📚 Year 11 WJEC Politics: Key Formulas and Principles Quick Reference | Year 11 WJEC 政治公式与定理速查手册
This quick reference handbook consolidates the essential ‘formulas’ and ‘theorems’ in the WJEC Year 11 Politics specification — from electoral mathematics to core constitutional principles. Understanding these aids quick recall and analytical precision in exams.
这本速查手册汇集了 WJEC 11 年级政治学科中关键的“公式”与“定理”——从选举数学到核心宪法原理。掌握这些内容有助于考试中快速回忆和精确分析。
1. The Core ‘Formula’ of Democracy | 民主的核心“公式”
Democracy can be distilled as: Government = (Consent + Participation + Rights) ÷ Concentration of Power. Legitimacy requires free, fair and regular elections, universal adult suffrage, and protected civil liberties.
民主可以概括为：政府 = （同意 + 参与 + 权利） ÷ 权力集中度。合法性取决于自由、公正和定期的选举、成人普选权以及受保障的公民自由。
A simple numerical test for democratic health is the effective number of parties or the turnout ratio: Turnout % = (Votes cast ÷ Registered electors) × 100. Higher turnout with genuine choice strengthens the consent element of the formula.
检验民主健康与否的一个简单数值测试是有效政党数目或投票率：投票率 % = (投票数 ÷ 登记选民数) × 100。具有真实选择的高投票率加强了该公式中的同意要素。
2. First-Past-the-Post (FPTP) Seat Calculation | 简单多数制议席计算
In a First-Past-the-Post electoral system, the candidate who polls more votes than any other single rival wins the constituency seat — even without an absolute majority. Win condition: Votes > Votes of highest opponent.
在简单多数选举制中，得票多于任何单一对手的候选人即赢得选区席位——即使并未获得绝对多数。获胜条件：得票 > 最高对手的得票。
Seat bonus formula for a winning party: Seat share % − Vote share %. A positive bonus indicates the system’s disproportionality. The cube law approximation: Seat ratio ≈ (Vote ratio)³, though this is an empirical rule of thumb rather than a strict mathematical law for modern British elections.
获胜政党的席位红利公式：席位百分比 − 得票百分比。正红利表明制度的不成比例性。立方律近似：席位比 ≈ (得票比)³，但这仅是经验法则，并非适用于现代英国选举的严格数学定律。
| Party | Vote % | Seat % | Bonus (Seat% – Vote%) |
|---|---|---|---|
| A | 43.6 | 56.2 | +12.6 |
| B | 32.2 | 31.7 | −0.5 |
| C | 12.5 | 3.8 | −8.7 |
3. Proportional Representation Quota Formulas | 比例代表制配额公式
Proportional systems rely on formulas to convert votes into seats. Two fundamental quotas are used to determine the number of votes needed to win a seat.
比例代表制依靠公式将选票转化为席位。两个基本配额用于确定赢得一席所需的票数。
Hare quota: Q = Total valid votes ÷ Total seats
黑尔配额: Q = 总有效票数 ÷ 总席位数
Droop quota: Q = [Total votes ÷ (Seats + 1)] + 1
特洛普配额: Q = [总票数 ÷ (席位数 + 1)] + 1
The Droop quota is designed to be lower than the Hare quota, reducing the number of seats awarded by remainder and therefore favouring slightly larger parties. The ‘+1’ ensures that no more candidates can reach the quota than there are seats to fill.
特洛普配额设计得比黑尔配额更低，从而减少了依靠余数分配的席位，因此略微有利于大党。“+1”确保了达到配额的候选人不会多于所需填补的席位。
4. D’Hondt Divisor Method | 唐特除数法
The D’Hondt method (also known as the Jefferson method) allocates seats sequentially by dividing each party’s total votes by a series of divisors (1, 2, 3, …). The highest quotients win seats.
