📚 IGCSE Cambridge Politics: Formula & Theorem Quick Reference Handbook | IGCSE 剑桥政治：公式定理速查手册
Political science, unlike mathematics, does not operate with fixed formulas, but it is built upon recurring principles, models, and mechanisms that function much like theorems in explaining how power is distributed, exercised, and challenged. This quick reference handbook presents the essential ‘formulas’ of IGCSE Cambridge Politics – from definitions of sovereignty and legitimacy, to electoral system calculations, ideological spectra, and models of governance. Each entry follows a paired bilingual format, enabling rapid revision and deep cross-linguistic understanding. Use these concise formulations to decode political arguments, predict outcomes, and excel in your examinations.
政治学虽然不像数学那样依赖公式，但它建立在反复出现的原理、模型和机制之上，这些原理和机制在解释权力如何分配、行使和受到挑战时，发挥着类似定理的作用。本速查手册呈现 IGCSE 剑桥政治的核心“公式”——从主权与合法性的定义，到选举制度的计算，再到意识形态光谱和治理模式。每个条目都采用中英对照的形式，既便于快速复习，又能加深跨语言的理解。运用这些精炼的表述来解读政治论点、预判结果，并在考试中脱颖而出。
1. Power, Authority and Legitimacy | 权力、权威与合法性
Power is the ability to make others do something they would not otherwise do. It can be exercised through coercion (force), influence (persuasion), or authority (recognised right).
权力是让他人做其本不会做的事情的能力。它可以通过强制（武力）、影响（说服）或权威（公认的权利）来行使。
Authority is legitimate power – power that is accepted as rightful by those subjected to it. Legitimacy, according to Max Weber, rests on three pure types: traditional (custom, hereditary), charismatic (personal magnetism), and legal-rational (rules, bureaucracy).
权威是合法化的权力——也就是被行使对象视为正当而接受的权力。根据马克斯·韦伯的理论，合法性建立在三种纯粹类型之上：传统型（习俗、世袭）、超凡魅力型（个人感召力）和法理型（规则、官僚制）。
The ‘social contract’ formula: Citizens trade some freedom to a government in return for security and order. If the government breaks the contract, citizens may resist. Think of it as: Freedom surrendered → Protection received; Protection failed → Obedience withdrawn.
“社会契约”公式：公民将部分自由让渡给政府，以换取安全与秩序。如果政府违背契约，公民可以抵抗。可以理解为：让渡自由 → 获得保护；保护失效 → 不再服从。
2. Sovereignty and the State | 主权与国家
A state has four essential features: a defined territory, a permanent population, a government, and sovereignty (the capacity to enter into relations with other states). Sovereignty means the supreme and unrestricted power to make laws and enforce them within a territory.
国家有四个基本要素：确定的领土、常住人口、政府以及主权（与其他国家建立关系的能力）。主权意味着在一国领土内制定和执行法律的最高且不受限制的权力。
Internal sovereignty refers to the state’s ultimate authority over all individuals and associations within its borders. External sovereignty means that the state is not subject to any external authority and is recognised as independent by other states.
对内主权指国家对其境内所有个人和团体的最终权威。对外主权则意味着国家不受任何外部权威的支配，并被其他国家承认为独立体。
Pooled sovereignty: In the European Union, member states transfer some law-making powers to shared institutions. The formula: National sovereignty – transferred competences = pooled sovereignty.
共享主权：在欧盟，成员国将部分立法权移交给共同机构。公式为：国家主权 – 让渡的权能 = 共享主权。
3. Government Systems: Parliamentary vs Presidential | 政体：议会制与总统制
In a parliamentary system, the executive (prime minister and cabinet) is drawn from and accountable to the legislature (parliament). The head of state (monarch or president) is separate from the head of government. A vote of no confidence can force the government to resign or call an election.
在议会制中，行政机关（总理和内阁）产生于立法机关（议会）并对其负责。国家元首（君主或总统）与政府首脑分开。不信任投票可以迫使政府辞职或提前大选。
In a presidential system, the president is both head of state and head of government, elected separately from the legislature. The president and legislature have fixed terms and independent mandates; no vote of confidence applies. The separation of powers is more rigid.
