📚 Year 10 Eduqas Politics: Formula & Theorem Quick Reference Handbook | Year 10 Eduqas 政治：公式定理速查手册
This essential quick reference handbook gathers all the key electoral formulas, political theorems, and constitutional rules that Year 10 Eduqas Politics students need to master. Designed to support revision for both Component 1 (Democracy, Elections, Voting Behaviour and the Media) and Component 2 (Devolution, Government and Politics of the UK), it explains each concept clearly with a paired English-Chinese breakdown. Save time, deepen your understanding, and revise with confidence.
这份必备速查手册汇集了 Year 10 Eduqas 政治学科所有关键的选举公式、政治定理和宪制规则，覆盖单元一（民主、选举、投票行为与媒体）及单元二（权力下放、英国政府与政治）的核心内容。每个概念均以英中对照形式清晰解释，助你节省时间、加深理解、自信备考。
1. First Past the Post (FPTP) | 简单多数制
FPTP is used in UK general elections for the House of Commons. Each constituency elects one MP. Voters put a cross (X) next to one candidate. The candidate with the most votes wins, even if they do not have an absolute majority (over 50%). This is the simplest voting system: plurality rule.
简单多数制用于英国下议院大选。每个选区选出一名议员，选民在心仪候选人旁画叉（X）。得票最多者获胜，即使未获得绝对多数（超过50%）。这是最简单的投票制度：相对多数规则。
The formula for winning is straightforward: highest vote total wins. No mathematical quota is used. However, a candidate’s ‘majority’ is calculated as: Winner’s Votes − Second Place Votes.
获胜公式简单明了：得票总数最高者胜出，无需计算配额。但候选人的“多数票差”计算方式为：胜者得票 − 第二名得票。
The seat share in Parliament is not proportional to the national vote share. This is why FPTP is described as a ‘disproportional’ system. The effective number of parties (ENP) can be approximated by 1 / Σ(vote shareᵢ²), but this is not required for GCSE.
议会中席位比例与全国得票比例不一致，因此简单多数制被称为“非比例”代表制。有效政党数（ENP）可用 1/Σ(得票率ᵢ²) 估算，但 GCSE 不要求掌握。
2. Additional Member System (AMS) & D’Hondt Method | 附记名代表制与洪德法
AMS combines constituency MPs elected by FPTP with regional list MPs chosen using a proportional formula. In Scotland and Wales, the D’Hondt method is used to allocate regional seats. The goal is to make the overall result more proportional.
附记名代表制将简单多数制选出的选区议员与按比例公式选出的区域名单议员相结合。苏格兰和威尔士使用洪德法分配区域议席，旨在让总体结果更趋比例化。
The D’Hondt formula divides each party’s regional vote total by a series of divisors: 1, 2, 3, 4, etc. The highest resulting numbers (quotients) win seats. Before allocation, a party’s constituency seats already won in that region are taken into account. The first divisor applied to a party is (seatswon + 1).
洪德法将各党在区域中的得票总数除以一连串除数：1、2、3、4 等。所得商数最高的数字赢得席位。分配前，该党在该区域已赢得的选区席位会被计入，首次除数变为（已获席位数 + 1）。
Quotient = Regional Votes ÷ (Seats Already Won + 1) for first round; then divisors increase to 2, 3, 4 …
商数 = 区域得票 ÷ (已获席位数 + 1) 首轮；随后除数逐步增至 2、3、4 …
3. Single Transferable Vote (STV) & Droop Quota | 单记可让渡投票制与特罗普名额
STV is used in Northern Ireland Assembly and Scottish local council elections. Voters rank candidates in order of preference (1, 2, 3 …). A candidate must reach the Droop quota to be elected. Surplus votes are transferred, and if no candidate reaches the quota, the lowest candidate is eliminated and their votes redistributed.
单记可让渡投票制用于北爱尔兰议会和苏格兰地方议会选举。选民按偏好排序（1、2、3…）。候选人必须达到特罗普名额才能当选。多余选票会被转让；若无候选人达到配额，最低票者被淘汰并重新分配其选票。
Droop Quota = (Total Valid Votes ÷ (Seats + 1)) + 1 (rounded down to the next integer)
特罗普名额 = (总有效票数 ÷ (席位数 + 1)) + 1（向下取整至整数）
For example, in a 4‑seat constituency with 10,000 valid votes: (10,000 ÷ 5) + 1 = 2,000 + 1 = 2,001. This is the minimum number of votes a candidate needs to be elected.