唐特法（也称杰弗逊法）通过将每个政党的总票数依次除以一系列除数（1, 2, 3……）来逐席分配，最高的商值依次赢得席位。
V₁ = Party votes ÷ 1, V₂ = Party votes ÷ 2, V₃ = Party votes ÷ 3, … Vₙ = Party votes ÷ n
V₁ = 政党票数 ÷ 1, V₂ = 政党票数 ÷ 2, V₃ = 政党票数 ÷ 3, … Vₙ = 政党票数 ÷ n
Example: Total 3 seats to fill. Party X: 50,000 votes; Party Y: 30,000; Party Z: 20,000. Quotients: X/1=50,000 (seat1), Y/1=30,000 (seat2), X/2=25,000 (seat3). Z/1=20,000 never wins a seat. The method generates a sequence of average votes per seat and slightly favours larger parties.
示例：共需分配3席。X党50,000票；Y党30,000票；Z党20,000票。商值：X/1=50,000（第1席），Y/1=30,000（第2席），X/2=25,000（第3席）。Z/1=20,000无法获席。该方法产生每席平均票数序列，并略微偏向大党。
5. Hare Quota and Largest Remainder Method | 黑尔配额与最大余数法
This two‑step proportional allocation uses the simple Hare quota and then any unfilled seats are given to the parties with the highest vote remainders.
这种两步式比例分配法使用简单的黑尔配额，然后将未分配席位授予余数最高的政党。
Step 1: Compute Hare quota Q = Total votes ÷ Total seats. Each party initially receives seats equal to the integer part of (Party votes ÷ Q).
第1步：计算黑尔配额 Q = 总票数 ÷ 总席位。各党最初获席数 = 整数部分（政党票数 ÷ Q）。
Step 2: Remainder R = Party votes – (Seats won × Q). Remaining seats awarded in descending order of R. This formula ensures high overall proportionality but can lead to paradoxes like the Alabama paradox when total seats change.
第2步：余数 R = 政党票数 − (已获席位 × Q)。剩余席位按R从大到小分配。该公式确保了高度整体比例性，但在总席位变化时可能出现如阿拉巴马悖论等问题。
6. Separation of Powers Theorem | 权力分立定理
Separation of powers is a constitutional theorem holding that the three branches of government — legislature (makes law), executive (implements law), and judiciary (interprets law) — must be kept distinct in both institutions and personnel. Overlap creates a risk of tyranny.
权力分立是一项宪法定理，主张政府的三个分支——立法机关（制定法律）、行政机关（执行法律）和司法机关（解释法律）——必须在机构与人员上保持独立。职能重叠会造成暴政风险。
The UK’s partial fusion of executive and legislature (ministers are drawn from Parliament) is a deliberate modification, checked by judicial independence and constitutional conventions. The formula: Liberty ≈ Separation + Checks and Balances, where checks prevent any single branch from dominating.
英国行政与立法的部分融合（大臣来自议会）是一种有意的调整，同时受司法独立和宪法惯例制约。公式可表示为：自由 ≈ 权力分立 + 制衡，其中制衡机制防止任何单一分支独大。
7. Parliamentary Sovereignty Principle | 议会主权原则
Parliamentary sovereignty is the foremost constitutional ‘theorem’ in the UK: Parliament is the supreme legal authority and can make or unmake any law. No court or other body can override an Act of Parliament.
议会主权是英国首要的宪法“定理”：议会是最高法律权威，可制定或废除任何法律。任何法院或其他机构均不能推翻议会法令。
The traditional hierarchy formula: Statute > Common Law > Royal Prerogative. Recent developments (EU membership, Human Rights Act, devolution) have challenged this pure model, but the principle remains that Parliament can theoretically repeal any previous statute, restoring its supremacy.
传统位阶公式：成文法 > 普通法 > 王室特权。近年来的发展（欧盟成员身份、《人权法》、权力下放）对这一纯粹模型构成了挑战，但理论上议会仍可废除任何旧法，恢复其至上地位。
8. Rule of Law ‘Theorem’ | 法治“定理”
The rule of law can be expressed as a set of core conditions: laws must be public, clear, prospective, and applied equally to all. The classical Diceyan formula: No one is punishable except for a distinct breach of law established in the ordinary legal manner.
法治可表述为一组核心条件：法律必须公开、明确、具有前瞻性，并平等适用于所有人。经典戴雪公式：任何人除非以普通法律方式被证实有明确违法行为，否则不得受罚。
Modern version: Government under law, not law under government. Compliance indicator = Judicial independence + access to courts + limits on discretionary power. Respect for the rule of law is measured by whether executive action can be challenged by judicial review.