在总统制中，总统既是国家元首又是政府首脑，由选民单独选举产生，与立法机关分开。总统和立法机关都有固定任期和独立的授权；不适用不信任投票。权力分立更为严格。
Key diagram: Parliamentary: Executive ← confidence → Legislature; Presidential: Executive — separated — Legislature.
关键图示：议会制：行政机关 ← 信任关系 → 立法机关；总统制：行政机关 —— 分立 —— 立法机关。
4. Electoral Systems: Plurality, Majority and Proportional | 选举制度：简单多数、绝对多数与比例代表制
First-Past-the-Post (FPTP): The candidate with the most votes in a single-member constituency wins, even if they do not secure an absolute majority (>50%). Formula: Winner = max(votesi). It tends to produce a two-party system and strong, single-party governments, but can distort the popular vote.
简单多数制（FPTP）：在单议席选区中，得票最多的候选人获胜，即便未获得绝对多数（超过 50%）。公式：胜者 = 最高票数者。它往往导致两党制和强势的一党政府，但可能扭曲民意。
Proportional Representation (PR): Seats are allocated in proportion to the votes each party receives. A common threshold formula: a party must gain at least, say, 5% of the national vote to enter parliament. PR yields multi-party systems and coalition governments, offering greater representativeness but potentially weaker governance.
比例代表制（PR）：议席按照各党所获选票的比例进行分配。常见的门槛公式：一个政党必须至少获得全国选票的 5% 才能进入议会。比例代表制产生多党制和联合政府，代表性更强，但治理可能更弱。
The effective number of parties can be estimated by the Laakso-Taagepera index: N = 1 / Σ(pi²), where pi is the seat share of party i. A higher N indicates greater fragmentation.
有效政党数目可以通过拉索-塔格佩拉指数估算：N = 1 / Σ(pi²)，其中 pi 是政党 i 的议席比例。N 值越高，表明政党体系越碎片化。
5. Political Ideologies: The Left-Right Spectrum | 政治意识形态：左右光谱
Political ideologies are often placed on a spectrum from left (advocating for greater equality, state intervention, collective provision) to right (emphasising individual freedom, free markets, traditional values). The classic formula: Left: equality > liberty; Right: liberty > equality.
政治意识形态通常被置于从左边（主张更大的平等、国家干预、集体供给）到右边（强调个人自由、自由市场、传统价值）的光谱上。经典公式：左派：平等 优先于 自由；右派：自由 优先于 平等。
Liberalism: Core theorem – the individual is rational and the primary unit of society. Limited government, rule of law, negative freedom (freedom from interference). Economic liberalism adds free-market capitalism.
自由主义：核心定理——个人是理性的，是社会的基本单位。有限政府、法治、消极自由（免于干涉的自由）。经济自由主义还加上自由市场资本主义。
Socialism: Core theorem – collective ownership or control of the means of production reduces exploitation. Emphasis on positive freedom (freedom to fulfil one’s potential) and social justice.
社会主义：核心定理——生产资料的集体所有或控制能减少剥削。强调积极自由（实现自身潜能的自由）和社会正义。
Conservatism: Core theorem – society is an organic, fragile entity. Change should be incremental, guided by tradition, pragmatism, and respect for authority and property.
保守主义：核心定理——社会是一个有机的、脆弱的实体。变革应是渐进的，并受传统、实用主义以及对权威和财产的尊重的指导。
6. Democracy: Direct, Representative and Liberal | 民主：直接、代议与自由民主
Democracy means ‘rule by the people’. Direct democracy: citizens themselves make decisions on policy initiatives, usually through referendums. Representative democracy: citizens elect representatives who make decisions on their behalf. The formula of representation: 1 citizen = 1 vote; 1 representative = many citizens’ delegated authority.
民主意为“人民统治”。直接民主：公民自己通过投票（通常是全民公投）对政策倡议做出决定。代议制民主：公民选举代表，由代表代为决策。代议的公式：1 个公民 = 1 张选票；1 名代表 = 众多公民的委托授权。
Liberal democracy combines representative democracy with protections for individual rights, rule of law, and constraints on government power (constitutionalism, separation of powers, free press). Robert Dahl’s criteria for polyarchy (effectively liberal democracy) include: elected officials, free and fair elections, inclusive suffrage, right to run for office, freedom of expression, alternative information, and associational autonomy.
