📚 The impact of different electoral systems on party representation and on voter choice | 不同选举制度对政党代表性与选民选择的影响
Electoral systems are the formal rules that convert votes into seats. They shape not only who wins office but also how fairly parties are represented and how freely voters can express their preferences. This article examines the main types of electoral systems used in the UK and elsewhere, using both qualitative and quantitative methods to assess their impact on party representation and voter choice.
选举制度是把选票转化为席位的正式规则。它们不仅决定谁当选，还影响政党的代表是否公平，以及选民能否自由表达偏好。本文分析英国及其他地区使用的主要选举制度，并结合定性与定量方法，评估它们对政党代表性和选民选择的影响。
1. What Are Electoral Systems? | 什么是选举制度？
An electoral system is the set of rules that determines how votes are cast, counted, and translated into legislative seats. The three broad families are plurality/majority systems, proportional representation (PR), and mixed systems. Within these families there are many variants, such as First Past the Post, the Additional Member System, and the Single Transferable Vote. The choice of system has profound consequences for the number of parties, the proportionality of outcomes, and the nature of voter choice.
选举制度是一套规定选票如何投出、计票以及如何转化为议会席位的规则。三大类分别是相对多数/绝对多数制、比例代表制以及混合制。在这些类别中有许多变体，例如简单多数制、附加议员制和可转移投票制。制度的选择对政党数量、结果的相称性以及选民选择的性质都有深远影响。
In this article, we will use simple mathematical indicators to compare systems, including the Gallagher index of disproportionality, the effective number of parties, and wasted vote calculations. These tools help make the impact of electoral systems measurable and examinable.
本文将使用简单的数学指标来比较不同制度，包括衡量不比例性的 Gallagher 指数、有效政党数以及废票计算。这些工具使得选举制度的影响变得可以量化和考核。
2. First Past the Post: Mechanism and Mathematical Character | 简单多数制：机制与数学特征
First Past the Post (FPTP) operates in single-member constituencies. The candidate with the largest number of votes wins the seat, regardless of whether that number exceeds 50%. This ‘winner takes all’ feature means that votes for losing candidates do not contribute to representation at all. Mathematically, in a constituency with three candidates receiving 40%, 35%, and 25% of the vote, the winner takes 100% of the seat with only 40% of the support.
简单多数制在单一选区中运作。获得最多票数的候选人赢得席位，无论其票数是否超过 50%。这种“赢者通吃”的特征意味着投给落选候选人的选票对代表性毫无贡献。从数学上看，在一个选区中，三位候选人分别获得 40%、35% 和 25% 的选票，获胜者仅以 40% 的支持率就拿下了 100% 的席位。
This creates a high level of wasted votes, defined as votes that do not help elect a candidate. In the example above, 60% of votes are wasted. High wasted votes distort the relationship between national vote share and national seat share, typically favouring the largest party and penalising smaller parties whose support is geographically dispersed.
这造成了高比例的废票，即未能帮助候选人当选的选票。在上面的例子中，60% 的选票被浪费了。高废票率扭曲了全国得票率与全国席位率之间的关系，通常有利于大党，惩罚那些支持者地理分布分散的小党。
As a result, FPTP tends to produce single-party majority governments even when no party wins a majority of votes. For example, in the 2019 UK general election, the Conservative Party won 43.6% of the vote but 56.2% of the seats, while the Liberal Democrats won 11.6% of the vote but only 1.7% of the seats. This is a clear example of disproportional representation.
因此，简单多数制往往产生一党多数政府，即使没有任何政党赢得多数选票。例如，在 2019 年英国大选中，保守党获得 43.6% 的选票却赢得 56.2% 的席位，而自由民主党获得 11.6% 的选票却只得到 1.7% 的席位。这是代表性不成比例的明显例子。
3. Proportional Representation: List Systems and Divisor Methods | 比例代表制：名单制与除数法
List proportional representation aims to allocate seats in proportion to each party’s share of the vote. Voters choose a party list, and seats are distributed using a mathematical formula. The two most common divisor methods are D’Hondt and Sainte-Laguë. In D’Hondt, seats are allocated by dividing each party’s vote total by the sequence 1, 2, 3, 4, and so on, then awarding seats to the highest resulting quotients. In Sainte-Laguë, the divisors are 1, 3, 5, 7, and so on, which favours smaller parties slightly more.
