This is going to be a longish post so apologies in advance but please stick with it as I think I have uncovered something very interesting.
I had a thought when I was walking the dog yesterday. Could our First Past the Post electoral system have contributed to the scandal of MPs expenses?
My reasoning was that in our system, there are a lot of safe seats. In a typical General Election maybe a hundred or so change hands between the parties. In a landslide this can go up but you still have maybe 2/3rds of MPs who have very little to worry about in terms of the chances of them losing their seat. I then wondered if there was any sort of correlation between how safe a seat is and the likelihood of its MP having been involved in this expenses scandal.
When I got home, I noticed that Alix had posted a similar thought on LDV. I added a comment asking if anybody had tried any sort of statistical analysis of this. I have not seen anyone respond to this so for now I have assumed that they have not. I thought, therefore I would have a stab at this myself.
The first thing I should say is that I am not a statistician. I did however study stats as part of my Computing and Maths degree and am generally OK with numbers. The method I have used is as follows:
1) I found a list of all MPs from 2005 on this Keele university website. I took this data and put it into MS Excel and then sorted the MPs so that they are ordered by majority, largest to smallest and numbered 1 for the largest, 2 for the second largest and so on until I got to 647 (I assume there are 647 because the Speaker is included).
2) I found a page on the Telegraph website that lists all the MPs that have been covered in one way or another by them since this scandal broke as of 9:35am on Friday 15th May. I then went through this list and removed anyone for whom the coverage was positive (yes, there are a few) or Norman Baker who is about as clean as you can get but they were desperate to find something so he was included! I have also excluded Northern Ireland MPs from this because I felt that their majorities are generally very large because of the specific political situation there and it could distort things.
3) I noted the position in the majority listing for each MP who was implicated in one way or another.
4) I then totalled up all the numbers and divided this by the number of MPs implicated (74).
Now, what I think is that if there is no correlation between size of majority (safeness of seat) and the likelihood of being implicated in this expenses scandal I would expect the number to come out at 323 (646/2) or thereabouts. If there was an even distribution throughout the list this is what we should see. If the number is lower than 323 then it means that there is some correlation between safeness of seat and likelihood of being implicated (weak at first but getting stronger the further away from 323 we get). Commensurately, if the number is higher than 323, this would mean that there is actually a negative correlation and that we could conclude an MP was more likely to be implicated in this scandal if they had a smaller than median average majority.
The number comes out at just over 253.
Now I repeat, I am not a statistician or an expert on methodological analysis for this sort of thing. I fully accept that there may be flaws in my methodology here. I know that there may be interference from other factors that may contribute to the result. But still, I think this is a significant deviation from the median safe seat number you would expect if there was no correlation at all.
After this, it got me thinking even more. I decided to do a little bit more analysis on this. I divided the data set up into 4 sections. The top 25% of safe seats, the second 25%, the third 25% and the bottom 25%. Because 647 does not divide perfectly into 4 I have had to make them very slightly different sizes. I then totalled up the number of implicated MPs in each quartile. I have taken a snapshot of the result from Excel and put it here:
Now again, I need to caveat that this is not scientific etc. etc. However, using this methodology again there is a clear increase in the likelihood of an MP being implicated in the expenses scandal the safer their seat. It is in fact a fairly steady progression until it leaps up in the top quartile. Using this data, an MP is more than 3 times more likely to have been implicated in this scandal if their seat is in the top quartile as compared with the bottom quartile. They are almost twice as likely when comparing the top quartile with the second quartile.
I had suspected there might be a correlation but I had not expected it to be this stark.
If I am right about this then there are surely very serious questions to be asked about our electoral system. Advocates of First Past the Post always claim as one of their main arguments that the constituency link needs to be maintained (even though STV, a much more proportional system with multi-member constituencies that the Electoral Reform Society and Make Votes Count advocate also has a constituency link). However looking at the above analysis it strikes me that FPTP does not serve its constituents well at all when it comes to this scandal.
When the dust of this scandal finally settles, I think we need a full "drains up" job in Westminster where everything is looked at in close detail. Proper analysis should be performed on the question I have posed, whether there is a correlation here and action taken to address this. I personally think an electoral system where there are no safe seats and the electorate can give their verdict without needing to vote tactically and where every vote counts towards the final result is needed.
UPDATE1: I have been in touch with Iain Dale and he feels that my exclusion of Norman Baker and the Northern Ireland MPs is wrong. I do not want to appear partisan here about NB, that was not my intention so I have redone the exercises including NB and all the NI MPs mentioned by the Telegraph as of 9:35am yesterday.
With these extra MPs added in the total becomes 82 and the figure is now just below 254.5 so there is a marginal difference which moves it back very slightly towards the median.
I have also redone the chart and graph which still looks similar with the top three quartiles all increasing and the bottom one not:
Costigan Quist has also posted an excellent analysis of this situation and what the alternatives are on his blog.
UPDATE2: I have posted a more up to date version of this here.
UPDATE3: I have noticed a lot of traffic to this post from StumbleUpon. Welcome to all stumblers and if you like this post please give it the stumble "thumbs up" and let other people know about it too.