自由民主制将代议制民主与对个人权利的保护、法治以及对政府权力的约束（宪政主义、权力分立、新闻自由）结合起来。罗伯特·达尔提出的多头政体（即实质上的自由民主）标准包括：选举产生的官员、自由公正的选举、包容性的普选权、竞选公职的权利、表达自由、可选择的信息来源以及结社自主。
7. Judiciary and the Rule of Law | 司法机关与法治
The rule of law is a foundational principle stating that all individuals and institutions, including the government, are subject to and accountable under the law. Key formulas: Law > any individual; No punishment without a pre-existing law (nullum crimen sine lege).
法治是一项基本原则，它表明所有个人和机构，包括政府，都受法律约束并依法负责。关键公式：法律 > 任何个人；没有事先存在的法律，不得施加惩罚（法无明文不为罪）。
Judicial independence means courts can decide cases impartially, free from government or political pressure. Judicial review is the power of courts to invalidate laws or government actions that violate a constitution. This creates a check: Legislative/Executive act → Judicial review → Compliance with constitution.
司法独立意味着法院可以公正地裁决案件，不受政府或政治压力的影响。司法审查是法院宣告违反宪法的法律或政府行为无效的权力。这就形成了一个制衡：立法/行政行为 → 司法审查 → 合宪性。
In some systems, the judiciary can be considered a ‘third chamber’ of government, enforcing the superior law of the constitution against the elected branches.
在某些制度中，司法机关可被视为政府的“第三院”，以其上位法——宪法——来约束民选分支。
8. Political Participation and Pressure Groups | 政治参与和压力集团
Political participation encompasses voting, joining a party, protest, and digital activism. The classic participation ladder: from non-participation → passive participation (voting) → active participation (campaigning) → citizen-initiated participation (stand for office, referendums).
政治参与包括投票、加入政党、抗议和数字行动主义。经典的参与阶梯：从不参与 → 被动参与（投票）→ 主动参与（竞选活动）→ 公民发起的参与（竞选公职、发起公投）。
Pressure groups are organised groups that seek to influence government policy without seeking office. Insiders work closely with government, relying on expert knowledge and access; outsiders use public campaigns, direct action, and media to apply pressure. The formula of influence: Insider: access + expertise = policy impact; Outsider: mobilisation + visibility = agenda-setting.
压力集团是有组织的团体，旨在影响政府政策而不寻求担任公职。圈内集团与政府密切合作，依赖专业知识和接触渠道；圈外集团利用公众活动、直接行动和媒体施加压力。影响力公式：圈内：渠道 + 专业知识 = 政策影响；圈外：动员 + 能见度 = 议程设置。
The ‘iron triangle’ in policy-making: Congressional committees, bureaucratic agencies, and interest groups form a stable, symbiotic triangle that dominates a policy area.
政策制定中的“铁三角”：国会委员会、官僚机构和利益集团形成一个稳定、共生的三角，主导着某个政策领域。
9. Constitutions: Codified vs Uncodified | 宪法：成文与不成文
A codified (written) constitution is a single authoritative document that sets out the fundamental rules, limits government power, and is entrenched (harder to amend than ordinary law). Formula: Codified constitution = supreme law + entrenchment.
成文宪法是一份具有权威性的单一文件，规定了基本规则、限制政府权力，并具有刚性（比普通法律更难修改）。公式：成文宪法 = 最高法 + 刚性条款。
An uncodified (unwritten) constitution exists where constitutional rules are found across several documents, conventions, statutes, and judicial decisions. The United Kingdom has an uncodified constitution, meaning that Parliament, in legal theory, can make or unmake any law – parliamentary sovereignty.
不成文宪法是指宪法性规则分散在若干文件、惯例、法规和司法判例中的情况。英国拥有不成文宪法，这意味着在法律理论上，议会可以制定或废除任何法律——即议会主权。
The separation of powers in a constitution can be either fused (parliamentary system) or strictly separated (presidential system), while federal systems (USA, Germany) divide power geographically between central and state governments – a vertical dimension of power distribution.
