It has been about a month and a half since the recent UK elections and it has in some ways been the most important election of my life. I haven't seen a major change of government since 2010, when I was 14 years old. Rather coincidental that I'm now double that - 28 - clearly the UK have been planning their transitions around me. Anyhow, I'm not going to delve into any discussion around which party had the best manifesto, or who I wanted to win. Instead, I'm going to take a more philosophical route and discuss some thoughts around democracy and voting systems.
Democracy
The first question - what is a democracy? I've looked through a few definitions, but I'm going to start with the one from Brittanica:
Democracy is a system of government in which laws, policies, leadership, and major undertakings of a state or other polity are directly or indirectly decided by the 'people'
Different countries will have different notions of a democracy - this can be the degree to which decision are made directly (e.g. referendums) or indirectly (putting trust in a trusted set of officials). It can also be the degree to which decisions are made locally (e.g. local government) or centrally (e.g. central government). There are also some questions around what the 'people' refers to - is it everyone? Is it a 'meritocratic' group?
Usually central to the notion of a democracy is a concept of an election, where the 'people' are able to have their say on the management of the country through voting for different candidates that have their own plan of governance. The theory is that the 'people' will vote in accordance to their own preference relations, and that consequently, candidates will need to have plans that take these preferences into account.
The UK democratic system
In the UK, we have the house of commons which is comprised of 650 elected members of parliament (MP). Each member of parliament is associated with a constituency - a defined area of the country. During elections - which must be called minimum every 5 years - the members of the constituency will vote for who will be their representative to the house of commons. This is also known as their local MP.
When a new law is being passed, all MPs are given a vote and a majority is required to pass it. This creates a delegated authority - the 'people' want to vote for an MP who will in turn vote in accordance to policies that will benefit the 'people'.
While voting is done on the individual level (i.e. voters vote for a candidate), candidates tend to represent different political parties. The idea is that members of the same political party would demonstrate similar interests in policy, and more crucially - that they would tend to vote together. Thus if one political party was able to get a majority of the 650 seats, then they could almost guarantee that their laws would pass.
Citizens might not know much about the individual candidates in their constituency, but they do tend to know the individual parties (e.g. Labour, Conservative), which means they will usually vote based on which party they want to win.
The UK uses a 'First past the post' voting system. This means that voters only vote for a single candidate, and the candidate with the most votes will win the seat. As a result, parties will usually only field a single candidate from their party for each constituent. This is to avoid the case where a vote is split between two candidates from the same party, leading to a secondary party getting the majority of votes (and thus winning the seat).
What happened in the UK election 2024?
I mentioned that I'm only going to talk about the results from a system level. So I want to begin by showing some interesting statistics from the election. The following image comes from BBC news: https://www.bbc.co.uk/news/articles/c4nglegege1o
A few observations. First is that Labour got 34% of the votes but won 63% of seats. This means that 34% of all votes went to Labour party, but Labour got the majority of the votes in 63% of constituencies.
In striking comparison, Reform UK and Green party won 14% and 7% of votes respectively, but only won 1% of seats each. This means in practice that while around a 5th of the voters voted for either Reform or Green party, they actually only won 9 seats out of 650 (about 1.5%).
This oddness is even more explicit when you comparison votes for reform v votes for Lib Dem. Reform actually got 2% more votes than Lib Dem, but won less than a 10th of the seats.
Now there a few practical reasons why this occurred. One is the Labour and Lib Dem coordinated to maximise conservative losses. This means that they did not invest campaign resources that would contest the strong seats of each other. In other words, Labour did not try and fight the Lib dem strongholds. This meant that the competition was usually Labour v Conservative or Lib Dem v Conservative. The vote did not get split between Labour and Lib Dem. This would also happen on an individual voter's level. Many voters focussed on maximising Tory losses and thus would vote for whichever party (be it Labour, Lib Dem or otherwise) that would be most likely to beat Tory.
Let's call this observation tactical voting, where voters do not reveal their preference to ensure an overall preferred voting split.
We saw the opposite result happen with Conservative and Reform. It was suggested that a large majority of Reform voters would have otherwise voted Conservative. As a result, their vote was effectively split. This was devastating to both parties - as it meant that conservative kept having to fight the strongest of Labour / Lib Dem, while their own votes were being eaten by Reform. It also meant that Reform was unlikely to win many seats - many of their votes came from areas that were predominantly Tory. So they ended up splitting the vote to an even greater degree.
Lets call this observation split voting, where third-preferred party wins as a result of voters splitting their votes between their first two preferred.
Note how both of these phenomenon are indicative of a larger worry of wasted votes. If a party does not win a constituency, their votes they won are effectively useless. Similarly, voters who want to vote for fringe options, may effectively be making wasted votes.
A final point that's worth mentioning. Parties campaign and voters vote with the knowledge that we have a first past the post system. This means that candidates may and are likely to vote differently if the voting system was different. This doesn't mean that we should take a neutral stance towards voting a system. For example, we could have a voting system where only one person's vote actually matters (effectively dictatorship). Everyone else might vote in this manner and make votes that don't align to their preference at all, as they know their vote doesn't matter. This is clearly not a good system.
What makes a good voting system?
This question has been asked for a while. I think one of the challenges here is that there is a distinction and potentially, a tension, between a good voting system, and a good governance system.
For example, we can consider a system where there is only one constituency. All votes are distributed towards this one constituency, and then we split the 650 seats based on the proportion of votes given to a specific party. In some ways this is very positive, as no vote is wasted. On the other hand, try passing a law when there are 30 parties each with 10 MPs. For example, even in the current set up, Labour only having 34% (~220) seats would make it enormously difficult to pass laws, as they would need to get another 105 votes from other parties.
