📚 Formulae & Theorems Quick Reference for SQA Politics | SQA 政治公式定理速查手册
In SQA Higher Politics, a solid grasp of quantitative electoral formulas, indices, and established political theorems is essential for evaluating systems, comparing outcomes, and understanding political behaviour. This handbook brings together the most important numerical tools and theoretical laws, providing clear definitions, worked symbolism, and concise explanations for rapid revision. Master these and you will be well equipped to tackle data‑response questions, source analysis, and extended essays with confidence.
在 SQA Higher 政治课程中，牢固掌握定量选举公式、指数和经典政治学定理是评估制度、比较结果和理解政治行为的关键。本手册汇集了最重要的数值工具与理论法则，提供明确定义、符号用法和简明解释，方便快速复习。掌握了这些内容，你就能自信地应对数据回答题、资料分析题和长篇论文。
1. Hare Quota | 黑尔配额
The Hare quota is the simplest formula for determining the number of votes needed to win a seat under the Single Transferable Vote (STV) system. It is calculated by dividing the total number of valid votes cast by the total number of seats to be filled in the constituency.
黑尔配额是单一可转移投票制 (STV) 下确定赢得一个席位所需票数的最简单公式。其计算方法是：将总有效票数除以选区应选席位数。
Quota = Total valid votes ÷ Total seats
The result is a simple quota. However, because this does not account for wasted votes or surplus transfers efficiently, it is rarely used in pure form for STV elections; instead the Droop quota is preferred.
计算结果是一个简单配额。但由于该配额不能有效处理选票浪费或剩余票转移，因此在实际的 STV 选举中很少直接使用，通常更倾向于使用德鲁普配额。
2. Droop Quota | 德鲁普配额
The Droop quota is the standard minimum number of votes a candidate requires to be elected under STV. It is designed to produce just enough winners to fill all seats while minimising the number of surplus votes.
德鲁普配额是 STV 选举中候选人当选所需的最低票数标准。它的设计既能刚好选出足够当选者填满所有席位，又能最大限度地减少剩余票数。
Quota = [Total valid votes ÷ (Total seats + 1)] + 1
The addition of 1 ensures that only the exact number of candidates required can reach the quota. Any votes a candidate receives above this quota are transferred to other candidates according to voters’ subsequent preferences.
公式中加 1 确保了只有恰好所需数量的候选人能达到配额。候选人获得超出此配额的选票将根据选民的后续偏好转移给其他候选人。
3. D’Hondt Method | 洪德法
The D’Hondt method is a highest‑average system used to allocate seats in party‑list proportional representation (e.g. for the European Parliament elections in some countries). It tends to slightly favour larger parties.
洪德法是一种最高平均数法，用于政党名单比例代表制（如某些国家的欧洲议会选举）中的席位分配。它通常略微偏向大党。
The method works by dividing each party’s total votes successively by 1, 2, 3, 4, … and then awarding seats to the parties with the highest quotients. The formula for the quotients is:
该方法将各政党的总票数依次除以 1, 2, 3, 4……，然后将席位分配给商数最高的政党。商数公式如下：
Quotient = Votes ÷ (s + 1), where s is the number of seats already won by that party.
This is repeated until all seats are allocated. A small party may need a very strong vote share to win its first seat because the divisor for its first seat is 1, while a larger party with several seats already will be divided by a higher number.
重复此过程直至所有席位分配完毕。小党可能需要非常高的得票率才能赢得第一个席位，因为其第一个席位除数为 1，而已经赢得多个席位的大党则会被较大的数除。
4. Sainte‑Laguë Method | 圣拉格法
The Sainte‑Laguë method is another highest‑average divisor method but uses odd numbers as divisors: 1, 3, 5, 7, … This makes it more proportional than the D’Hondt method and gives smaller parties a better chance of winning seats.
圣拉格法是另一种最高平均数除数法，但使用奇数作为除数：1、3、5、7……这使得它比洪德法更具比例性，并使小党有更好的机会赢得席位。
Quotient = Votes ÷ (2s + 1), where s is the number of seats already won.
Because the divisor grows more slowly for the first few seats, a party’s initial quotient remains relatively high, allowing smaller parties to compete with larger ones on a more equal basis. A modified version (1.4, 3, 5, …) is sometimes used to further reduce fragmentation.
由于最初几个席位的除数增长较慢，政党的初始商数保持相对较高，使得小党可以在更平等的基础上与大党竞争。有时会使用改良版本（1.4, 3, 5……）以进一步减少碎片化。
5. Laakso‑Taagepera Effective Number of Parties | 拉克索‑塔格佩拉有效政党数
The effective number of parties index translates a set of party vote or seat shares into a single number representing how many “relevant” parties exist in a party system, weighted by their size.
有效政党数指数将各政党的得票率或席次率转换成一个单一数字，代表政党体系中按规模加权计算后有多少个“相关”政党。
N = 1 ÷ Σ (pi)²
Here pi is the fractional share of votes (or seats) for party i. If two parties each have 50% of the vote, N = 1 ÷ (0.5² + 0.5²) = 2. If one party has 70% and another 30%, N ≈ 1.72, reflecting a dominant‑party lean. Higher values indicate a more fragmented system.
