研究 01 · 评价模型Research 01 · Evaluation model

地铁成绩单The Metro Report Card

我们按 IMMC 格式为校内模拟赛写的一道题，英文原名 The Metro Report Card，中英双语，共五问。A problem we wrote in IMMC format for our own mock contest, in Chinese and English, with five tasks.

• IMMC 格式IMMC format
• 评价类模型Evaluation model
• 北京地铁Beijing metro

背景Background

过去二十年间，北京建成了世界上最长的地铁网络之一，最繁忙的日子里单日客运量超过一千万人次。城市之间比较地铁，经常使用几个醒目的数字：线路里程、车站数量、日客运量。每开通一条新线，这些数字就会发生变化。但线网更长，就一定更有利于市民吗？Over the past twenty years Beijing has built one of the longest metro networks in the world, carrying more than ten million passengers on its busiest days. Cities are usually compared by a few headline numbers: route length, number of stations, daily ridership. Every new line changes them. Yet does a longer network always serve the people who ride it better?

图中 25 条线路按 OpenStreetMap 的数据画成，未收录 S1 线、西郊线与亦庄 T1 线，只作示意。The 25 lines are drawn from OpenStreetMap data. The S1, Xijiao and Yizhuang T1 lines are not included; the diagram is illustrative.

五个任务Five tasks

1. 1选一个你认为最重要的方面，度量现有线网，看看是否真有「好线路」和「坏线路」。Choose the aspect that matters most, measure it for today’s network, and see whether good and bad lines really exist.
2. 2构建一个综合评价指标，并论证它的公式和系数。Build a composite metric and justify its formula and coefficients.
3. 3给北京地铁下结论：它在哪些方面失分最多？Reach a verdict on the Beijing metro: where does it lose the most?
4. 4为一条长度超过 10 公里的新线比较备选方案。Compare alternatives for a new line longer than 10 km.
5. 5归纳判断「好车站」的经验法则。Find rules of thumb for telling a good station from a bad one.

这是一道评价题Why it is an evaluation problem

评价类题目的常规路径，是先选指标，再定权重，最后排出先后。这道题的难处落在权重上：里程与客流都查得到，哪一项该占多大比重，须由参赛者自行论证。An evaluation problem is usually handled in the same order: pick the criteria, fix the weights, then rank. Here the work sits in the weights. Route length and ridership can be looked up; how much each of them should count is for the team to argue.

最简单的综合指标是加权和。z_ij 是第 i 条线在第 j 项指标上标准化后的得分，w_j 是这项指标的权重。公式本身不难写，排名却对 w 相当敏感：换一组权重，第一名就可能易主。任务 2 要求论证系数，原因在此。The simplest composite score is a weighted sum. Here z_ij is line i's standardized score on criterion j, and w_j is the weight of that criterion. Anyone can write the formula down. Rankings are often sensitive to w, and a different set of weights can put a different line on top, which is why Task 2 asks for the coefficients to be defended.

训练营第 1 至 4 周讲评价类模型，层次分析法、熵权法和 TOPSIS 都在里面。看训练营安排Evaluation models come up in weeks 1 to 4 of our training camp, AHP, the entropy weight method and TOPSIS among them. See the camp outline

为什么选地铁Why the metro

地铁的数据是公开的，乘车的体感则人人都有：哪条线拥挤，哪一站换乘要走很远。模型给出的排名，可以与这种体感相互印证；两者相左，多半是指标选得太窄。Metro data is out in the open, and everyone already has a feel for it. Which line is packed, which interchange means a long walk, anyone who rides knows. A model's ranking can be held against that feeling, and when the two disagree the criteria are often too narrow.

任务 4 把题目推到尚未建成的线路上。走向一旦定下，几十年都难以更改，比较方案时多算一步，大概是值得的。Task 4 pushes the problem onto a line that has not been built. Once an alignment is fixed it is hard to change for decades, so one more round of comparison is probably worth the effort.