名单比例代表制旨在按照各政党得票比例分配席位。选民选择一个政党名单，席位则使用数学公式进行分配。两种最常见的除数法是 D’Hondt 法和 Sainte-Laguë 法。在 D’Hondt 法中，将各政党的总票数除以 1、2、3、4 等序列，然后将席位授予所得商数最大的政党。在 Sainte-Laguë 法中，除数为 1、3、5、7 等，这对小党稍微更有利。
For example, consider a four-party election where parties A, B, C, and D win 40,000, 30,000, 20,000, and 10,000 votes respectively for 5 seats. Using D’Hondt, the seat allocation would typically be 2 for A, 2 for B, and 1 for C, leaving D with none. The mathematical process makes the allocation transparent but also reveals how large parties are advantaged under D’Hondt.
例如，假设一场选举中有四个政党 A、B、C、D，分别获得 40,000、30,000、20,000 和 10,000 票，争夺 5 个席位。使用 D’Hondt 法，席位分配通常为 A 得 2 席、B 得 2 席、C 得 1 席，而 D 颗粒无收。数学过程使分配透明化，但也揭示了 D’Hondt 法下大党的优势。
Seat allocation under D’Hondt = max quotients of Vᵢ ÷ 1, 2, 3, …
Seat allocation under Sainte-Laguë = max quotients of Vᵢ ÷ 1, 3, 5, …
4. Mixed Systems: The Additional Member System | 混合制：附加议员制
The Additional Member System (AMS) combines single-member constituencies with party-list top-up seats. Voters have two votes: one for a constituency MP under FPTP, and one for a regional party list. The list seats are allocated to compensate for the disproportionality of the constituency results. In Scotland and Wales, the D’Hondt method is used within each region to determine the number of top-up seats each party receives, taking into account the constituency seats already won.
附加议员制结合了单一选区制和政党名单补偿席位。选民拥有两张选票：一张投给简单多数制下的选区议员，另一张投给地区政党名单。名单席位用于补偿选区结果的不比例性。在苏格兰和威尔士，各地区使用 D’Hondt 法确定每个政党应得的补偿席位，同时考虑到他们已经赢得的选区席位。
AMS produces a more proportional outcome than pure FPTP, but it is not fully proportional because the number of top-up seats is fixed and the constituency element still favours larger parties. Voter choice is widened because voters can split their two votes, supporting a local candidate from one party and a regional list from another. This creates a strategic dimension: voters may use their list vote to support a smaller party without worrying about wasting it.
附加议员制比纯粹的简单多数制产生更相称的结果，但由于补偿席位数量固定，且选区部分仍然有利于大党，因此并非完全相称。选民选择范围扩大，因为选民可以分开两张选票，一张支持某党的本地候选人，另一张支持另一党的地区名单。这创造了策略性维度：选民可以使用名单票支持小党，而不必担心浪费选票。
5. Preferential Systems: Single Transferable Vote | 偏好投票制：可转移投票制
The Single Transferable Vote (STV) uses multi-member constituencies and ranked ballots. Voters rank candidates in order of preference, and candidates are elected if they reach a quota. The most common quota is the Droop quota, defined as:
可转移投票制使用多议员选区和排序选票。选民按偏好顺序排列候选人，候选人达到配额即可当选。最常用的配额是 Droop 配额，其定义为：
Droop quota = ⌊ Total valid votes ÷ (Seats + 1) ⌋ + 1
Surplus votes for elected candidates are transferred to the voters’ next preferences, and the lowest-placed candidates are eliminated sequentially with their votes redistributed. This process reduces wasted votes and gives smaller parties a fairer chance if their supporters are geographically concentrated.
当选候选人的多余选票会转移给选民的次优偏好，排名最低的候选人被依次淘汰，其选票重新分配。这一过程减少了废票，并在小党支持者地理集中的情况下给予他们更公平的机会。
STV gives voters a high degree of choice because they can rank candidates across parties and express nuanced preferences. However, the counting process is complex and less transparent to the average voter. The mathematical transfers mean that the final seat allocation often reflects the broad preference structure of the electorate more accurately than FPTP.
