📚 Analysis of National Voting Behaviour Patterns for the 1979, 1997 and 2010 Elections | 1979、1997 与 2010 年大选全国投票行为模式的数学分析
This article uses A-Level Mathematics statistics to analyse national voting behaviour across three UK general elections: 1979, 1997 and 2010. We treat vote shares, turnout, swings and social patterns as data sets, applying percentages, correlation, regression and measures of dispersion. Every technique used here is examinable content: percentage change, index numbers, mean and standard deviation, scatter diagrams, the product moment correlation coefficient, least squares regression, weighted means and the chi-squared test.
本文运用 A-Level 数学中的统计方法，分析 1979、1997 和 2010 年三次英国大选的全国投票行为。我们将得票率、投票率、摆动值和社会模式视为数据集，运用百分比、相关性、回归和离散程度指标进行计算。文中涉及的每一个技术点都是考纲内容：百分比变化、指数、平均数与标准差、散点图、积矩相关系数、最小二乘回归、加权平均以及卡方检验。
1. Data Sources and Overview | 数据来源与总览
The data are drawn from official UK general election results published by the House of Commons Library and the Electoral Commission. We focus on three election years: 1979, 1997 and 2010. These elections are chosen because they represent turning points: 1979 brought the Conservatives to power under Margaret Thatcher, 1997 produced a landslide Labour victory under Tony Blair, and 2010 produced the first hung parliament since 1974.
数据来自英国下议院图书馆和选举委员会公布的官方大选结果。我们聚焦三个选举年份：1979、1997 和 2010。选择这三次是因为它们代表转折点：1979 年撒切尔夫人领导的保守党上台执政；1997 年布莱尔领导工党取得压倒性胜利；2010 年产生了自 1974 年以来第一个悬浮议会（无多数议会）。
A-Level statistics requires you to state the source and the nature of your data before you calculate anything. Here the observations are national aggregate percentages, not individual voters, so the data are secondary and already summarised. That matters for reliability: any conclusion we draw describes the electorate as a whole, not individual electors.
A-Level 统计要求我们在计算之前先说明数据来源与数据性质。本文的观测值是全国汇总百分比，而不是单个选民的数据，因此属于二手数据，且已经被汇总处理。这一点对可靠性很重要：我们得出的任何结论描述的都是整体选民，而不是单个选民。
The key figures used throughout this article are summarised below. Vote shares are UK-wide percentages of valid votes cast; seat numbers are for the House of Commons as it was at each election.
本文后续使用的关键数据汇总如下。得票率为全英范围内的有效票百分比；议席数为各次大选时下议院的实际情况。
| Election | Turnout | Con % | Lab % | Lib/LD % | Seats Con/Lab/LD | Outcome |
| 1979 | 76.0% | 43.9 | 36.9 | 13.8 | 339 / 269 / 11 | Conservative majority |
| 1997 | 71.4% | 30.7 | 43.2 | 16.8 | 165 / 418 / 46 | Labour landslide |
| 2010 | 65.1% | 36.1 | 29.0 | 23.0 | 306 / 258 / 57 | Hung parliament |
2. Vote Share as Percentage Data | 得票率作为百分比数据
A vote share is a percentage of a whole, so the shares of all parties must sum to 100% way to catch errors. In 1979 the three largest parties recorded 43.9 + 36.9 + 13.8 = 94.6%, leaving 5.4% her parties combined. In 2010 the three largest parties recorded 36.1 + 29.0 + 23.0 = 88.1%, leaving 11.9% for others - more than double the 1979 figure.
得票率是整体的百分比，因此所有政党的得票率之和必须等于 100%。检验这一点是快速发现错误的方法。1979 年三大党为 43.9 + 36.9 + 13.8 = 94.6%，其余所有政党合计 5.4%。2010 年三大党为 36.1 + 29.0 + 23.0 = 88.1%，其余政党合计 11.9%，是 1979 年的两倍多。
m error is confusing percentage points with percent. The Conservative share fell from 43.9% in 1979 to 30.7% hat is a fall of 13.2 percentage points, but the relative fall is 13.2 ÷ 43.9 × 100 = 30.1%. Both answers are correct; only the wording of the question tells you which is wanted.
最常见的考试错误是把"百分点"和"百分比"混为一谈。保守党得票率从 1979 年的 43.9% 降到 1997 年的 30.7%，下降了 13.2 个百分点，但相对下降幅度为 13.2 ÷ 43.9 × 100 = 30.1%。两个答案都对，只有题目措辞能告诉你题目要的是哪一个。
agrams are appropriate. A pie chart works when you want to show that parts make a whole, but it is poor at distinguishing 43.2% from 43.9%, because the angles differ by only 0.7% g parties over time, a comparative bar chart or a line graph is usually the better choice.
