According to this, living in North-West Bristol my vote is worth just 0.521 of a vote. More shocking than that though, is the fact that this is apparently over twice the average amount of voting power of most UK citizens (the average is 0.253). At first glance this is really useful way of illustrating the obvious deficiencies of the UK’s first past the post system, which last time out elected a majority Labour government despite the fact that they only won around 37% of the votes cast
But how accurate is the voter power index? How is is worked out? And does it actually provide more useful information than simply looking at the numbers and percentages of the votes cast in each constituency alongside the constituency size (both of which are also provided by the VPI page but appear lower down)? And does the fact that no-one in the UK has a vote equal to one vote make the figures look artificially low? Well… from about voter power index
By Nic Marks, fellow, nef (the new economics foundation)
I went to vote at the last general election with a heavy heart as I knew full well that my vote wouldn’t really count towards the result as I live in a safe seat. Straight after voting I felt really angry about the whole system and whilst out walking my dog the idea came to me that I must be able to work out how much my vote didn’t count – you see if you make a statistician angry he tries to fight back with numbers.
So how did I calculate the Voter Power Index? Well I figured there were two main factors that would illustrate how much or little power voters had. The first is how marginal the constituency you happen to live in is (the more marginal the more power) and the second is how many registered voters there are (fewer voters means each individual vote counts more). The problem was how to estimate exactly how much power you have in a particular constituency. I decided that if I looked at as many elections as possible I would be able to figure out what was the probability of a seat changing hands for different levels of marginality. By creating a probabilistic model I could then estimate this probability for every constituency and hence calculate (to three decimal places) the Voter Power Index. The details of all the calculations are available in the original report but much more fun is that web designer Martin Petts has created an interactive web-site so everyone can see how much their vote is actually worth.
I must admit that even I was staggered when I first calculated the VPI just how much most people’s votes don’t count. It is clear that our current system is hugely inefficient at translating the will of the people into the result of a general election. In fact the VPI allows us to put a number on the level of this inefficiency – the current system is only 25% efficient – whereas some sort of proportional representation system would approach 100% efficiency (for example the 2004 European Elections were about 96% efficient). Not only is the system inefficient it is also chronically unjust with Voter Power very unevenly distributed in the UK, with the luckiest 20% of voters having over 33 times more power than the unluckiest 20% – the graph below shows this spread. Note that this is a far more uneven distribution than household income in the UK. Even before the redistribution through taxes and benefits – the richest 20 per cent of households ‘only’ earn 15 times as much as the poorest. After redistribution this inequity factor is reduced to under 4 times.
The Voter Power Index shows that the first past the post system is profoundly undemocratic in that it gives considerably more power to some voters than others and so betrays the fundamental principle of democracy – one person one vote. It is high time we changed the whole rotten system.
The biggest problem I have with their stated methodology is that they think marginality should be calculated by how many times a seat has changed hands in the past going back to the 1954 election and only looking at the top two parties votes. This isn’t what they say on the about page (confusingly) but if you go back to the original report they link to this is what they appear to have done. That this isn’t what their about page suggests does little for clarity.
While frequent changes would suggest a marginal seat, this is a very broad brush stroke approach which doesn’t seem to factor the actual number of votes or percentages involved in the elections into account. The idea of a three way marginal seat is completely alien to this method and I find that lack of complexity concerning. Furthermore they seem to give equal weighting to every electoral change since 1954, meaning that a seat which was very marginal between 55 and 25 years ago changing hands every election, but which has remained in the same hands in every election since then is still counted as fairly marginal, although in practice it may now be a very safe seat.
Essentially despite the pretty pictures on the VPI website this means that in many cases you can get a better idea of how marginal your constituency is by looking at the results from the last two elections and seeing how close they have been. At the last election Bristol NW was 38% labour, 32.5% tory 25% lib dem. Anyone with half a brain can tell that’s a marginal seat. Similarly if you look at somewhere like Henley and see figures for the last election of 53% tory, 26 % Libdem and 15% labour you can easily understand that it’s a safe seat. Trying to put a three figure decimal place number on how much more likely Bristol SW is to change hands than Henley is always going to be a rough and inexact endeavour. Except admitting this would remove the rationale for the VPI existing.
An interesting statistic which isn’t included in the VPI is the percentage of voters who turned out per seat. For example while the VPI site lists Henley as having 72,681 voters it doesn’t tell you that at the last election only 67% of the electorate there voted. It would be interesting to see whether safe seats have similar, lower or higher turnouts than marginals. Do people who live in safe seats feel sufficiently disenfranchised to not bother voting? Or is voter apathy evenly distributed across the country as people turn of from politics as they feel that the three main parties are so similar to one another that there is no point in voting at all?
Another problem I have with the way the VPI’s presentation of the issue is the claim made by Nic Marks that the voting system is more unequal than household income in the UK. In order to justify this he looks only at the top and bottom 20% of each. Firstly both on the website and the original document the income figures are unreferenced. It’s hard to check on the figures someone has used if they decide not to link to where they obtained those figures from. Secondly there’s a question as to why only one figure, for 20% and 80% were used in the report. If he had decided to look at different numbers such as the top and bottom 5% of income and voting power the figures may well be completely different. However that wasn’t what he intended to say so perhaps he used the statistic which suited his argument. Without referencing the data who knows? Does the data actually look at per capita income for everyone in the UK or does it exclude pensioners and people on benefits? If it does (as most government stats which look at income look at those paying income tax only) then this would again distort the data into giving an appearance of economic equality which does not exist in practice among the electorate. This kind of statistical cherry picking does nothing to add to the important point that voting power in the UK is unequal, and in fact casts doubts on the honesty and integrity of the research as a whole.
On the whole while I like the idea of VPI site, the fact that it does present some very useful and easily comprehended information about the differing worth of UK votes dependent on area, there are always likely to be problems with adopting the kind of reductionist quantitative approach they implement. While some of the information displayed there is really interesting and informative, particularly the last election result pie chart, the percentage of votes discarded and the size of the constituency, in general it just produces answers which are extremely obvious: first past the post is a highly undemocratic system in which voters have differing abilities to impact the make up of parliament depending on their constituency, a safe seat is by its very nature undemocratic, and that electoral systems based on proportional representation give far more agency to voters.
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