Factors Helping Bismarck: An A-Level Mathematical Modelling Study | 帮助俾斯麦的因素：A-Level 数学建模研究

📚 Factors Helping Bismarck: An A-Level Mathematical Modelling Study | 帮助俾斯麦的因素：A-Level 数学建模研究

This article uses A-Level Edexcel Mathematics tools – probability, decision theory, game theory, weighted scoring and regression – to quantify the main factors that helped Otto von Bismarck unify Germany between 1862 and 1871.

本文运用 A-Level Edexcel 数学工具——概率、决策论、博弈论、加权评分与回归分析——来量化 1862 至 1871 年间帮助俾斯麦统一德国的主要因素。

1. From History to Algebra: Setting Up the Variables | 从历史到代数：设定变量

We define the outcome Y as the probability that Bismarck achieves a Prussian-led unification of Germany. The explanatory variables are x₁ = Prussian military strength, x₂ = diplomatic isolation of rivals, x₃ = railway and industrial capacity, x₄ = nationalist sentiment, and x₅ = mistakes by Austria and France.

我们将结果 Y 定义为俾斯麦实现以普鲁士为主导的德国统一的概率。解释变量为 x₁ = 普鲁士军事实力，x₂ = 对竞争对手的外交孤立，x₃ = 铁路与工业能力，x₄ = 民族主义情绪，x₅ = 奥地利和法国的失误。

These variables can be treated as inputs in a mathematical model, allowing us to compare their relative contribution rather than relying on narrative history alone.

这些变量可以作为数学模型中的输入，使我们能够比较它们的相对贡献，而不是仅仅依赖叙述性历史。

• Y: probability of Prussian-led unification, from 0 to 1
• Y：普鲁士主导统一的概率，范围从 0 到 1
• x₁ to x₅: scored from 0 to 10 scale
• x₁ 至 x₅：按 0 到 10 分制打分

2. Probability Trees and the Unification Scenarios | 概率树与统一情景

Bismarck had to win three limited wars: against Denmark (1864), Austria (1866) and France (1870-71). A probability tree can link

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