举例来说，一个4席选区有10,000张有效票：(10,000 ÷ 5) + 1 = 2,000 + 1 = 2,001，这就是候选人当选所需的最低票数。
4. Supplementary Vote (SV) | 补充投票制
SV is used for electing Police and Crime Commissioners in England and Wales, and for some directly elected mayors. Voters mark a first and second preference (X in column one, X in column two). If no candidate receives over 50% of first preferences, only the top two candidates remain. Second preferences from the eliminated candidates are added to their totals – but only if the second preference is for one of the top two.
补充投票制用于选举英格兰和威尔士的警务及犯罪专员以及部分直选市长。选民标记第一和第二偏好（第一栏一个叉，第二栏一个叉）。若无候选人获得超过50%的第一偏好，则只保留前两名候选人，并将淘汰候选人中指向这两位候选人的第二偏好票加至其总票数中。
The formula is not a quota but a conditional redistribution: Top two advance, second preferences from all other candidates are counted only when they support candidate A or B.
这不是配额公式，而是有条件的重新分配：前两名晋级，其他候选人中凡第二偏好指向 A 或 B 的选票才被计入。
5. Regional Party List & Hare Quota | 区域政党名单制与哈尔名额
The Hare quota is used in some proportional list systems to allocate seats. In the UK, closed party lists are used for European Parliament elections (historically) and could appear in other contexts. The Hare quota determines how many votes are needed for one seat.
哈尔名额在一些比例名单制中用于分配席位。英国曾用于欧洲议会选举的封闭式政党名单制，也可能出现在其他情境中。哈尔名额确定赢得一个席位所需票数。
Hare Quota = Total Valid Votes ÷ Total Seats
哈尔名额 = 总有效票数 ÷ 总席位数
Larger remainder methods may be applied after the initial allocation, but the pure Hare quota is the simplest expression of proportionality.
初次分配后还可采用最大余数法，但单纯的哈尔名额是最简洁的比例表达方式。
6. Duverger’s Law | 迪韦尔热定律
Duverger’s Law states that single-member district plurality systems (like FPTP) tend to produce a two-party system. This happens because of two effects: the ‘mechanical’ effect – small parties get disproportionately few seats – and the ‘psychological’ effect – voters avoid wasting their votes on candidates unlikely to win.
迪韦尔热定律指出，单席选区相对多数制（如简单多数制）倾向于产生两党制。这源于两种效应：“机械效应”——小党获得席位数严重偏少；以及“心理效应”——选民不愿把票浪费在胜算渺茫的候选人身上。
In the UK, Duverger’s Law helps explain why the Conservative and Labour parties have dominated Westminster, though recent devolved elections using AMS have allowed multi-party systems to emerge.
在英国，迪韦尔热定律有助于解释保守党和工党为何长期主导西敏寺，尽管近年采用附记名代表制的地方选举使多党制得以出现。
7. Median Voter Theorem | 中间选民定理
The Median Voter Theorem, from public choice theory, suggests that in a two-party system with a single policy dimension, both parties will converge towards the preferences of the median voter. This is because the median voter represents the tipping point needed to secure 50%+1 of the vote.
中间选民定理源自公共选择理论，认为在单一政策维度下的两党制中，两党都会向中间选民的偏好靠拢，因为中间选民代表了赢得50%+1 选票所需的转折点。
This theorem can explain why Labour and the Conservatives often adopt centrist policies in the run-up to a general election, especially in marginal seats where the median voter is particularly influential.
这一定理可以解释为什么工党和保守党在大选前往往采取中间路线政策，尤其在中间选民影响力尤为显著的优势选区。
8. Theories of Representation | 代表理论
The three classical theories of representation are the trustee model (Edmund Burke), the delegate model, and the mandate model. No single election formula governs representation, but these models shape how voters interpret their MP’s role.
