KS3 Edexcel Politics: Formula & Theorem Quick Reference Guide | KS3 Edexcel 政治：公式定理速查手册

📚 KS3 Edexcel Politics: Formula & Theorem Quick Reference Guide | KS3 Edexcel 政治：公式定理速查手册

Politics is not just about speeches and debates – it follows clear rules, structures and sometimes even mathematical formulas. This revision guide collects the essential formulas, theorems and principles you need to master for the KS3 Edexcel Politics course. Each entry explains how the ‘formula’ works, why it matters, and how to apply it to real‑world political situations.

政治不仅仅是演讲和辩论——它遵循明确的规则、结构，有时甚至遵循数学公式。本复习手册汇集了KS3爱德思政治课程中你需要掌握的基本公式、定理和原理。每个条目都解释了“公式”如何运作、为何重要，以及如何将其应用于现实世界的政治情境。

1. Majority Election Formula | 多数决选举公式

In a majoritarian election, a candidate wins if they receive more than half of the total votes cast. The simplest version is the first‑past‑the‑post system, where the candidate with the highest number of votes is declared the winner, even if they do not reach 50%.

在多数制选举中，候选人如果获得超过总票数的一半即可获胜。最简单的版本是“领先者当选”制度，在该制度下，得票最多的候选人被宣布为获胜者，即使其票数未达到50%。

The mathematical condition for an absolute majority is: Votes for candidate > Total valid votes ÷ 2. If no candidate meets this threshold, a second round or run‑off election may be required.

获得绝对多数的数学条件是：候选人得票数 > 有效票总数 ÷ 2。如果没有候选人达到这一门槛，则可能需要进行第二轮或决选投票。

2. Hare Quota for Proportional Representation | 比例代表制黑尔配额公式

The Hare quota is used to allocate seats in proportional representation systems such as the Single Transferable Vote (STV). It determines the minimum number of votes a candidate needs to be elected in a multi‑member constituency.

黑尔配额用于在比例代表制（如单一可转让投票制）中分配席位。它决定了在多议员选区中，候选人当选所需的最低票数。

Hare Quota = Total Valid Votes ÷ Number of Seats

黑尔配额 = 有效票总数 ÷ 席位数

For example, if 100 000 votes are cast for 5 seats, the quota is 20 000 votes. Once a candidate reaches the quota, any surplus votes are transferred to other candidates according to voter preferences.

例如，如果为5个席位投出100 000张选票，配额就是20 000票。一旦候选人达到配额，剩余票数将根据选民偏好转移给其他候选人。

3. D’Hondt Method of Highest Averages | 德洪特最高平均法

The D’Hondt method is a formula for allocating seats in party‑list proportional representation. It favours larger parties slightly, because it uses a series of divisors to calculate the highest averages.

德洪特法是一种用于在政党名单比例代表制中分配席位的公式。它稍微偏向大党，因为它使用一系列除数来计算最高平均数。

The formula works by dividing each party’s total votes by 1, then by 2, then by 3, and so on, up to the number of seats to be filled. The seats are awarded to the parties with the highest resulting quotients.

该公式的运作方式是将每个政党的总票数依次除以1、2、3……直至待填补的席位数。席位分配给所得商数最高的政党。

Example table for 4 seats and parties A, B, C:

4个席位和A、B、C三个政党的示例表格：

Party / 政党	Votes / 得票	÷1	÷2	÷3
A	5000	5000 (1st)	2500 (3rd)	1666
B	3200	3200 (2nd)	1600 (4th)	1066
C	1800	1800	900	600

The four highest quotients are 5000, 3200, 2500, 1600, so Party A gets 2 seats, Party B gets 2 seats, Party C gets 0.

四个最高商数是5000、3200、2500、1600，因此政党A获得2个席位，政党B获得2个席位，政党C获得0个席位。

4. Democracy Index: The Participation Formula | 民主指数：参与公式

A simple way to measure the strength of a democracy is to look at voter turnout and the fairness of elections. The Participation Formula combines turnout with the effective number of choices.

