📚 IGCSE CAIE Politics: Formula & Theorem Quick Revision Handbook | IGCSE CAIE 政治：公式定理速查手册
This handbook summarises the key definitions, models, rules and quantitative tools needed for IGCSE CAIE Politics. It is designed for quick revision before tests and exams.
本手册总结了 IGCSE CAIE 政治所需的关键定义、模型、规则和定量工具，专为考前快速复习设计。
1. Core Concepts: Power, Authority and Sovereignty | 核心概念：权力、权威与主权
Power is the ability to make others do something they would not otherwise do, even against their will.
权力是让他人做其原本不愿做的事情的能力，即使违背其意愿。
Authority is legitimate power: people obey because they accept that the ruler has the right to rule.
权威是合法的权力：人们服从是因为他们接受统治者拥有统治权。
Sovereignty means supreme legal and political authority within a state, free from external control.
主权指一个国家内部最高的法律和政治权威，不受外部控制。
Weber’s three types of authority are traditional, charismatic and legal-rational authority.
韦伯提出的三种权威类型是传统型、魅力型和法理型权威。
2. Forms of Government: Democracy vs Authoritarianism | 政体：民主与威权
Democracy is a system of government in which citizens participate, directly or through elected representatives, in decision-making.
民主是一种公民直接或通过选举代表参与决策的政府体制。
Free and fair elections, political competition, civil liberties and the rule of law are essential features of democracy.
自由公正的选举、政治竞争、公民自由和法治是民主的基本特征。
Authoritarianism is a form of government in which power is concentrated in one leader or a small elite, with little or no meaningful participation by citizens.
威权主义是权力集中于一个领导人或少数精英手中、公民几乎没有有意义参与的政府形式。
Key indicators of democracy include regular elections, universal suffrage, freedom of expression and an independent judiciary.
民主的关键指标包括定期选举、普选权、言论自由和独立的司法机构。
3. Constitutions and the Rule of Law | 宪法与法治
A constitution is a set of fundamental rules that establishes how a state is governed, the powers of institutions and the rights of citizens.
宪法是一套根本规则，规定国家的治理方式、机构的权力和公民的权利。
Constitutions may be codified, such as the United States Constitution, or uncodified, such as the United Kingdom’s constitutional arrangements.
宪法可以是成文的，如美国宪法，也可以是不成文的，如英国的宪法安排。
The rule of law means that everyone, including government officials, is subject to the law and that laws must be clear, public and fairly applied.
法治意味着包括政府官员在内的所有人都受法律约束，法律必须明确、公开并公平适用。
Constitutional supremacy means the constitution is the highest law, and any ordinary law that conflicts with it is invalid.
宪法至上意味着宪法是最高法律，任何与宪法冲突的普通法律均无效。
4. Separation of Powers and Checks & Balances | 三权分立与制衡
The separation of powers divides government into three branches: the legislature, the executive and the judiciary.
三权分立将政府分为三个部门：立法机关、行政机关和司法机关。
Each branch has distinct functions: making law, implementing law and interpreting law.
每个部门有不同职能：制定法律、执行法律和解释法律。
Checks and balances allow each branch to limit the powers of the others, preventing any single branch from becoming too powerful.
制衡机制允许各部门限制其他部门的权力，防止任何一个部门权力过大。
For example, a president may veto legislation, but the legislature may override the veto by a supermajority.
例如，总统可以否决议会通过的法律，但立法机关可以以绝对多数推翻否决。
5. Electoral Systems: Majoritarian vs Proportional | 选举制度：多数制与比例代表制
Electoral systems are the rules by which votes are translated into seats in a legislature.
选举制度是将选票转化为立法机关席位的规则。
Majoritarian systems, such as First Past the Post (FPTP), award seats to the candidate with the most votes in each constituency.
多数制，如简单多数制（FPTP），将席位授予每个选区得票最多的候选人。
Proportional representation (PR) allocates seats roughly in proportion to each party’s share of the vote.
比例代表制大致按照每个政党的得票比例分配席位。
FPTP tends to produce stable single-party governments, while PR tends to produce coalition governments and greater representation of smaller parties.
简单多数制往往产生稳定的单一政党政府，而比例代表制往往产生联合政府，并更好地代表小党。
Winner = candidate with max votes in district (FPTP)
席位比例 ≈ 得票比例 (PR)
6. Electoral Quotas and Seat Allocation Formulas | 选举配额与席位分配公式
A quota is the minimum number of votes a party needs to win one seat under a proportional list system.
配额是在比例名单制下，政党赢得一个席位所需的最低票数。
The Hare quota is the total number of valid votes divided by the total number of seats.
黑尔配额等于有效票总数除以席位总数。
The Droop quota is slightly lower and favours larger parties; it is widely used in single transferable vote systems.
德鲁普配额略低，对大党更有利；广泛用于可转移单票制。
The D’Hondt method allocates seats using divisors 1, 2, 3, 4, 5, while the Sainte-Laguë method uses divisors 1, 3, 5, 7, 9.
