Some Mathematical Perspectives on Voting in the UK

With voting for the 2015 General Election about to get underway it looks set to be a wonderful demonstration of voter confusion. Smaller parties have an even greater chance to chip votes away from the two main parties as no single party has managed to convince enough of the electorate that they represent our diverse communities. Whilst UKIP even stands a decent chance of passing the Liberals not least due to the Liberal party having been smeared into near invisibility due to their role in the coalition government, it is still not a certain bet that a hung parliament will even be necessary.

In advance of the impending day of our media showing charts, polls and repeatedly rearranging the same information in a different graphic while waiting for each result to come in, here are a couple of trend charts that I’ll be updating following the 2015 results to see if they tell us anything new about voter confidence and if the political campaigns of our parties have inspired our nation.

The charts help represent something that has troubled me in terms of using percentages rather than numbers to demonstrate a situation set against how little media organisations truly analyse and report as opposed to showing ‘headline statistics’ which look nice but tell us what we can already plainly see.

One of the main problems with most governmental statistical analysis is that samples are too small to provide truly accurate representation of a situation however clever an algorithm one applies to scale up. Opinion polls taken by organisations such as MORI are even less representative yet are often taken as indicators that politicians will respond to whilst quoting ‘public opinion’ or ‘consumer demand’ (recently we were told that most parents worry about the mental health of their children – based on a sample of 900 people – Is that then representative of most parents?). In recently attempting to obtain some detailed statistical data from the ONS, I was surprised to hear that the largest data set they were able to work with totals about one million records. This apparently due to… wait for it …underfunding of another government body. So, for those even slightly interested in statistical analysis, a General Election provides wonderful fodder.

We can be certain that we will continue to sit and watch organisations such as Vodafone, Google, Microsoft, Ebay and Apple (as well as the many more unknown holding companies that hide even more) let alone bankers, suck the fortunes of our nation dry whilst pointless politicians expect us to vote for candidates who will continue to allow such profiteering whilst pleading poverty to the functional services of our nation.

This seems to have led the nation to reach a sort of ‘Catch 22’ state whereby people who don’t vote have proven that it makes no difference if they vote or not, the system that they lost faith in still remains. People who do vote have proven that their voting has maintained a democratically elected government and that however good or bad it may be, by voting the system will continue to function. If both are correct and neither side makes concessions nor takes an alternative approach, this situation will remain in perpetuity.

The following two charts are set out to demonstrate the interrelationship between the percentages and actual numbers of voters and non-voters in General Elections since 1945. This range is of more interest due to the current reminiscences over the past 70 years as well as providing some interesting comparisons between our levels of democratic engagement since then and today.

Electorate percentageThe first chart denotes results based on percentages clearly showing the points where first the percentage of non-voters exceeded the percentage of the electorate supporting the winning party and second when the percentage of non-voters exceeded the percentage of voters who supported the winning party.

The positive signs denoted by this chart show that following the trough of despair marked by the 40% of the electorate who refused to vote for a UK government during Tony Blair’s regime. The percentage of non-voters has steadily decreased to the point where, in 2010, the percentage of non-voters fell again below the percentage of voters who supported the party winning the most votes. Of course, this is little consolation when considering that just below 35% of the electorate were still not happy enough with the existing system of government to vote for any party.

Even so, when looking back through elections during the past 70 years, until the 1990s, percentages fall within a fairly constant range wherein the relationship between voters to non-voters remained reasonable constant and had certainly not exceeded the percentage of the electorate supporting the winning party.

I recall joking when Gordon Brown was at the helm that here was someone who could make John Major appear a popular Prime Minister. Sadly the percentages certainly don’t fail to support this when looking at the 2005 election result where our government gained the support of only 21.5% of the electorate. Nearly four out of every five people thus left feeling unrepresented. Hardly a representative government by any measure and to be fair, David Cameron only managed to move a smidgeon back towards the pre-2001 average of 33% by gaining the support of 23.5% of the electorate.

Electorate numericIn considering the second chart denoting actual numbers of people it is possible to see similar yet perhaps more interesting views on a developing trend that is not as clearly visible when only considering percentages.

In 1945 the electorate comprised 33 million voters and eight million chose not to vote. Five years later with an electorate of 34 million only five million chose not to vote.

From these heights of electoral validation, by the time of the 2001 General Election with an electorate that had grown by ten million and the average number of non-voters since 1945 standing at nine million, the number who chose not to vote doubled that average with a staggering 18 million choosing not to vote.

As can clearly be seen in the second chart yet is invisible on the first, whilst the electorate has steadily increased since 1945, the number of people who choose to vote has, for the most part failed to close the gap with the electorate and in the past 20 years that gap has steadily increased.

Again, the positive view here is that at least two million voters seem to have been convinced to vote again since the 2005 election decreasing the gap slightly more than the growth of the electorate, as can be seen on the chart. This is tempered perhaps by the fact that the electorate grew by over 1.3 million voters in that time and there were therefore still 16 million who chose not to vote.

The most stunning trend the second chart displays is that relating to the number of voters supporting the party winning the most votes. In 1945 with an electorate of 33 million, 12 million voters supported the winning party. In 2010 when the electorate had reached 45 million, just over 10 million voted for the winning party.

What conclusions can be drawn from these figures? Well, probably none that haven’t been discussed and debated extensively by far more capable and learned people than I. As is the purpose of the posts I make in this vein, the aim is to share personal opinions relating to simple approaches that could help in the development of a set of modern mechanisms of social governing and spur more focused and accurate debate in that arena. (Realising too that with my non-existent readership they will really be available retrospectively or just for me to be able to look back at!)

From my perspective, fundamentally what has been proven in the past twenty years is that it does not matter if less people vote in a General Election as the electoral process is capable of weathering even only a few million of the electorate voting as the seats and percentage calculations will still determine the overall victor or requirement for a hung parliament.

Therefore the argument doesn’t hold that it is a case of convincing people who choose not to vote that they are wrong in not voting (See Russell and Ed for my attempt at a wryly cynical interpretation of modern political approach). If such significant numbers of people currently choose not to vote and have a rational and compelling reason to not support the existing system of government, then surely addressing their concerns is the only way to gain their support. Cajoling, lambasting and ridiculing intelligent British people generally fails.

So, whilst the ‘Non-Voting Lobby Party’ has always represented a significant proportion of the electorate, in the past fifteen years, they have represented far more of our population than those who supported our governing political party. The ultimate aim should be to decrease the non-voting proportion to ever decreasing numbers as well as percentages to truly be able to hold up our democracy as enlightened and developing.

As I keep considering, the election tomorrow is going to prove very interesting from the perspective of how these charts will look by Friday. Will the gap close again between voters and electorate and will non-voters still exceed the supporters of the winning party?

In compiling these charts, I drew figures from Richard Kimber’s fine work at
after cross referencing to confirm the validity of information from a variety of differing sources and finding his to be the best presented and validated. If you wish to look in more detail at any more statistics with regards to UK elections I would recommend this site as a fantastic resource to aid research.

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