📚 IGCSE AQA Politics: Formula & Theorem Quick Reference Guide | IGCSE AQA 政治：公式定理速查手册
This quick reference guide brings together the essential calculation formulas and established theorems encountered in IGCSE AQA Politics. From electoral quotas and seat allocation methods to foundational principles of democracy, each entry is paired with a concise explanation in both English and Chinese to speed up revision.
本速查手册汇集了 IGCSE AQA 政治学中的核心计算公式与经典定理。从选举配额、席位分配方法到民主制度的基本原则，每一条目均配有中英双语简明解析，帮助快速梳理考点。
1. Droop Quota | 德鲁普配额
Q = ⌊ V ÷ (S + 1) ⌋ + 1
The Droop quota determines the minimum number of votes a candidate needs to secure a seat under the Single Transferable Vote (STV) system. It ensures that at most S candidates can reach the threshold, preventing more winners than available seats.
德鲁普配额用于确定在单一可转移票制 (STV) 下候选人赢得席位所需的最低票数。该公式确保最多只有与席位数量相等的候选人能达到门槛，避免胜出者多于席位。
V represents the total valid votes cast; S is the number of seats to be filled.
V 表示总有效票数；S 表示待填补的席位数量。
The formula adds 1 after taking the integer floor of V/(S+1), making the quota as low as possible while maintaining exclusivity.
该公式在对 V/(S+1) 取整数下限后加 1，使配额尽可能低的同时保持排他性。
2. Hare Quota | 黑尔配额
Q = V ÷ S
The Hare quota is the simplest proportional quota, used in some STV elections and for calculating ideal representation. It represents the exact proportion of votes needed to win one seat under perfect proportionality.
黑尔配额是最简单的比例配额，用于某些 STV 选举及计算理想代表数。它表示在完全比例代表制下赢得一个席位所需的精确票数比例。
Unlike the Droop quota, the Hare quota does not add 1, so it can allow more candidates to reach the quota than there are seats, requiring additional tie-breaking rules.
与德鲁普配额不同，黑尔配额不加 1，因此可能导致达到配额的人数多于席位，需要额外的打破平局规则。
It is often used as a benchmark for measuring disproportionality in electoral systems.
它常被用作衡量选举制度不比例性的基准。
3. D'Hondt Method | 洪德法
Seats awarded to highest values of V / 1, V / 2, V / 3, …
The D'Hondt method is a highest-averages formula used to allocate seats in party-list proportional representation. Each party's total votes are divided successively by 1, 2, 3, and so on, and the resulting quotients are ranked. Seats go to the largest quotients.
洪德法是一种最高平均数方法，用于政党名单比例代表制中的席位分配。各党的总票数依次除以 1、2、3…，所得商值从大到小排序，席位依次分配给商值最大的政党。
It tends to favour larger parties slightly more than the Sainte-Laguë method, because divisors start at 1 not 0.5.
它比圣拉古法略微有利于大党，因为除数从 1 开始而非 0.5。
In practice, for a party with V votes, its quotients are V/1, V/2, V/3, … U̳p to the total number of seats.
实际操作中，对于得票数为 V 的政党，其商值序列为 V/1、V/2、V/3… 直到席位数满额。
4. Simple Majority Threshold | 简单多数门槛
T = ⌊Vtotal ÷ 2⌋ + 1
Under First Past the Post (FPTP) in single-member constituencies, a candidate wins by securing more votes than any other single candidate. The majority threshold needed to guarantee victory without any other condition is one more than half of all votes cast.
在单席位选区的简单多数制 (FPTP) 下，候选人获得超过其他所有候选人中最高票数即获胜。不附加其他条件时，确保获胜的绝对门槛为总票数一半加一。
Vtotal is the total valid votes in the constituency.
Vtotal 指该选区的总有效票数。
Because FPTP does not require an absolute majority, a candidate can win with less than 50% of the vote, but the threshold formula shows the absolute-majority safety line.
由于 FPTP 不要求绝对多数，候选人可能以少于 50% 的票数胜出，但该门槛公式表明了绝对多数的安全线。
5. Voter Turnout Calculation | 投票率计算
Turnout % = (C ÷ E) × 100
Voter turnout measures the proportion of registered electors who actually cast a ballot. It is a critical indicator of political participation and legitimacy.
投票率衡量的是已登记选民中实际投出选票的比例，是参与政治和政权合法性的重要指标。
C represents the number of valid votes cast; E represents the total registered electorate.
