Parliamentary Seat Allocation: Ratio, Percentage and Fair Division | 议会席位分配：比例、百分比与公平划分

📚 Parliamentary Seat Allocation: Ratio, Percentage and Fair Division | 议会席位分配：比例、百分比与公平划分

Parliamentary elections convert millions of votes into a fixed number of seats. Although Edexcel A-Level Mathematics does not have a unit called “Parliament”, the underlying mathematics is firmly rooted in ratio, proportion, percentage error, rounding and algorithms. This article uses the apportionment of parliamentary seats as a modelling context to strengthen the skills needed for pure and applied papers.

议会选举将数百万张选票转化为固定数量的席位。虽然 Edexcel A-Level 数学没有一个叫 “Parliament” 的单元，但其背后的数学牢牢扎根于比率、比例、百分比误差、取整和算法。本文以议会席位分配为建模背景，强化纯数和应用卷所需的技能。

1. From Votes to Seats: The Core Problem | 从选票到席位：核心问题

Suppose a parliament has S seats and n parties receive votes P₁, P₂, …, Pₙ. The total number of votes is P = P₁ + P₂ + … + Pₙ. The exact fair share of seats for party i is the quota qᵢ = (Pᵢ ÷ P) × S. This quota is usually not an integer, so a rounding rule is needed.

假设一个议会有 S 个席位，n 个政党获得的票数为 P₁、P₂、…、Pₙ。总票数为 P = P₁ + P₂ + … + Pₙ。第 i 党的精确公平席位份额为配额 qᵢ = (Pᵢ ÷ P) × S。这个配额通常不是整数，因此需要一条取整规则。

qᵢ = (Pᵢ ÷ P) × S

2. Quota and Fair Share | 配额与公平份额

A party’s quota is its exact proportional entitlement. For example, if a party wins 40% of the vote and there are 100 seats, its quota is 40 seats. If the quota is 32.7, no party can receive 32.7 seats, so allocation methods must assign

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