可转移投票制赋予选民高度的选择权，因为他们可以跨政党对候选人进行排序，表达细致的偏好。然而，计票过程复杂，对普通选民而言透明度较低。数学上的票数转移意味着最终的席位分配往往比简单多数制更准确地反映选民的总体偏好结构。
6. Quantifying Representation: The Gallagher Index | 量化代表性：Gallagher 指数
To compare the proportionality of different electoral systems, political scientists use the Gallagher index, also known as the least squares index. It measures the difference between each party’s vote share and its seat share. The formula is:
为了比较不同选举制度的比例性，政治学家使用 Gallagher 指数，也称为最小二乘指数。它衡量每个政党的得票率与席位率之间的差异。公式如下：
LSq = √( ½ × Σ (vᵢ − sᵢ)² )
Here, vᵢ is the vote share of party i expressed as a decimal, and sᵢ is the seat share of party i. The index ranges from 0 (perfect proportionality) to 100 (total disproportionality). Lower values indicate fairer representation. In UK general elections under FPTP, the Gallagher index often falls between 10 and 20, while in countries using list PR, it is typically below 5.
这里，vᵢ 是政党 i 的得票率（以小数表示），sᵢ 是政党 i 的席位率。该指数范围从 0（完全相称）到 100（完全不相称）。数值越低代表代表性越公平。在英国简单多数制下的大选中，Gallagher 指数通常在 10 到 20 之间，而在采用名单比例代表制的国家，该指数通常低于 5。
This mathematical tool allows us to state precisely that FPTP produces more disproportional outcomes than PR, and that AMS and STV fall somewhere in between. It is a key skill in A-level Politics to be able to interpret such data and explain the reasons behind the numbers.
这一数学工具使我们能够精确地指出，简单多数制产生的不比例结果比比例代表制更大，而附加议员制和可转移投票制介于两者之间。在 A-level 政治学中，能够解读此类数据并解释数字背后的原因是关键技能。
7. Effective Number of Parties | 有效政党数
The effective number of parties (ENP) is another quantitative measure that reflects how fragmented a party system is. The Laakso–Taagepera index is the most common formula:
有效政党数是另一项量化指标，反映政党体系的碎片化程度。Laakso–Taagepera 指数是最常用的公式：
ENP = 1 ÷ Σ sᵢ²
where sᵢ is the seat share of party i. If one party wins all seats, ENP = 1. In a perfectly balanced two-party system, ENP = 2. In a fragmented multi-party system, ENP can exceed 5 or 6. FPTP tends to produce ENP values close to 2, reflecting Duverger’s law that plurality systems encourage two-party competition. List PR systems often produce ENP values above 4, reflecting multi-party politics.
其中 sᵢ 是政党 i 的席位率。如果一个政党赢得所有席位，ENP = 1。在一个完全平衡的两党制中，ENP = 2。在碎片化的多党制中，ENP 可以超过 5 或 6。简单多数制往往产生接近 2 的 ENP 值，反映了 Duverger 定律，即相对多数制鼓励两党竞争。名单比例代表制通常产生 4 以上的 ENP 值，反映多党政治。
This measure helps explain why FPTP countries like the UK and USA have dominated by two main parties, while PR countries like the Netherlands or Israel have many parties in parliament. The mathematical mechanism is that FPTP creates high barriers for small parties due to wasted votes, whereas PR lowers those barriers.
这一指标有助于解释为什么英国和美国等简单多数制国家由两大政党主导，而荷兰或以色列等比例代表制国家议会中有许多政党。数学机制在于，简单多数制因废票问题为小党设置了高门槛，而比例代表制则降低了这些门槛。
8. Voter Choice and Strategic Voting | 选民选择与策略性投票
Electoral systems not only shape representation but also influence how voters behave. In FPTP, many voters cast strategic or tactical votes: they do not vote for their most preferred party because they believe it cannot win in their constituency. Instead, they vote for a less preferred but more viable candidate to prevent an even less preferred candidate from winning. This is a direct consequence of the winner-takes-all mathematics.
选举制度不仅塑造代表性，还影响选民的行为方式。在简单多数制下，许多选民会投出策略性或战术性选票：他们不投给自己最偏爱的政党，因为他们认为该党在自己的选区无法获胜。相反，他们投票给一个不那么喜欢但更有胜算的候选人，以防止更不喜欢的候选人获胜。这是赢者通吃数学的直接后果。
For example, suppose a constituency has three candidates: Labour (40%), Conservative (35%), and Green (25%). A Green supporter who prefers Labour over Conservative might vote Labour to stop the Conservative candidate from winning. This means the Green vote is understated in the official result, and voter choice is constrained by the fear of wasting a vote.