洪德法用除数 1、2、3、4、5 分配席位，而圣拉格法用除数 1、3、5、7、9 分配席位。
Hare quota = valid votes ÷ seats
Droop quota = [valid votes ÷ (seats + 1)] + 1
D’Hondt divisors: 1, 2, 3, 4, 5
7. Party Systems and Duverger’s Law | 政党制度与杜瓦杰定律
A party system is the number and relative strength of political parties that compete in a state.
政党制度是一个国家内竞争政党的数量和相对力量。
One-party, two-party and multi-party systems are the main types of party system.
一党制、两党制和多党制是政党制度的主要类型。
Duverger’s law states that single-member district plurality electoral systems tend to produce a two-party system.
杜瓦杰定律指出，单一选区相对多数选举制往往产生两党制。
Proportional representation tends to favour the development of multiple parties because small parties can win seats.
比例代表制往往有利于多党发展，因为小党也能赢得席位。
FPTP → two-party system (Duverger’s law)
8. Effective Number of Parties (ENP) | 有效政党数
The effective number of parties measures how many parties are significant after weighting by their vote shares or seat shares.
有效政党数根据政党得票率或席位率加权后衡量有多少个重要政党。
The Laakso-Taagepera index uses the sum of the squares of each party’s vote share.
拉克索-塔格佩拉指数使用各政党得票率平方之和。
A lower ENP indicates a concentrated party system; a higher ENP indicates fragmentation.
有效政党数越低，政党体制越集中；越高，政党体制越碎片化。
ENP = 1 ÷ Σ pᵢ²
where pᵢ is the vote share or seat share of party i.
其中 pᵢ 是政党 i 的得票率或席位率。
For example, if two parties each win 50%, then ENP = 1 ÷ (0.5² + 0.5²) = 2.0.
例如，若两个政党各得 50%，则 ENP = 1 ÷ (0.5² + 0.5²) = 2.0。
9. Political Spectrum: Left, Right and Centre | 政治光谱：左、右、中间
The political spectrum is a way of positioning political ideologies from left to right based on their view of equality, state intervention and social change.
政治光谱是根据对平等、国家干预和社会变革的看法将政治意识形态从左到右排列的方法。
Left-wing politics generally favours greater equality, redistribution of wealth and a larger role for the state in the economy.
左翼政治通常主张更大的平等、财富再分配和国家在经济中发挥更大作用。
Right-wing politics generally favours individual freedom, free markets, limited government and traditional values.
右翼政治通常主张个人自由、自由市场、有限政府和传统价值观。
Centrist politics combines elements of both left and right, often supporting pragmatism and compromise.
中间派政治结合左右两翼的元素，通常支持实用主义和妥协。
Left → Equality + State intervention
Right → Liberty + Free market
10. Human Rights and Civil Liberties | 人权与公民自由
Human rights are basic rights and freedoms that belong to every person simply because they are human.
人权是每个人因其为人而享有的基本权利和自由。
Civil liberties are protections against government actions, such as freedom of speech, religion and assembly.
公民自由是防止政府侵害的保护措施，如言论自由、宗教自由和集会自由。
The Universal Declaration of Human Rights (1948) sets out fundamental rights recognised internationally.
《世界人权宣言》（1948 年）规定了国际公认的基本权利。
Rights may be absolute, such as freedom from torture, or qualified, such as the right to liberty, which can be limited by law.
权利可以是绝对的，如免受酷刑，也可以是有限制的，如自由权可由法律加以限制。
11. International Organisations and Sovereignty | 国际组织与主权
International organisations are institutions formed by states to cooperate on shared issues such as peace, trade and development.
国际组织是国家为在和平、贸易和发展等共同议题上合作而建立的机构。
The United Nations is the main global organisation, with principal organs including the General Assembly and the Security Council.
联合国是主要的全球性组织，其主要机关包括大会和安全理事会。
Membership of international organisations often requires states to pool some sovereignty, meaning they accept collective decisions.
加入国际组织往往要求国家让渡部分主权，即接受集体决定。
Supranational organisations, such as the European Union, have the power to make laws that bind member states directly.
超国家组织，如欧洲联盟，有权制定直接约束成员国的法律。
12. Revision Checklist and Key Formulae | 复习清单与关键公式
Before the exam, make sure you can define power, authority, sovereignty, democracy, rule of law and human rights.
考试前，确保你能定义权力、权威、主权、民主、法治和人权。
You should also be able to compare majoritarian and proportional electoral systems and explain their effects on party systems.
你还应该能够比较多数制和比例代表制选举制度，并解释它们对政党制度的影响。
Memorise the key formulae: Hare quota, Droop quota and the effective number of parties.
记住关键公式：黑尔配额、德鲁普配额和有效政党数。
| Formula | 公式 | Use |
|---|---|---|
| Hare quota = valid votes ÷ seats | 黑尔配额 = 有效票数 ÷ 席位数 | Seat allocation |
| Droop quota = [valid votes ÷ (seats + 1)] + 1 | 德鲁普配额 = [有效票数 ÷ (席位数 + 1)] + 1 | STV seats |
| ENP = 1 ÷ Σ pᵢ² | 有效政党数 = 1 ÷ Σ pᵢ² | Party system fragmentation |
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