现代版本：政府服从法律，而非法律服从政府。合规指标 = 司法独立 + 法院可及性 + 自由裁量权限制。对法治的尊重程度可通过行政行为是否能被司法审查质疑来衡量。
9. Proportionality Principle in Human Rights | 人权法中的比例原则
Under the Human Rights Act 1998, any restriction on qualified rights (such as Article 8 privacy or Article 10 expression) must satisfy the proportionality test. This test acts as a legal ‘formula’ to check whether a limitation is justified.
根据1998年《人权法》，对受限权利（例如第8条隐私权或第10条表达自由）的任何限制都必须通过比例检验。这一检验充当法律“公式”，用以核实限制是否正当。
The four-stage test: (1) Legitimate aim of sufficient importance; (2) Rational connection – the measure must be rationally connected to the aim; (3) Necessity – is the measure no more than necessary? (4) Fair balance – does the public benefit outweigh the individual right infringement? Courts ask: is there a less restrictive alternative?
四阶段检验：(1) 具有足够重要性的合法目的；(2) 合理关联——措施必须与目的有合理关联；(3) 必要性——该措施是否无过于必要？(4) 公平平衡——公共利益是否大于个人权利受损？法院会问：是否存在限制性更小的替代方案？
10. Unitary vs Federal State Models | 单一制与联邦制国家模型
A fundamental constitutional choice can be expressed by two opposing formulas. Unitary state: Sovereignty resides at the centre; sub-national governments exercise powers delegated by the centre, which can be revoked.
一种根本性的宪法选择可通过两个对立公式表达。单一制国家：主权归属于中央；次国家级政府行使中央授予并可撤销的权力。
Federal state: Sovereignty is divided between central and regional governments, each with constitutionally guaranteed powers. Quasi-formula: Federalism = Shared Sovereignty ÷ Constitutional Entrenchment. The UK is a union state with devolution, not a federation, because Westminster retains legal supremacy.
联邦制国家：主权在中央和地区政府之间划分，各自的权力受宪法保障。准公式：联邦制 = 共享主权 ÷ 宪法刚性。英国是一个下放权力的联合王国，而非联邦，因为威斯敏斯特议会保留了法律最高性。
11. Turnout and Electoral Legitimacy Ratio | 投票率与选举合法性比率
Turnout is a simple but crucial political formula: Turnout % = (Number of votes cast ÷ Total electorate) × 100. It is used to assess democratic mandate strength. A mandate ratio can be constructed: Mandate strength = (Winning party vote share × Turnout %) ÷ 100.
投票率是一个简单却关键的政治公式：投票率 % = (投票人数 ÷ 选民总数) × 100。它用于评估民主授权力度。可构建授权比率：授权强度 = (胜选党得票率 × 投票率 %) ÷ 100。
For example, if a governing party wins 40% of the vote on a 65% turnout, its mandate share of the entire electorate is only 26%. This highlights the gap between electoral victory and popular consent, a recurring theme in UK general elections.
举例而言，若执政党以40%的得票率在65%的投票率下获胜，其在全体选民中的授权份额仅为26%。这突显了选举胜利与民众同意之间的差距，是英国大选中反复出现的议题。
12. Referendums and the Simple Majority Rule | 公投与简单多数规则
Referendum result formula: Option wins if Votes_for > ½ × (Total valid votes). In the absence of a supermajority rule, a 50%+1 threshold suffices. Some argue for a double majority rule: (Votes_for > 50%) AND (Turnout > threshold, e.g. 40%).
公投结果公式：若选项所得票数 > ½ × (总有效票数)，则其获胜。在无绝对多数规则的情况下，50%+1 的门槛已足够。有人主张双重多数规则：(赞成票 > 50%) 且 (投票率 > 门槛，如40%)。
WJEC contexts include the 2016 EU referendum (51.9% Leave) and devolution referendums. The pure simple majority formula creates decisive outcomes but can polarise, hence the theoretical debate about thresholds.
WJEC课程背景包括2016年脱欧公投（51.9%离欧）和权力下放公投。纯粹简单多数公式创造出果断结果但可能引发分裂，因此引发了关于设定门槛的理论争论。
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