例如，假设一个选区有三名候选人：工党（40%）、保守党（35%）和绿党（25%）。绿党支持者若比起保守党更倾向于工党，可能会投工党以阻止保守党候选人获胜。这意味着绿党的实际支持率在官方结果中被低估，选民选择受到害怕浪费选票的制约。
Under PR and STV, strategic voting is much less common. Voters can support their genuine first preference because the proportional allocation or preference transfers reduce the risk of wasted votes. This increases voter satisfaction and produces a more accurate reflection of public opinion.
在比例代表制和可转移投票制下，策略性投票要少得多。选民可以支持他们真正的第一偏好，因为比例分配或偏好转移降低了废票风险。这提高了选民满意度，并更准确地反映公众舆论。
9. Thresholds and Minority Representation | 阈值与少数群体代表性
Many PR systems impose an electoral threshold, such as 5% of the national vote, to prevent very small parties from winning seats. The mathematical effect is straightforward: a party below the threshold receives no seats even if it has a small but significant vote share. In Germany, the 5% threshold at the national level has kept many minor parties out of the Bundestag, though exceptions exist for parties winning three constituency seats.
许多比例代表制设定选举阈值，例如全国得票率的 5%，以防止极小的政党获得席位。数学效果很直接：低于阈值的政党即使拥有少量但重要的选票，也无法获得席位。在德国，全国 5% 的阈值使许多小党无法进入联邦议院，尽管赢得三个选区席位的政党有例外。
In the UK, FPTP acts as a de facto threshold because a party must win a plurality in at least one constituency. A party with 10% of the national vote spread evenly across all constituencies will win zero seats. This is a major criticism from supporters of PR, who argue that minority viewpoints are underrepresented.
在英国，简单多数制实际上起到事实上的阈值作用，因为一个政党必须至少在一个选区赢得相对多数。一个在全国均匀获得 10% 选票的政党将赢得零个席位。这是比例代表制支持者的主要批评，他们认为少数群体的观点没有得到充分代表。
On the other hand, thresholds can prevent extreme fragmentation and make government formation easier. The trade-off between representativeness and governability is a key theme in any discussion of electoral system design.
另一方面，阈值可以防止议会过度碎片化，使政府组建更容易。代表性与管理能力之间的权衡是讨论选举制度设计时的关键主题。
10. Comparative Summary and Conclusion | 对比总结与结论
The table below summarises the typical effects of four major electoral systems on party representation and voter choice. The indicators used are qualitative but are consistent with the quantitative measures discussed above.
下表总结了四种主要选举制度对政党代表性和选民选择的典型影响。所使用的指标是定性的，但与上文讨论的量化指标一致。
| Electoral system | Party representation | Voter choice |
|---|---|---|
| FPTP | Disproportional, favours large parties, two-party tendency | Strategic voting common, wasted votes high |
| List PR | Highly proportional, multi-party systems | Sincere voting, low wasted votes |
| AMS | More proportional than FPTP, but still favours larger parties | Split-ticket voting, moderate strategy |
| STV | Proportional within multi-member areas, fair to smaller parties | High choice, ranked preferences, less strategic voting |
In conclusion, electoral systems are not neutral rules. They determine the mathematical translation of votes into seats, and in doing so they shape party systems and voter behaviour. FPTP produces strong, stable governments but weak proportionality and often forces voters to vote tactically. PR systems produce fairer representation and more sincere voting but may lead to coalition governments and higher fragmentation. AMS and STV offer compromises that balance local representation with proportionality. Understanding these trade-offs is essential for any A-level Politics student analysing electoral reform.
总之，选举制度并非中立的规则。它们决定了选票转化为席位的数学方式，并由此塑造政党体系和选民行为。简单多数制产生强大而稳定的政府，但比例性较弱，常常迫使选民采取策略性投票。比例代表制产生更公平的代表和更真诚的投票，但可能导致联合政府以及更高的碎片化。附加议员制和可转移投票制提供了折中方案，在地方代表性与比例性之间取得平衡。理解这些权衡对于任何分析选举改革的 A-level 政治学学生来说都是必不可少的。
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