代表制的三大经典理论为：受托模型（埃德蒙·伯克）、委任模型和授权模型。虽然没有单一的选举公式来规定代表制，但这些模型塑造了选民如何看待其议员的角色。
- Trustee: MPs use their own judgement to act in the best interest of their constituents. | 受托：议员凭自己判断为选区最佳利益行事。
- Delegate: MPs act strictly on the wishes of their constituents, almost like a mouthpiece. | 委任：议员严格按选民意旨行事，如同传声筒。
- Mandate: MPs are elected to carry out the policies set out in their party manifesto. | 授权：议员当选为执行其政党宣言中的政策。
9. Voter Turnout and Political Participation Formulas | 投票率与政治参与公式
Turnout is a key measure of democratic health. It is calculated simply:
投票率是衡量民主健康状况的关键指标，其计算方式十分简单：
Turnout (%) = (Total Votes Cast ÷ Registered Electorate) × 100
投票率 (%) = (总投票数 ÷ 登记选民数) × 100
Other participation measures include party membership density, petition signing rates, and protest attendance. No fixed formula exists, but students should interpret data comparing turnout across different elections (e.g., general vs. local vs. devolved).
其他参与指标包括政党成员密度、请愿签署比例及抗议活动出席率。虽无固定公式，但学生需解读不同选举（如大选 vs. 地方选举 vs. 权力下放选举）的投票率数据。
10. Whip System and Party Discipline | 党鞭制度与政党纪律
The whip system is not a formula, but a crucial mechanism of control in Parliament. Understanding it helps explain how the executive maintains legislative support. Three-line whip is the strongest instruction to attend and vote with the party line.
党鞭制度虽非公式，却是议会中至关重要的控制机制。理解它有助于解释行政机关如何维持立法支持。三线党鞭是最强的指令，要求议员出席并按政党路线投票。
MPs who defy the whip can have the whip withdrawn (suspension), which often forces them to sit as an independent. Party cohesion is measured by voting unity scores, but no GCSE formula is applied.
违反党鞭指示的议员可被撤销党鞭资格（暂停党内身份），通常迫使他们以独立议员身份列席。政党凝聚度可用投票一致性分数衡量，但 GCSE 不作公式要求。
11. Devolution & the Barnett Formula | 权力下放与巴奈特公式
The Barnett formula is the mechanism used by the UK Treasury to allocate changes in public spending to Scotland, Wales, and Northern Ireland based on population and comparability factors. It is not a precise equality formula, but a population-based proportion:
巴奈特公式是英国财政部根据人口和可比性因素向苏格兰、威尔士和北爱尔兰分配公共支出变动的机制。它并非一个精确的均等式，而是一个基于人口的比例分配：
Change in Block Grant = Change in England’s Spending × (Comparability Percentage) × (Devoted Population Proportion)
区块拨款变动 = 英格兰支出变动 × (可比百分比) × (相关人口比例)
For instance, if health spending in England increases by £100 million, and the comparability percentage for Scotland is 100% with a population share of 10%, Scotland’s block grant would increase by roughly £10 million.
例如，若英格兰医疗卫生支出增加1亿英镑，苏格兰的可比百分比为100%，人口占比为10%，则苏格兰的区块拨款将增加约1000万英镑。
12. Referendums & Turnout Thresholds | 公投与投票率门槛
Some referendums require a supermajority or a minimum turnout threshold to be valid. In the UK, the 2014 Scottish independence referendum had no minimum turnout threshold but used a simple majority. The Trade Union Act 2016 introduced a 50% turnout requirement for strike ballots in key public services.
某些公投要求绝对多数或最低投票率门槛方为有效。英国2014年苏格兰独立公投未设最低投票率门槛，但采用了简单多数决。《2016年工会法》则对关键公共服务部门的罢工投票引入了50%投票率要求。
Validity Check: If Turnout < Required Threshold, Result is Advisory or Invalid.
有效性检验：若投票率 < 所设门槛，结果仅具参考性或无效。
Another important threshold is a supermajority, for example a ⅔ majority required for certain constitutional changes in some parliaments, though not typically used in UK-wide referendums.
另一重要门槛是绝对多数，例如某些议会中修宪需三分之二多数，但在全英公投中并不常用。
In electoral politics, a deposit (currently £500) is required to stand as a candidate for the UK Parliament; it is forfeited if the candidate wins less than 5% of the votes cast in that constituency. This discourages frivolous candidates and can be expressed as a percentage check: votes/candidate ≥ 5% of total valid votes to retain deposit.
在选举政治中，参选英国议会需缴纳押金（目前为500英镑），若候选人得票低于该选区总票数的5%，押金将被没收。这一规定遏制随意参选，并可表达为百分率检验：候选人得票 ≥ 总有效票数的5%方可保留押金。
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