Year 10 WJEC Politics: Quick-Reference Formula & Theorem Handbook | Year 10 WJEC 政治：公式定理速查手册

📚 Year 10 WJEC Politics: Quick-Reference Formula & Theorem Handbook | Year 10 WJEC 政治：公式定理速查手册

This quick-reference handbook presents key formulas and theorems for Year 10 WJEC Politics in a bilingual format. Understanding these concepts will help you analyse electoral systems, political behaviour, and government structures effectively. Each entry provides a concise definition, a mathematical model or logical rule, and a practical illustration.

本速查手册以双语形式呈现 Year 10 WJEC 政治课程中的重要公式和定理。掌握这些概念将有助于你有效分析选举制度、政治行为和政府结构。每个条目包括简明定义、数学模型或逻辑规则，以及实际应用示例。

1. Duverger’s Law | 杜瓦杰定律

Duverger’s law describes the relationship between electoral systems and party systems. Under first-past-the-post (FPTP) in single-member districts, the electoral mechanism tends to produce two-party systems because smaller parties often cannot gain any seats unless they have geographically concentrated support.

杜瓦杰定律描述了选举制度与政党制度之间的关系。在单一选区相对多数决制（FPTP）下，选举机制往往产生两党制，因为小党派除非拥有地理上集中的支持，否则通常无法获得任何席位。

In contrast, proportional representation (PR) lowers the barrier for smaller parties, resulting in multi-party systems. This law is often summarised as: FPTP → two-party dominance; PR → multi-party coalition politics.

相比之下，比例代表制（PR）降低了小党派的进入门槛，从而形成多党制。这一定律常被概括为：FPTP → 两党主导；PR → 多党联合政治。

2. The Cube Rule | 立方法则

The cube rule estimates how votes translate into seats in a two-party system. The ratio of seats won by two parties is approximately proportional to the cube of their vote ratio. This highlights the winner’s bonus in FPTP systems.

立方法则用于估算两党制下选票如何转换成席位。两党赢得的席位比大致与其得票比的立方成正比，这突显了FPTP制度中的赢家红利。

Seats₁ / Seats₂ ≈ (Votes₁ / Votes₂)³

席位₁ / 席位₂ ≈ (得票₁ / 得票₂)³

For example, if Party A receives 55% of the vote and Party B 45%, the votes ratio is 1.22; cubing gives 1.22³ ≈ 1.82, meaning Party A could expect about 1.82 times as many seats as Party B, far more than the simple vote margin suggests.

例如，如果A党获得55%的选票，B党获得45%，得票比为1.22；立方后得到1.22³ ≈ 1.82，意味着A党预计获得的席位大约是B党的1.82倍，远超简单得票差距所显示的优势。

3. Effective Number of Parties (ENP) | 有效政党数

The Laakso-Taagepera index measures the number of relevant parties in a system by weighting parties by their vote shares. It reveals the real fragmentation of a party system beyond the mere count of parties.

拉索-塔格佩拉指数通过按得票份额加权来衡量体系中相关政党的数量，它揭示了政党体系真实的碎片化程度，而不仅仅是政党的数量。

ENP = 1 ÷ Σ(vᵢ²)

有效政党数 = 1 ÷ Σ(vᵢ²)

Here vᵢ is the decimal vote share of party i. If two parties each have 50% of the vote, ENP = 1 ÷ (0.5² + 0.5²) = 2.0. If four parties hold equal shares of 25%, ENP = 1 ÷ (4 × 0.0625) = 4.0. Because larger parties are weighted more heavily, ENP is always smaller than or equal to the actual number of parties.

其中vᵢ是政党i的得票率（小数形式）。如果两个政党各得50%选票，ENP = 1 ÷ (0.5² + 0.5²) = 2.0。如果四个政党各占25%，ENP = 1 ÷ (4 × 0.0625) = 4.0。由于大党被赋予更大权重，ENP总是小于或等于实际政党数量。

4. Representation Bias Formula | 代表比例偏差公式

Representation bias measures the difference between the percentage of seats a party wins and its percentage of national votes. A positive bias indicates over-representation, while a negative bias signals under-representation.

代表比例偏差衡量一个政党赢得的席位百分比与其全国得票百分比之间的差值。正偏差表示过度代表，负偏差则表示代表不足。

Bias = %Seats − %Votes

偏差 = 席位百分比 − 得票百分比

For example, in the 2019 UK general election, the Conservative Party won 43.6% of the

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