Year 10 SQA Politics: Quick Reference Handbook of Formulas and Theorems | Year 10 SQA 政治：公式定理速查手册

📚 Year 10 SQA Politics: Quick Reference Handbook of Formulas and Theorems | Year 10 SQA 政治：公式定理速查手册

In SQA Year 10 Politics (often studied within Modern Studies), mastering foundational ‘formulas’ and ‘theorems’ helps you analyse how power is distributed, how elections work and how citizens participate. This handbook distils the most critical political concepts into clear statements and equations, allowing you to revise key ideas at a glance and apply them to exam questions with confidence.

在 SQA Year 10 政治课程（常融入现代研究）中，掌握基础‘公式’与‘定理’有助于分析权力分配、选举运作及公民参与方式。本手册将最关键的政治概念提炼为清晰的陈述与等式，让你能一目了然地复习核心思想并有信心地应用于考题。

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1. Separation of Powers Theorem | 权力分立定理

The Separation of Powers theorem, articulated by Montesquieu, states that the legislative, executive and judicial functions of government must be divided among separate branches to prevent tyranny. This principle can be expressed as a simple equation for limited government:

权力分立定理由孟德斯鸠阐述，指出政府的立法、行政与司法职能必须由不同分支分别行使以防暴政。这一原则可表示为限制性政府的简洁等式：

Legislature + Executive + Judiciary → Balanced, Limited Government

Each branch operates independently while being checked by the others, ensuring no single institution amasses absolute power.

立法机构 + 行政机关 + 司法机关 → 平衡且受限制的政府

每一分支独立运作同时受其他分支制衡，确保没有任何单一机构积聚绝对权力。

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2. Rule of Law Formula | 法治公式

The Rule of Law is a founding principle that all individuals and institutions are subject to and accountable to law. Its operational strength can be represented by a basic multiplicative formula:

法治是一项基本原则，所有个人与机构都受法律约束并对法律负责。其运作力度可用一个基本乘积公式表示：

Authority = Law × Consent

If consent collapses, authority loses legitimacy, no matter how well-crafted the laws appear. This formula underpins the idea that democratic governments must enjoy the consent of the governed.

权威 = 法律 × 同意

若同意崩塌，无论法律制定得多好，权威都会丧失合法性。该公式支撑着民主政府必须拥有被统治者同意的理念。

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3. Electoral Systems: The D’Hondt Formula | 选举制度：顿特公式

The D’Hondt formula is the arithmetic engine used in the Additional Member System (AMS) to allocate regional list seats for the Scottish Parliament. The formula works by repeatedly dividing each party’s total regional votes by the number of seats that party has already won plus one. The party with the highest quotient at each round wins the next seat:

顿特公式是用于苏格兰议会额外成员制（AMS）分配地区名单席位的算术引擎。该公式将各政党的地区总得票一次次除以该党已获席位数加一。每轮商数最高的政党赢得下一个席位：

Priority Quotient = Total Votes ÷ (Seats Won + 1)

Consider an example with 3 regional seats available and three parties with the following regional votes: Party A 10,000, Party B 8,000, Party C 5,000.

优先商数 = 总得票 ÷ (已获席位数 + 1)

假设有3个地区席位待分配，三党的地区得票分别为：A党10,000票，B党8,000票，C党5,000票。

Round 1 quotients: A = 10,000 ÷ (0+1) = 10,000, B = 8,000, C = 5,000 → A wins first seat. Round 2: A = 10,000 ÷ (1+1) = 5,000, B = 8,000, C = 5,000 → B wins. Round 3: A = 5,000, B = 8,000 ÷ (1+1) = 4,000, C = 5,000 → A wins. Final seats: A 2, B 1, C 0. This demonstrates how the formula benefits parties with larger vote shares but still allows smaller parties to gain representation.

第1轮商数：A = 10,000 ÷ (0+1) = 10,000，B = 8,000，C = 5,000 → A胜。第2轮：A = 10,000 ÷ (1+1) = 5,000，B = 8,000，C = 5,000 → B胜。第3轮：A = 5,000，B = 8,000 ÷ (1+1) = 4,000，C = 5,000 → A胜。最终席位：A 2席，B 1席，C 0席。这显示了该公式对得票份额较大的政党有利，但仍允许小党获得代表席次。

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4. Droop Quota for STV | 单记可让渡投票制的德鲁普配额

The Droop Quota determines the minimum number of votes a candidate needs to secure election under the Single Transferable Vote (STV). It ensures that only as many candidates are elected as there are seats, and surplus votes can be redistributed:

德鲁普配额决定候选人在单记可让渡投票制（STV）下当选所需的最低票数。它确保只有与席位数相当的候选人当选，剩余选票可再分配：

Quota = ⌊ Total Valid Votes ÷ (Total Seats + 1) ⌋ + 1

The floor function gives an integer. For example, if 1000 valid votes are cast for 3 seats, the Droop Quota is (1000 ÷ (3+1)) + 1 = 250 + 1 = 251. A candidate reaching 251 votes is mathematically assured of victory.

配额 = ⌊ 总有效票 ÷ (总席位数 + 1) ⌋ + 1

取整确保整数。例如，若1000张有效票竞争3个席位，德鲁普配额为 (1000 ÷ (3+1)) + 1 = 250 + 1 = 251。达到251票的候选人从数学上保证当选。

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5. Duverger’s Law | 迪韦尔热法则

Duverger’s Law is a political science rule that explains how electoral systems shape party competition. It states: First-Past-the-Post (FPTP) generally favours a two-party system. Two mechanisms drive this: the mechanical effect (small parties rarely win seats) and the psychological effect (voters avoid wasting votes on candidates unlikely to win).

迪韦尔热法

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