📚 IGCSE Cambridge Politics: Formulae and Principles Quick Reference | IGCSE 剑桥政治：公式与定理速查手册
This quick reference handbook collects the essential formulae, rules and principles used in the Cambridge IGCSE Politics course. It is designed for revision, essay planning and source-based analysis. Each section gives a concise definition, a working rule or formula, and a comparison where relevant.
本速查手册汇集了剑桥 IGCSE 政治课程中常用的核心公式、规则与原理，适用于复习、论文规划和材料分析。每节提供简明定义、可操作的规则或公式，并在相关处进行比较。
1. Core Concepts: Authority, Power, Legitimacy | 核心概念：权力、权威与合法性
Power is the ability to make someone do something they would not otherwise do. Authority is the right to exercise power, and legitimacy is the acceptance of that right by those subject to it.
权力是使他人做出原本不会做出的行为的能力。权威是行使权力的正当资格，合法性则是指被统治者对这种资格的接受。
Weber’s typology distinguishes traditional, charismatic and legal-rational authority. In a modern state, legitimacy is strongest when it combines legal-rational procedures with fair outcomes.
韦伯的类型学区分了传统型、魅力型和法理型权威。在现代国家中，当法理程序与公正结果相结合时，合法性最强。
A simple revision rule: Power + right = authority; authority + acceptance = legitimacy.
速记规则：权力 + 正当资格 = 权威；权威 + 民众接受 = 合法性。
2. Sovereignty and the State | 主权与国家
A state has four features: population, territory, government and sovereignty. Sovereignty means ultimate legal authority within a territory, free from external control.
国家有四个要素：人口、领土、政府和主权。主权意味着在一国领土内拥有最高法律权威，不受外部控制。
Internal sovereignty refers to the state’s authority over domestic affairs; external sovereignty refers to recognition by other states and freedom in foreign policy.
对内主权指国家对国内事务的权威；对外主权指其他国家对该国的承认及其外交政策的自主性。
The principle of non-intervention follows from sovereignty: no state may legally intervene in the internal affairs of another without justification under international law.
不干涉原则源自主权：任何国家不得在没有国际法依据的情况下合法干涉他国内政。
Statehood = population + territory + government + sovereignty
3. Democracy and Representation | 民主与代议制
Democracy means rule by the people. Direct democracy gives citizens the vote on each decision; representative democracy gives citizens the vote to choose representatives who then make decisions.
民主意味着人民统治。直接民主让公民对每项决策投票；代议民主让公民投票选出代表，再由代表作出决策。
Accountability is the key link in representative democracy: representatives must face regular, free and fair elections, and citizens must be able to remove them peacefully.
问责是代议民主的关键环节：代表必须定期面对自由、公正的选举，公民应能通过和平方式将其撤换。
Majority rule must be limited by minority rights, otherwise democracy can become tyranny of the majority.
多数统治必须受到少数群体权利的限制，否则民主可能变成多数人的暴政。
Democratic legitimacy ≈ free elections + civil liberties + rule of law
4. Electoral Systems: Majoritarian vs Proportional | 选举制度：多数制与比例代表制
Electoral systems translate votes into seats. Majoritarian systems, such as first-past-the-post (FPTP), award victory to the candidate with the most votes in each district.
选举制度将选票转化为席位。多数制，例如简单多数制 (FPTP)，在每个选区中把胜利授予得票最多的候选人。
Proportional representation (PR) aims to match each party’s share of seats to its share of votes. Mixed systems, such as the additional member system, combine a constituency element with a proportional list element.
比例代表制 (PR) 旨在使各政党的席位比例与其得票比例相匹配。混合制，例如附加议员制，将选区代表制与比例名单制结合起来。
A candidate or party wins an outright majority only when votes exceed 50% of all valid votes cast; otherwise the result is a plurality or requires a second round.
候选人或政党只有在得票超过全部有效选票的 50% 时才获得绝对多数；否则结果为相对多数，或需要进行第二轮投票。
- FPTP: simple, strong constituency link, tends to produce wasted votes and disproportional outcomes. 简单多数制：操作简单、选区联系强，但容易产生废票和比例失真。
- PR: more proportional, encourages coalition, may weaken constituency link. 比例代表制：更具比例性、鼓励联合政府，但可能削弱选区联系。
5. Seat Allocation Formulae | 席位分配公式
Seat allocation formulae are used in proportional and single transferable vote systems. The two main quota methods are the Hare quota and the Droop quota.
席位分配公式用于比例代表制和单一可转移投票制。两种主要配额方法是黑尔配额和德鲁普配额。
Hare quota: Q = total valid votes ÷ total seats
The Hare quota is the simplest quota. A party or candidate needs that many votes to win one seat.
黑尔配额是最简单的配额。政党或候选人需要获得这一数量的选票才能赢得一个席位。
Droop quota: Q = ⌊ total valid votes ÷ (seats + 1) ⌋ + 1
The Droop quota is lower than the Hare quota and avoids wasting surplus votes, so it is widely used in STV elections.
德鲁普配额低于黑尔配额，可避免剩余选票浪费，因此广泛用于单一可转移投票制选举。
Divisor methods allocate seats by dividing each party’s vote total by a series of divisors. D’Hondt uses 1, 2, 3, … and Sainte-Laguë uses 1, 3, 5, …
除数法通过将每个政党的得票总数除以一系列除数来分配席位。汉狄法使用 1、2、3……，圣拉格法使用 1、3、5……
| Method 方法 | Divisors 除数 | Bias 倾向 |
| D’Hondt 汉狄法 | 1, 2, 3, … | favours larger parties 偏向大党 |
| Sainte-Laguë 圣拉格法 | 1, 3, 5, … | more neutral to small parties 对小党更中立 |
6. Duverger’s Law and Party Systems | 迪韦尔热定律与政党制度
Duverger’s law states that single-member plurality electoral systems tend to produce two-party systems, while proportional representation tends to produce multiparty systems.
迪韦尔热定律指出，单一选区相对多数制倾向于产生两党制，而比例代表制倾向于产生多党制。
The mechanical effect occurs because small parties cannot win seats under FPTP unless their support is geographically concentrated. The psychological effect occurs because voters and donors avoid wasting support on likely losers.
机械效应之所以发生，是因为小党在简单多数制下除非支持高度集中于某些地区，否则无法赢得席位。心理效应则因选民和资助者不愿把支持浪费在可能落败的政党上。
Effective number of parties: N = 1 ÷ Σ pᵢ²
A score close to 2 indicates a two-party system; a score above 3 normally indicates a fragmented multiparty system.
该指数接近 2 表示两党制；超过 3 通常表示分散的多党制。
7. Separation of Powers and Checks and Balances | 权力分立与制衡
The doctrine of separation of powers divides government into three branches: legislative, executive and judicial. Each branch has distinct functions, and no person should belong to more than one branch at the same time.
权力分立学说将政府分为三个分支：立法、行政和司法。每个分支有不同职能，同一人不应同时属于一个以上分支。
Checks and balances allow each branch to limit the others. For example, the legislature passes laws, the executive implements them, and the judiciary declares whether they are lawful.
制衡机制允许
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