Does One Vote Make a Difference? Analyzing Electoral Impact

The age-old question of whether one vote can make a difference in an election has been a subject of deep scrutiny and debate. In the context of parliamentary and congressional elections, the sheer number of votes cast makes it virtually impossible for every individual vote to impact the outcome. However, different electoral systems can lead to varying degrees of impact, with some systems much more responsive to individual votes than others.

Electoral Systems and Their Impact

Most European countries use a system of proportional representation, where the number of seats a party gains is closely aligned with the percentage of votes it receives. This system ensures that a higher percentage of votes do make a difference, as seats are allocated based on the total votes a party receives. Conversely, the first-past-the-post system, used in the United Kingdom, the United States, and Canada, distributes seats based on which candidate wins the most votes in their district, often leading to a much smaller percentage of votes having impact.

Consider the UK general election in 2019. In this system, the winner of a parliamentary seat needs only the highest number of votes in their district, often far less than half the total votes cast. As a result, the majority of votes do not contribute to securing seats for their preferred candidate or party. This system is designed to protect majorities and reduce the number of wasted votes, but it also significantly diminishes the individual voter's impact.

An In-depth Study: The Value of an Individual Vote

My research group conducted an extensive investigation into the value of an individual's vote, following the 2019 UK general election. We employed a 'leave one out' modeling approach to simulate 32,014,110 elections and leave out one person's vote in each scenario. Through this method, we aimed to determine the electoral impact value (EIV) of each vote.

The results of our simulations revealed that each individual vote had an EIV of exactly zero. This means that during the 2019 general election, no vote cast had any actual impact on the outcome. This finding suggests that voters in this system are essentially casting valueless votes, which is practically equivalent to not voting at all.

From these results, we deduced that the 2019 UK general election could be mathematically described as having no votes cast at all, as each vote's impact is zero. This does not imply voter apathy or disengagement but rather a structural flaw in the electoral system where individual votes do not influence the overall result.

The Fictional Britain Hypothesis

While the implications of a zero EIV vote in democratic systems have been widely discussed, some fringe groups in experimental democracy have proposed that a truly democratic system where no votes have EIV of zero is a fictional construct. This led to the development of the 'Fictional Britain' hypothesis, which suggests that the UK can be described as a fictional democracy, where the general election results could be fabricated with no impact from individual votes.

This hypothesis is not without its critics and some argue that it represents a gross overinterpretation of the data. However, the uniqueness of this finding does provide a compelling explanation for the surprising electoral outcomes, such as Boris Johnson's re-election as Prime Minister.

Ultimately, the value of one vote in an election depends significantly on the electoral system in place. In the case of the UK's first-past-the-post system, the likelihood of an individual vote making a difference is extremely low, leading to the possibility of a zero EIV outcome. This is an important consideration for both policymakers and voters when they engage in the democratic process.