Northern Ireland Assembly and Executive: Mathematical Models in Power-Sharing | 北爱尔兰议会与行政：权力分享中的数学模型

📚 Northern Ireland Assembly and Executive: Mathematical Models in Power-Sharing | 北爱尔兰议会与行政：权力分享中的数学模型

The Northern Ireland Assembly and its power-sharing Executive are usually studied in politics, but they also provide rich contexts for A-Level Mathematics. From seat quotas and ministerial allocation to polling statistics and hypothesis tests, the numerical rules behind this institution connect directly to Edexcel topics such as percentages, proportional reasoning, binomial distributions and hypothesis testing.

北爱尔兰议会及其权力分享行政机构通常在政治学科中研究，但它们也为 A-Level 数学提供了丰富的应用背景。从席位配额和部长职位分配到民调统计和假设检验，这一机构背后的数值规则与 Edexcel 考点直接相关，例如百分比、比例推理、二项分布和假设检验。

1. Introduction to the Northern Ireland Assembly and Executive | 北爱尔兰议会与行政简介

The Northern Ireland Assembly is the devolved legislature for Northern Ireland, with 90 Members of the Legislative Assembly (MLAs). The Executive is the power-sharing government, led by a First Minister and deputy First Minister. From a mathematical standpoint, the Assembly’s composition and the allocation of Executive posts both depend on precise counting rules, quotas and proportional methods.

北爱尔兰议会是北爱尔兰的权力下设立法机构，共有 90 名立法会议员（MLA）。行政机构是权力分享政府，由首席部长和副首席部长领导。从数学角度看，议会的组成和行政职位的分配都依赖于精确的计票规则、配额和比例方法。

2. Assembly Seats and Proportional Representation | 议会席位与比例代表制

Elections to the Assembly use the Single Transferable Vote (STV) system in 18 constituencies, each returning 5 MLAs. This is a form of proportional representation, so the percentage of first-preference votes a party receives is not always equal to its percentage of seats, but the system aims to reduce disproportionality.

议会选举在 18 个选区采用单记可转移投票制（STV），每个选区选出 5 名议员。这是一种比例代表制，因此政党获得的第一偏好票百分比并不总是等于其席位百分比，但该制度旨在减少比例偏差。

A key measure is the seat share: seat share = (number of seats won ÷ total seats) × 100%. Comparing this with vote share helps analysts assess proportionality.

一个关键指标是席位份额：席位份额 =（赢得的席位数 ÷ 总席位数）× 100%。将其与得票份额进行比较，有助于分析比例性。

3. The Droop Quota in STV Elections | 单记可转移投票中的德鲁普配额

In each 5-seat constituency, a candidate needs to reach a quota to be elected. The Droop quota is calculated as:

在每个 5 席选区中，候选人需要达到一定配额才能当选。德鲁普配额的计算公式为：

Q = ⌊V ÷ (S + 1)⌋ + 1

where V is the total number of valid votes and S is the number of seats.

其中 V 是有效票总数，S 是席位数。

For example, if 60,000 valid votes are cast in a 5-seat constituency, then V = 60000 and S = 5. The quota is Q = ⌊60000 ÷ 6⌋ + 1 = 10000 + 1 = 10001 votes. This threshold ensures that no more than five candidates can reach it.

例如，如果一个 5 席选区有 60,000 张有效票，则 V = 60000，S = 5。配额为 Q = ⌊60000 ÷ 6⌋ + 1 = 10000 + 1 = 10001 票。这个门槛确保最多只有五名候选人能达到。

The floor function ⌊ ⌋ means ’round down to the nearest whole number’. In Edexcel questions, you may be asked to compute quotas from given vote totals and seat numbers.

下取整函数 ⌊ ⌋ 表示“向下取整到最接近的整数”。在 Edexcel 考题中，你可能需要根据给定的票数和席位数计算配额。

4. D’Hondt Allocation of Executive Posts | 行政职位的 D’Hondt 分配

Once MLAs are elected, Executive ministerial posts are allocated among parties using the D’Hondt method. For each party, divide its number of seats by 1, 2, 3, and so on. The resulting quotients are ranked from highest to lowest, and posts are awarded to the highest quotients in turn.

议员选出后，行政部长职位使用 D’Hondt 方法在政党之间分配。将每个政党的席位数除以 1、2、3 等。将得到的商数从高到低排序，按顺序把职位授予商数最高的政党。

For example, suppose Party A has 28 seats,

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