There has been some mathematical analysis involved in this discussion. Probably the most basic and relevant discussion is to talk about Arrow's impossibility theorem. Arrows theorem begins by discussing a few useful properties we might expect from a voting system. The idea of course is that each individual expresses their vote into the system, and then the system outputs a 'collective' vote (which for the UK system, is just the end output of MP numbers by party). Preferences must be transitive - this means that if an individual prefers A to B and B to C, then they must prefer A to C.
- Unanimity: preferences that are agreed by all individuals must be respected
- Unrestricted domain: all agents can have any preference and order their choices in any way, including by indicating ties
- Independence of irrelevant alternatives: an assessment between two options only depends on those options - no other options or comparisons matter.
- Non dicatorship - there is no individual who's vote will fully define the collective vote
The point of the impossibility theorem is to show that these four properties actually contradict one other. In other words, a voting system that meets the first three properties, will always have an individual with dictatorial powers.
Note that there are three dimensions worth considering here:
First is the agents actual preferences - who the actually prefer. (this tends to have no constraint)
Second is the agents vote - who they end up voting for (this is constrained by the voting system - in first past the post they only have one choice)
Third is what the system outputs from the votes - in the UK this is an allocation of MPs.
Note that mathematically, the second dimension is abstracted, as it is simply a method from people's preferences to system outputs. But in practice the second dimension is very pertinent and can very much lead to a distinction between the preferences and their system ouputs.
Let's briefly talk about why these properties matter:
1) Unanimity: If all agents agree on a specific preference (i.e. A over B) then the system output will agree with this preference. Note that first past the post will meet this preference - if all individuals vote exactly in accordance to their first choice. But if people don't vote according to their preference, then its likely the system outputs will not align with the outputs.
2) Unrestricted domain: individuals are free to vote however they wish - there are no artificial restrictions.
3) Independence of irrelevant alternatives (IIA): the idea here is that we can add or remove choices without affecting a preference between two original choices. For example, suppose I ask who you prefer between option A and B, and you choose A. Suppose now I tell you that option C exists - it would seem bizarre for you now to prefer option B to option A.
4) Non dicatorship: intuitively, a dictator is someone who has total control over a system - whatever they want, goes. A dictator in an election can therefore be considered a voter with the power to fully influence the vote. Whatever they vote - goes. Clearly have a dicatorial voter is a bad thing, as it means that no one elses vote really matters.
An analysis of first past the post
Now let's talk again about the UK election system, i.e first past the post. We've previously described issues such as tactical voting, split voting and wasted votes.
Many of the problems with first past the post relates to its violation of IIA. This is usually because even though candidates will have preferences that are in line with IIA, their votes often go against their preferences in a way that the system output violates IIA.
Tactical voting:
The agent might prefer A > B and A > C. But they might think that other people are more likely to vote for B. So they end up voting for B instead so that C can't win. In otherwords, the existence of third choice (C) means that end up voting in a way that B > A! This violates IAA.
Practically - someone might flat-out prefer the green party (meaning they prefer green to labour and conservative). But they might know that very few people will vote Green and they really don't want conservative to win. As a result, they choose to vote labour.
Note that this leads to another problem - agents have some sense of what other people are voting. If they had no idea what other people would vote for, then it would be optimal for them to vote in accordance to their preferences. This is a potential problem with having 'polls' before elections. People use them to get a sense of other votes. Note, that's not to say that they should be banned, as I'm not sure how effective that is. Neither is it to say whether poll-influenced voting is better or worse in terms of overall result. But there is a sense in which it does not feel democractic and is not based on the original interests of the people.
Split voting:
A similar problem that violates IIA. We can have the majority of people have preferences like:
Conservative > reform > labour or Reform > conversative > labour.
However the end system is one in which labour wins - so the fact that we have two similar options of conservative and reform means the third choice wins.
Or in other words, we could have a system where the majority of people prefer option A to option C. But the existence of an option B (which splits the vote), means that the end system prefers option C to option A.
Note that split voting will occur even without polls. For example, suppose we have the following set up:
30%: A > B > C
30%: B > A > C
40%: C > B > A
Here we have 60% people who think that C should not win, they're just split between A and B. But if B did not exist, then C would definitely lose.
If people do not have polls then they might vote in accordance to their preference. But under first past the post, C still ends up winning, as we'd get a 30% vote for A, a 30% vote for B and a 40% vote for C. We'd need a system where second choice matters, to avoid this scenario.
Wasted votes:
As we know, first past the post allows for wasted votes. The wasted votes are very much connected to tactical voting. People vote tactically to ensure their votes are 'less wasted'. But because First Past the Post means that individuals can only vote for one thing (and said vote is frankly irrelevant if its not the top two choices), then individuals are encouraged to vote differently to their preference!
This is effectively another violation of IAA. The end system gets weird outputs because people are not voting in accordance to their preference.
Back to the UK election resultsSo I've discussed how disproportionate the UK election results are - where the proportion of votes do not really match the proportion of seats.
I've discussed how this result can be in part be related to three related phenomena:
Tactical voting
Split voting
Wasted votes
I've also talked about how these all violate certain principles of an optimal voting, and that it is in large party due to the disparity between an individuals' preference and their actual choice of vote.
I've also talked about how this can in part be solved by restricting information on who other people are voting for - to ensure that people are forced to vote in accordance to their preference. But that fundamentally, first past the post (and all voting systems) will have vulnerabilities that lead to such skewed results. That's frustrating!
I think my overall conclusion is that I don't really feel like our current system is very democratic. My personal choce was actually to spoil my vote as I wasn't a fan of any of the parties. But it does feel a bit weird that Labour is able to get a super majority, landslide victory while getting less than 10 million of the 48 million available. I'm not sure there's ever going to be anything we can do to avoid split voting in first past the post elections, but there's definitely something distasteful to me about tactical voting.
