📚 Year 12 WJEC Politics: Quick Reference Guide to Formulas & Theorems | WJEC政治：公式与定理速查手册
This quick reference guide compiles the essential formulas, well-known theorems, and analytical models that Year 12 WJEC Politics students need to master. From seat allocation methods to classical political laws, these tools help explain how elections are translated into power and why political behaviour follows certain patterns. The guide pairs each concept with a concise explanation in English and Chinese, making revision clearer and more structured.
这本速查手册汇总了12年级WJEC政治课程中必须掌握的核心公式、经典定理和分析模型。从席位分配方法到经典政治定律，这些工具帮助我们理解选举如何转化为权力，以及政治行为为何遵循特定模式。每个概念均配上简洁的中英文解释，让复习更清晰、更有条理。
1. D’Hondt Formula | 东特公式
The D’Hondt method is a highest averages system used to allocate seats in proportional representation. For each party, the total votes received are divided by a series of divisors (1, 2, 3, 4, …). The resulting quotients are ranked in descending order, and seats are awarded to the highest values. This formula slightly favours larger parties.
东特法是一种最高平均数法，用于比例代表制中的席位分配。每个政党获得的总票数依次除以除数序列（1, 2, 3, 4, …）。得出的商数按从大到小排列，席位分配给商数最大的那些值。该公式略微偏向大党。
Seats allocated by ranking Vₚ ÷ 1, Vₚ ÷ 2, Vₚ ÷ 3, …
2. Sainte-Laguë Formula | 圣拉格公式
The Sainte-Laguë method also uses divisors, but the sequence is 1, 3, 5, 7, … (odd numbers). This approach produces a more proportional outcome than D’Hondt and reduces the advantage given to larger parties. In the modified version, the first divisor is sometimes set at 1.4 to raise the effective threshold.
圣拉格法同样使用除数，但除数列为1, 3, 5, 7, …（奇数）。该方法比东特法产生更成比例的结果，并减少了大党享有的优势。在修正版本中，有时将第一个除数设为1.4，以提高实际门槛。
Divisors: 1, 3, 5, 7, …
3. Droop Quota | 德罗普配额
The Droop quota is used in the Single Transferable Vote (STV) system to determine the minimum number of votes a candidate needs to secure a seat. It ensures that only the required number of candidates are elected and that no vote is wasted unnecessarily.
德罗普配额用于单记可让渡投票制（STV）中，以确定候选人获得席位所需的最低票数。它确保只有必要数量的候选人当选，并尽量减少选票浪费。
Quota = [Total Valid Votes ÷ (Seats + 1)] + 1
4. Hare Quota | 黑尔配额
The Hare quota, also known as the simple quota, is the simplest formula for determining the number of votes needed to win a seat under STV. It divides total valid votes by the number of seats. The Droop quota is more common in practice because it avoids electing too many candidates.
黑尔配额，又称简单配额，是STV下计算赢得席位所需票数的最简单公式。它将总有效票数除以席位数。实践中德罗普配额更常用，因为它可以防止选出过多候选人。
Quota = Total Valid Votes ÷ Seats
5. Electoral Threshold | 选举门槛
Many proportional systems impose a legal threshold, usually expressed as a percentage of the national vote, which a party must exceed before it can receive any seats. For example, Germany’s Bundestag has a 5% threshold. The effective threshold can also be calculated using the formula based on district magnitude.
许多比例代表制设有法定门槛，通常以全国得票率的百分比表示，政党必须超过该比例才能获得席位。例如德国联邦议院设有5%的门槛。有效门槛也可以通过基于选区规模的公式计算。
Effective threshold ≈ 75% ÷ (District Magnitude + 1)
6. Duverger’s Law | 杜瓦杰定律
Duverger’s law states that single-member district plurality (SMDP) electoral systems tend to favour a two-party system. The ‘mechanical effect’ eliminates small parties from winning seats, while the ‘psychological effect’ discourages voters from wasting votes on them. This law helps explain the duopolistic nature of UK and US politics.
杜瓦杰定律指出，单一选区相对多数制（SMDP）倾向于形成两党制。“机械效应”使得小党难以赢得席位，而“心理效应”则阻止选民在其身上浪费选票。该定律有助于解释英美政治的两党垄断特征。
7. Iron Triangle | 铁三角
The Iron Triangle describes a stable, mutually beneficial relationship between congressional committees, interest groups, and bureaucratic agencies in the US political system. Each corner provides support or services to the others — for example, funding, favourable regulation, and electoral backing — often leading to policy capture and resistance to change.
铁三角描述了美国政治中国会委员会、利益集团和官僚机构之间稳定互利的关系。每个角都为其他两方提供支持或服务——例如资金、有利的监管和选举支持——往往导致政策被绑架，变革难以推动。
8. Olson’s Logic of Collective Action | 奥尔森的集体行动逻辑
Mancur Olson argued that large groups often fail to act in their common interest because individuals have an incentive to free-ride. Small groups can overcome this problem more easily through peer pressure and selective incentives. The formula highlights that collective good is not a sufficient condition for group mobilisation.
曼瑟·奥尔森认为，大群体常常无法为共同利益行动，因为个体有搭便车的动机。小群体则更容易通过同伴压力和选择性激励克服这一问题。该理论揭示，集体利益并非群体动员的充分条件。
9. Voter Turnout Formula | 投票率公式
Voter turnout is a key indicator of political participation and legitimacy. It is measured as the percentage of registered voters who cast a ballot in an election. Changes in turnout can be analysed across different election types or demographic groups to assess democratic health.
投票率是政治参与和合法性的关键指标。它以登记选民中实际投票人数的百分比来衡量。比较不同选举类型或人口群体的投票率变化，可以评估民主健康状况。
Turnout (%) = (Total Votes Cast ÷ Registered Voters) × 100
10. Wasted Vote Index | 浪费选票指数
The wasted vote concept measures how many votes do not contribute to electing a candidate. In safe seats, votes for the winner beyond the necessary plurality are surplus, while all votes for losing candidates are wasted. A high wasted-vote share can indicate low electoral efficiency and demand for reform.
浪费选票概念衡量了多少选票对选出候选人没有贡献。在安全席位中，胜选者超出所需相对多数的票数是溢余票，而落选者的所有选票都被浪费。高浪费选票比例可能表明选举效率低下，并催生改革诉求。
11. Gallagher Index of Disproportionality | 加拉格尔失衡指数
The Gallagher index quantifies the difference between the share of votes each party receives and the share of seats it wins. It uses a least-squares formula to give a single number representing overall disproportionality. A lower index indicates a more proportional electoral outcome.
加拉格尔指数量化了各政党得票率与赢得的席位比例之间的差异。它使用最小平方公式得出一个代表总体失衡程度的数值。指数越低，表明选举结果越成比例。
LSq = √(½ Σ(Vₚ − Sₚ)²)
12. Marginality and Swing | 边际选区与摇摆幅度
Marginality measures how close a constituency seat is to changing hands. The swing formula calculates the percentage point change in vote share from one party to another between elections. These tools are essential for understanding electoral strategy and predicting seat changes in first-past-the-post systems.
边际性衡量一个选区席位易手的接近程度。摇摆公式计算两次选举之间政党得票率的百分点变化。这些工具对于理解简单多数制下的选举策略和预测席位变动至关重要。
Swing (%) = (Change in Party A vote + Change in Party B vote) ÷ 2
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