百分比数据也限制了可用的图表类型。饼图适合展示"部分构成整体"，但很难区分 43.2% 与 43.9%，因为两者角度仅相差 0.7% × 360° = 2.5°。若要比较不同时期各党表现，复式条形图或折线图通常是更好的选择。
3. Turnout: Percentages and Change | 投票率：百分比与变化
Turnout is defined as the number of valid votes cast divided by the number of registered electors, expressed as a percentage. Across our three elections turnout fell steadily: 76.0% in 1979, 71.4% in 1997, 65.1% in 2010.
投票率的定义是：有效投票数除以登记选民人数，用百分比表示。在本文三次大选中，投票率持续下降：1979 年 76.0%，1997 年 71.4%，2010 年 65.1%。
is 76.0 − 65.1 = 10.9 percentage points, and the relative fall is 10.9 ÷ 76.0 × 100 = 14.3% seven who would have voted in 1979 did not vote in 2010, assuming comparable electorates.
从 1979 年到 2010 年，绝对下降为 76.0 − 65.1 = 10.9 个百分点，相对下降为 10.9 ÷ 76.0 × 100 = 14.3%。换言之，假设选民规模可比，1979 年会投票的选民中约每七人就有一人在 2010 年没有投票。
Turnout is also useful for weighted calculations. National turnout is not the simple mean of regional turnouts; it is the weighted mean, where the weights are the numbers of registered electors in each region. If turnout rᵢ applies to Nᵢ electors, then overall turnout equals Σ(Nᵢrᵢ) ÷ ΣNᵢ.
投票率还可用于加权计算。全国投票率不是各地区投票率的简单平均数，而是加权平均数，权重是各地区的登记选民人数。若第 i 个地区的投票率为 rᵢ、选民数为 Nᵢ，则总体投票率为 Σ(Nᵢrᵢ) ÷ ΣNᵢ。
4. Swing: The Mathematics of Two-Party Movement | 摆动值的数学：两党转移
Swing measures how support moves between two parties. The standard (Butler) formula for the swing from party A to party B is the average of A's loss and B's gain:
摆动值衡量的是支持度在两党之间如何转移。从 A 党转向 B 党的标准（巴特勒）公式，是 A 党的下降幅度与 B 党的上升幅度的平均值：
Swing = ½ [(%Aₜ₋₁ − %Aₜ) + (%Bₜ − %Bₜ₋₁)]
ained 8.1 points while Labour lost 2.3, so the swing to the Conservatives was ½(8.1 + 2.3) = 5.2 points.
其中 t−1 表示上一次大选，t 表示本次大选。据此可得本文三次大选的主要摆动值。1979 年保守党上升 8.1 个百分点，工党下降 2.3 个百分点，故向保守党的摆动为 ½(8.1 + 2.3) = 5.2 个百分点。
t explains why so many seats changed hands at once. In 2010, the Conservatives gained 3.7 points while Labour lost 6.2, giving a swing to the Conservatives of ½(3.7 + 6.2) ≈ 5.0 points.
1997 年工党上升 8.8 个百分点，保守党下降 11.2 个百分点，向工党的摆动为 ½(8.8 + 11.2) = 10.0 个百分点——两位数的摆动解释了为何大量议席同时易手。2010 年保守党上升 3.7 个百分点，工党下降 6.2 个百分点，向保守党的摆动约为 ½(3.7 + 6.2) ≈ 5.0 个百分点。
The concept of uniform national swing (UNS) assumes the same swing applies in every constituency. UNS is a powerful modelling tool but a simplification: it ignores third-party surges, differential abstention and tactical voting. In 2010, the Liberal Democrat share rose to 23.0%, and much of that support was concentrated rather than uniform.
"全国统一摆动"（UNS）假设每个选区都出现相同的摆动。UNS 是很有力的建模工具，但属于简化假设：它忽略了第三党的崛起、不同群体投票率的差异以及策略性投票。2010 年自由民主党得票率升至 23.0%，而这种支持在地区分布上并不均匀。
5. Measures of Dispersion | 离散程度指标
Summary statistics are only half the story. Two elections can have the same mean turnout but very different levels of variation, and variation is what decides marginal seats. Consider an illustrative set of nine constituency turnouts from one election year: 58, 61, 63, 65, 66, 68, 70, 72 and 78 (in percent).
概括性统计量只讲了一半的故事。两次大选可以有相同的平均投票率，但离散程度差别很大，而离散程度正是决定边缘选区归属的因素。考虑某次大选中九个选区投票率的示例数据（百分比）：58、61、63、65、66、68、70、72、78。
tage points. The lower quartile is 63 and the upper quartile is 70, so the interquartile range is IQR = 70 − 63 = 7 percentage points.
这里不存在众数，因为没有任何数值重复出现。中位数是排序后第五个值，即 66。平均数为 601 ÷ 9 ≈ 66.8。极差为 78 − 58 = 20 个百分点。下四分位数为 63，上四分位
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图