衡量民主强度的一个简单方法是观察选民投票率和选举的公正性。参与公式将投票率与有效选择数量结合起来。

Democracy Score = (Voter Turnout % × Effective Number of Parties) ÷ 100

民主得分 = (选民投票率 % × 有效政党数) ÷ 100

If turnout is 65% and the effective number of parties is 4, the Democracy Score is 2.6. A higher score suggests more meaningful participation and competition. However, this is only a rough indicator – real democracy indices consider many other factors such as civil liberties and media freedom.

如果投票率为65%，有效政党数为4，则民主得分为2.6。得分越高，表明参与和竞争越有意义。然而，这只是一个粗略的指标——真正的民主指数还考虑许多其他因素，如公民自由和媒体自由。

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

The doctrine of the separation of powers states that the three branches of government – legislature, executive and judiciary – should be kept distinct and check each other. This constitutional ‘formula’ prevents any one branch from becoming too powerful.

权力分立原则指出，政府的三个分支——立法、行政和司法——应保持独立并相互制衡。这一宪制“公式”防止任何一个分支变得过于强大。

The theorem can be represented as: Legislature ⇌ Executive ⇌ Judiciary, with arrows showing checks and balances. For example, the legislature makes laws, but the executive can veto them; the judiciary can declare laws unconstitutional. This dynamic balance maintains the rule of law.

该定理可以表示为：立法 ⇌ 行政 ⇌ 司法，箭头表示制衡关系。例如，立法机关制定法律，但行政机关可以否决；司法机关可以宣布法律违宪。这种动态平衡维护了法治。

6. Rule of Law Equation | 法治方程

The rule of law means that everyone, including those in power, must follow the law. Its strength can be captured by an equation measuring the absence of arbitrary power.

法治意味着每个人，包括掌权者，都必须遵守法律。其强度可以通过一个衡量任意权力缺失的方程来体现。

Rule of Law Index = (Accountability + Transparency + Judicial Independence) ÷ 3

法治指数 = (问责制 + 透明度 + 司法独立) ÷ 3

Each component is rated from 1 to 10. A country scoring highly across all three is considered to have a strong rule of law. This ‘formula’ reminds us that the rule of law is a combination of institutional safeguards, not a single principle.

每个组成部分的评分为1到10分。在所有三个部分都得分高的国家被认为具有强大的法治。这个“公式”提醒我们，法治是多种制度保障的结合，而非单一原则。

7. Left–Right Political Spectrum Theorem | 左右政治光谱定理

The political spectrum is a model that arranges ideologies from left (social equality, government intervention) to right (individual liberty, free markets). The position of a party can be plotted by evaluating its policies.

政治光谱是一种将意识形态从左翼（社会平等、政府干预）到右翼（个人自由、自由市场）排列的模型。政党的立场可以通过评估其政策来确定。

Spectrum Score = (Economic Score + Social Score) ÷ 2

光谱分数 = (经济分数 + 社会分数) ÷ 2

Economic score ranges from –10 (full state control) to +10 (laissez‑faire). Social score ranges from –10 (traditional authority) to +10 (progressive liberty). A party with scores –7 and –3 might be described as far‑left authoritarian, while +8 and +7 is libertarian right. This theorem helps compare parties across countries.

经济分数范围从–10（完全国家控制）到 +10（自由放任）。社会分数范围从–10（传统权威）到 +10（进步自由）。一个分数为–7和–3的政党可能被描述为极左威权主义，而+8和+7的则为自由意志右翼。这个定理有助于比较不同国家的政党。

8. Citizen Participation Rate | 公民参与率

In a healthy democracy, citizens do more than just vote. The Participation Rate formula sums up different forms of engagement.

在一个健康的民主国家，公民所做的不仅仅是投票。参与率公式总结了不同形式的参与方式。

Participation Index = (Voter Turnout % + Petition Signers % + Party Membership % + Protest Participants %) ÷ 4

参与指数 = (选民投票率 % + 请愿签名者 % + 政党成员 % + 抗议参与者 %) ÷ 4

For instance, if turnout is 60%, petition signers 25%, party members 3%, and protest participants 8%, the index is 24%. This ‘formula’ highlights that democracy depends on a mix of electoral and non‑electoral activities.