宪法中的权力分立可以是融合的（议会制），也可以是严格分离的（总统制）；而联邦制（美国、德国）则在地域上分割中央与州政府的权力——这是一种权力分配的垂直维度。
10. International Relations: Realism and Liberalism | 国际关系：现实主义与自由主义
Realism sees international politics as a struggle for power among states in an anarchic system. Formula: Anarchy (no world government) → self-help system → states prioritise security → balance of power. Key realist theorem: states are unitary, rational actors, and morality has a limited place.
现实主义将国际政治视为无政府体系中各国之间争夺权力的斗争。公式：无政府状态（无世界政府）→ 自助体系 → 国家优先考虑安全 → 均势。现实主义的核心定理：国家是单一、理性的行为体，道德的作用有限。
Liberalism argues that cooperation is possible through international institutions, economic interdependence, and the spread of democracy. Formula: Democracy + trade + institutions → reduced conflict (democratic peace theory). States are not the only actors; multinational corporations, NGOs, and intergovernmental organisations shape outcomes.
自由主义认为，通过国际制度、经济相互依存和民主的传播，合作是可能的。公式：民主 + 贸易 + 制度 → 减少冲突（民主和平论）。国家并非唯一的行为体；跨国公司、非政府组织和政府间组织都会影响结果。
The balance of power can be bipolar, multipolar, or unipolar, shaping strategic calculations. The security dilemma: when one state increases its military strength for defence, others perceive it as a threat, leading to arms races.
均势可以是两极、多极或单极的，并影响战略计算。安全困境：当一个国家为了防御而增强军事实力时，其他国家将其视为威胁，从而引发军备竞赛。
11. Human Rights and International Law | 人权与国际法
Human rights are inherent to all human beings, regardless of nationality, race, sex, or any other status. The Universal Declaration of Human Rights (1948) forms the basis, followed by binding covenants on civil/political rights and economic/social/cultural rights. The core formula: State sovereignty ≠ unlimited; it must respect universal human rights.
人权是所有人固有的权利，不论国籍、种族、性别或其他身份。1948 年的《世界人权宣言》奠定了基础，随后又有了具有约束力的《公民权利和政治权利国际公约》和《经济、社会及文化权利国际公约》。核心公式：国家主权 ≠ 无限；它必须尊重普遍人权。
International humanitarian law (laws of war) sets out the rules for conduct in armed conflict: distinction (between combatants and civilians), proportionality (force must not be excessive to military advantage), and precaution. Violations can constitute war crimes.
国际人道法（战争法）规定了武装冲突中的行为规则：区分（战斗员与平民）、比例（武力不得超出军事利益所必需）和预防。违反这些规则可能构成战争罪。
The International Criminal Court (ICC) prosecutes individuals for genocide, crimes against humanity, war crimes, and the crime of aggression. It complements national courts: it only acts when states are unable or unwilling to genuinely prosecute.
国际刑事法院（ICC）对灭绝种族罪、危害人类罪、战争罪和侵略罪行进行追究。它是对国内法院的补充：仅当国家不能或不愿真诚起诉时，它才会采取行动。
12. Political Economy: Capitalism, Socialism and the Mixed Economy | 政治经济学：资本主义、社会主义与混合经济
Capitalism is an economic system based on private ownership of the means of production, market competition, and profit motive. The ‘invisible hand’ theorem (Adam Smith): individuals pursuing self-interest unintentionally benefit society as a whole through market mechanisms.
资本主义是基于生产资料私有制、市场竞争和利润动机的经济体系。“看不见的手”定理（亚当·斯密）：个人在追求自身利益时，会通过市场机制无意中为社会整体带来好处。
State socialism involves public ownership, central planning, and production for use rather than profit. The formula: State planning + communal goals → allocation of goods and services. The mixed economy combines market mechanisms with government intervention to correct market failures, provide public goods, and redistribute income.
国家社会主义涉及公有制、中央计划和为使用而非利润而生产。公式：国家计划 + 公共目标 → 商品与服务的分配。混合经济则将市场机制与政府干预相结合，以纠正市场失灵、提供公共产品和再分配收入。
The welfare state operates on the principle that the state has a responsibility to secure a basic minimum standard of living for all citizens, often summarised as: Taxation + redistribution = social safety net.
福利国家根据这样的原则运作：国家有责任保障所有公民的基本最低生活水平，常被概括为：税收 + 再分配 = 社会安全网。
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