With the Tory leadership contest underway after Theresa May stepped down, we could potentially be heading towards another UK General Election.
It made me wonder whether the current electoral system that is in place – First-Past-the-Post (or FPTP) – really provides an adequate way of electing a governing body to represent the largest number of people.
How Does a General Election in the UK Work?
Firstly, I will give an explanation of the voting system in the UK and the conditions needed for a Political Party to gain an overall majority. In this case, I am ignoring the scenario of a hung parliament.
In the UK, there are numerous voting areas called constituencies or wards which offer multiple prospective candidates from the National Parties.
They each have a defined agenda aimed at representing the voters in their constituency.
By winning a local election, a representative gains a seat in the House of Commons, and can then drive the agenda to the benefit of their constituents.
The candidate with the greatest number of votes in each constituency wins the seat in Parliament.
How Many Constituencies are there in the UK?
There are currently 650 constituencies which make up the UK voting area, splitting up roughly 46 million eligible voters (where the voting age is 18).
For a Political Party to win a General Election, they need to gain a majority which is to achieve a minimum of 326 seats from the 650 available constituencies.
This raised a couple of interesting questions which I would like to explore in this article:
What is the Minimum Number of Votes to Win an Election?
To begin the analysis, I need to create a few assumptions. I understand that some readers will have differing opinions about the assumptions made, but this is for illustrative purposes:
- The 650 constituencies have an equal density of voters: 70,770 (46,000,000/650). I will call the total number of voters in a constituency “n”.
- There are four competing parties (an assumption made due to the prevalence of Labour, Conservative, Lib Dems and The Brexit Party in the UK). They are represented by Party i, where i = A, B, C, D. We can define the total number of political parties as “P” where P > 1 to expand the model further.
- There is a 100% voting turnout in each of the constituencies.
The minimum number of seats “Party A” needs to win an overall majority is 326.
In each of these constituencies, the minimum number of votes needed to win in a First-Past-the-Post system is defined as (n/P) + 1.
This where the other three parties share the other 74.99% of the vote equally, giving Party A the overall majority by one vote.
They need to win in 326 constituencies, so the minimum number of votes to win an election is then 326 * ((n/P) + 1).
They do not need to win a single vote in the other 324 constituencies.
By putting in the numbers, the minimum number of votes required by Party A to win a General Election as:
326 * ((70770/4) + 1) = 5,768,081 votes
That means that the UK could have (although this is idealistic and incredibly unlikely) a party with a majority which represents only 12.54% of a total voting population.
What is the Maximum Number of Votes to Lose an Election?
Going even further into this extreme situation, I wanted to calculate the maximum number of votes that a party could receive and still lose an election.
If I use the situation above as a basis where Party A has won the election, “Party B” could win the other 324 constituencies outright with 100% of the vote (defined as 324 * n).
Party B then could receive one vote less than Party A in each of the 326 constituencies it loses with Party C and D getting 0 votes.
When I enter the values into these two equations, we get:
(324 * 70770) + (326 * ((70770-2)/2)) = 34,430,574 votes
This means that the UK could theoretically have 74.85% of a voting population who agree on the manifesto of a single party, and still lose an election.
If the assumptions are relaxed to reflect the real state of the electoral system (uneven densities of voters in each constituency – e.g. Isle of Wight had 110,924 eligible voters in 2010, and Orkney & Shetland had just 33,755 – the results can look even worse.
Situations of this ‘unfair’ system have been demonstrated before in different elections.
In Canada, the Progressive Conservatives had previously won 16% of the total number of votes, but only 0.7% of the seats.
Similarly, in Lesotho, the Basotho National Party achieved a 24% vote share, but only 1% of the seats.
A move to change the current system was part of the promise from the Conservative and Lib Dem coalition Government who held a referendum to replace it with the Alternative Vote (AV) in 2011.
What is the Alternative Vote?
The Alternative Vote is a system where voters rank their preferences for candidates.
If from this first round of voting, one candidate gets over 50% of the vote (votes counting for first preference), the vote concludes.
If there isn’t a majority, the candidate with the lowest vote is eliminated, and for those voting papers, the second preference is added to a vote.
Each candidate is eliminated, and the next preference taken until there is an overall majority.
The referendum ruled in favour of keeping the current First-Past-the-Post system, although this has done little to dispel its critics.
By reassessing the past General Elections with the Alternative Vote, it was made clear that since 1900, there would have been no change to the overall outcome of an election in the UK had it been adopted.
Despite our dismissal of an alternative, FPTP still has its flaws, and we are perhaps only accepting it because the issues it can cause have not yet occurred.
Maybe it is time to explore some of the other voting possibilities, before we allow the First-Past-the-Post system to elect a party which is by far a minority rule.