例如，如果投票率为60%，请愿签名者为25%，政党成员为3%，抗议参与者为8%，则指数为24%。这个“公式”强调民主依赖于选举和非选举活动的结合。

9. Parliamentary Sovereignty Principle | 议会主权原则

In the UK, Parliament is the supreme legal authority. The principle of parliamentary sovereignty can be understood through a simple logical statement: no Parliament can bind its successors, and any law can be changed by a simple majority.

在英国，议会是最高法律权力机关。议会主权原则可以通过一个简单的逻辑陈述来理解：没有一届议会能约束其后继者，任何法律都可以通过简单多数加以修改。

Parliament Passes/Repeals any Law ⇔ No External Veto

议会可通过/废除任何法律 ⇔ 无外部否决权

This means that constitutional rules are not entrenched in the same way as in countries with a written constitution. The Human Rights Act 1998 can theoretically be repealed by a later act, because sovereignty resides with Parliament at any given moment.

这意味着宪法规则不像有成文宪法的国家那样被固定。1998年的《人权法》理论上可以被后来的法案废除，因为主权在任何特定时刻都属于议会。

10. Human Rights Protection Formula | 人权保护公式

International human rights law often uses a proportionality test to decide whether a government’s action is justified. This balancing exercise can be expressed as a formula.

国际人权法通常使用比例性检验来判断政府的行为是否合理。这种平衡行为可以用一个公式表示。

Justified Restriction = (Legitimate Aim × Rational Connection × Necessity) ÷ (Burden on Individual)

正当限制 = (合法目的 × 合理关联 × 必要性) ÷ (个人负担)

If the legitimate aim, rational connection and necessity are all strong and the burden on the individual is small, the restriction is likely to be upheld by courts. For example, a law banning hate speech may be justified because it protects the rights of others, whilst placing only a limited burden on free expression.

如果合法目的、合理关联和必要性都很强，而个人负担很小，法院很可能会支持这一限制。例如，禁止仇恨言论的法律可能是正当的，因为它保护了他人的权利，同时对言论自由只施加了有限的负担。

11. Power Index in Coalition Government | 联合政府中的权力指数

When no single party wins a majority, coalitions are formed. The Banzhaf power index helps measure the voting power of each party in a coalition, based on how often it can change a losing coalition into a winning one.

当没有一个政党赢得多数席位时，就会组成联合政府。班扎夫权力指数根据某个政党能将一个失败的联盟转变为获胜联盟的频率，来衡量每个政党在联盟中的投票权。

Banzhaf Index = (Critical Votes Count for Party) ÷ (Total Critical Votes for All Parties)

班扎夫指数 = (政党的关键票数) ÷ (所有政党的总关键票数)

A party is ‘critical’ if its withdrawal would cause the coalition to lose its majority. If party A has 3 critical votes out of 10, its Banzhaf index is 0.3 or 30%. This formula reveals that even smaller parties can wield substantial influence if their seats are pivotal.

如果某个政党退出会导致联盟失去多数席位，它就是“关键”的。如果政党A在10次关键投票中占了3次，其班扎夫指数就是0.3或30%。这个公式揭示出，如果其席位具有关键作用，即使是较小的政党也能发挥重大影响。

12. Turnout‑to‑Mandate Theorem | 投票率与授权定理

An election victory does not always equal a strong mandate. The Mandate Quotient relates the winning party’s share of the vote to overall turnout.

选举胜利并不总是等同于强有力的授权。授权商数将获胜政党的得票份额与总体投票率联系起来。

Mandate Strength = (Winning Party Vote Share %) × (Turnout %) ÷ 100

授权强度 = (获胜政党得票率 %) × (投票率 %) ÷ 100

If a party wins 40% of the vote on a 60% turnout, its mandate strength is only 24%. This means only 24% of eligible voters actively supported the winning party. This theorem is frequently used in debates about electoral reform and the legitimacy of governments.

如果某个政党在60%的投票率下赢得40%的选票，其授权强度仅为24%。这意味着只有24%的合格选民积极支持获胜政党。这一原理经常被用于关于选举改革和政府合法性的辩论中。

Published by TutorHao | Politics Revision Series | aleveler.com

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