C 表示投出的有效票数；E 表示登记选民总数。
omes (total votes cast ÷ E) × 100. Accurate interpretation depends on the definition used.
若计入废票，则公式变为 (投票总数 ÷ E) × 100。解读时需注意所使用的定义。
6. Duverger's Law | 迪韦尔热定律
SMDP (Single-Member District Plurality) ⇒ Two-party system
Duverger's Law states that single-member district plurality electoral systems tend to favour a two-party system. The mechanical effect (seat translation) and the psychological effect (voter strategy) combine to reduce the number of viable parties.
迪韦尔热定律指出，单席位选区简单多数选举制倾向于产生两党制。机械效应（席位换算）和心理效应（选票策略）共同作用，减少了有效政党的数量。
Small parties find it hard to win seats under FPTP, which discourages voters from wasting votes on them (the 'wasted vote' syndrome).
小党在 FPTP 下难以赢得席位，这促使选民不愿意在其身上浪费选票（‘废票’心理）。
The law is probabilistic, not deterministic; exceptions exist where strong regional parties survive.
该定律具有概率性而非决定性，存在强烈地区性政党的例外情况。
7. Separation of Powers | 权力分立原则
Legislative ≠ Executive ≠ Judiciary ⇒ Liberty preserved
The theorem of separation of powers, derived from Montesquieu, asserts that the three branches of government must be kept distinct and independent to prevent the concentration of power and protect individual freedom. Each branch acts as a check on the others.
权力分立原则源自孟德斯鸠，主张政府的三个分支必须保持分立和独立，以防止权力集中并保护个人自由。每一分支对其他分支形成制约。
In the UK, the fusion of executive and legislative branches is tempered by judicial independence and constitutional conventions.
在英国，行政与立法的部分融合通过司法独立和宪政惯例得到缓和。
The formula is a constitutional ideal: when the same body makes, executes, and judges laws, liberty is lost.
这一公式是宪制理想：若同一机构既立法、执行又司法，自由便不复存在。
8. Parliamentary Sovereignty | 议会主权
Parliament can make or unmake any law; no court or body can override
Parliamentary sovereignty, as articulated by A.V. Dicey, is the cornerstone of the UK constitution. It means that Parliament is the supreme legal authority, and there is no higher body that can strike down its legislation.
议会主权，正如戴雪所阐释，是英国宪法的基石。它意味着议会是最高法律权威，没有任何上级机构可以推翻其立法。
The theorem holds that no Parliament can bind its successors (the principle of 'implied repeal').
这一原则认为任何一届议会都不能约束其后继者（‘默示推翻’原则）。
EU membership and devolution have created practical limitations, but the legal doctrine remains central to UK politics.
欧盟成员身份与权力下放构成了实际操作上的限制，但在法律教义上议会主权依然是英国政治的核心。
9. Rule of Law | 法治
All are subject to the law → Law > any person
The rule of law is the principle that everyone— including government ministers, judges, and ordinary citizens—must abide by the law. It requires clear, publicised, stable laws applied equally, and independent courts to enforce them.
法治是指任何人都必须遵守法律的原则——包括政府部长、法官和普通公民。它要求法律明确、公开、稳定且平等适用，并由独立法院执行。
The equation 'Law > any person' captures the idea that no one is above the law.
等式‘法律 > 任何人’体现了无人凌驾于法律之上的理念。
Dicey's three strands: supremacy of regular law, equality before the law, and the constitution as a result of ordinary law.
戴雪的三项内涵：常规法律的至上性、法律面前人人平等以及宪法乃普通法律的自然结果。
10. Rights-Responsibilities Equilibrium | 权利-责任平衡
Rights ∝ Responsibilities
In a democratic society, the enjoyment of individual rights is often balanced by corresponding responsibilities. This equilibrium underpins the concept of active citizenship, where rights such as free speech come with duties to respect others' rights and obey the law.
在民主社会中，个人权利的享有通常与相应的责任相平衡。这一平衡是积极公民理念的基础，即言论自由等权利伴随着尊重他人权利和遵守法律的义务。
The proportional symbol indicates that as rights expand, so do responsibilities, though the relationship is political rather than strictly mathematical.
正比符号表示权利扩大时责任也随之加重，尽管此关系是政治意义上的而非严格数学量化。
In the UK, the Human Rights Act 1998 enumerates rights that must be exercised compatibly with the rights of others and the wider community.
在英国，1998 年《人权法案》列出的权利必须与他人的权利以及更广泛的社会相容地行使。
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