, culture, and smart city are approximate subjective scores, all marked "subject to official figures"; for specific values, please refer to the official statistics of each country/city. This model focuses on the objective supply side, material living standards, and the accessibility of public services, and does not include hard-to-quantify dimensions such as climate disaster risk and subjective satisfaction; approximations carry some error, and the ranking is for research and reference only.
人口、GDP、空气质量(PM2.5 年均值)、人均收入、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、文化、智慧城市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、物质生活水平与公共服务可及性,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
- Mercer:Quality of Living City Ranking(方法参照,非名次转载)。
- Economist Intelligence Unit(EIU):The Global Liveability Index(方法参照,非名次转载)。
- United Nations Human Settlements Programme(UN-Habitat):可持续城市与人居环境报告。
- 世界卫生组织(WHO):健康城市倡议(Healthy Cities)与空气质量指南。
- 世界银行、国际货币基金组织:城市经济、收入与人口数据。
- 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)。