其中 pi 是政党 i 的得票（或席位）比例。如果两个政党各占 50% 选票，N = 1 ÷ (0.5² + 0.5²) = 2。如果一个政党占 70%，另一个占 30%，N ≈ 1.72，反映了主导党倾向。数值越高表明体系越碎片化。
6. Gallagher Index | 加拉格尔指数
The Gallagher index (or least‑squares index) measures the disproportionality between the share of votes a party receives and the share of seats it wins. A lower index indicates a more proportional outcome.
加拉格尔指数（或最小平方指数）衡量一个政党所得选票份额与其赢得的席位份额之间的不均衡程度。指数越低，结果越合比例。
LSq = √( ½ Σ (Vi – Si)² )
Vi and Si are the vote and seat percentages for party i. The squared differences are summed, halved, and the square root taken. It is widely used in comparative politics, particularly when assessing the impact of electoral thresholds and district magnitude on fairness.
Vi 和 Si 分别是政党 i 的得票率和席次率。将差值的平方求和、减半再开方。该指数被广泛应用于比较政治学，尤其在评估选举门槛和选区规模对公平性的影响时。
7. Duverger’s Law | 迪韦尔热法则
Duverger’s law describes a systematic relationship between electoral systems and party systems: the single‑member plurality (first‑past‑the‑post) system tends to favour a two‑party system, while proportional representation tends to favour multiparty systems.
迪韦尔热法则描述了选举制度与政党制度之间的系统性关系：单一选区相对多数制（简单多数制）倾向于促进两党制，而比例代表制倾向于促进多党制。
The mechanism is both mechanical (small parties win few seats even with substantial votes) and psychological (voters do not want to “waste” their votes on candidates unlikely to win, so they gravitate towards the top two contenders). This rule is central to understanding UK and US party politics.
这一机制既有机械性（小党即使获得可观选票也赢得不了多少席位）也有心理性（选民不想把票“浪费”在不可能获胜的候选人身上，因而向两大竞争者靠拢）。这条法则是理解英国和美国政党政治的核心。
8. Median Voter Theorem | 中间选民定理
Proposed by Anthony Downs, the median voter theorem states that in a two‑party system with a single dimension of issue preference, rational parties will position their policies close to the preferences of the median voter to maximise their chance of winning elections.
由安东尼·唐斯提出的中间选民定理指出，在两党制和单一议题维度下，理性的政党会将其政策定位在靠近中间选民偏好的位置，以最大化赢得选举的机会。
If voters are normally distributed along a left‑right spectrum, the median voter lies exactly in the middle. Any party that moves too far from the centre risks losing moderate voters to its opponent. This theorem helps explain policy convergence in Westminster‑style politics and the tendency for major parties to avoid extremes.
如果选民在左右光谱上呈正态分布，中间选民恰好位于中点。任何偏离中间太远的政党都有可能将温和选民推向对手。这一定理有助于解释威斯敏斯特式政治中的政策趋同，以及主要政党回避极端的倾向。
9. Collective Action Problem (Olson) | 集体行动问题（奥尔森）
Mancur Olson’s logic of collective action asserts that rational, self‑interested individuals will not voluntarily contribute to the provision of a public good, even if they would benefit from it, because they can “free ride” on the efforts of others.
曼瑟尔·奥尔森的集体行动逻辑指出，理性的、自利的个人不会自愿为公共品的提供作出贡献，即使他们能从中获益，因为他们可以“搭便车”分享他人的努力成果。
This theorem explains why large, latent groups (such as consumers or taxpayers) are often politically underrepresented unless selective incentives (e.g. insurance, social pressure) compel participation. It is a foundational concept in understanding interest group formation and the challenges of mobilisation.
这一定理解释了为什么大型潜在群体（如消费者或纳税人）在政治上经常缺乏代表性，除非有选择性激励（如保险、社会压力）迫使他们参与。它是理解利益集团形成和动员挑战的基础概念。
10. Iron Triangle | 铁三角
The iron triangle is a model of the stable, mutually beneficial relationship between a congressional committee (or government department), a bureaucratic agency, and an interest group. Each corner supports the others, often leading to policy capture and resistance to change.
铁三角是一个描述国会委员会（或政府部门）、官僚机构和利益集团之间稳定互利关系的模型。每个角都支持其他角，往往导致政策被俘获并抵制变革。
For example, a parliamentary defence committee approves funding for a weapons programme, the defence ministry administers the contracts, and defence contractors provide campaign contributions and employment for former officials. This closed network can operate with minimal public scrutiny, undermining democratic accountability.
例如，议会国防委员会批准武器项目资金，国防部管理合同，而国防承包商则为竞选捐款并为前官员提供就业机会。这个封闭网络几乎不受公众监督，从而削弱民主问责。
Published by TutorHao | Politics Revision Series | aleveler.com
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