Thoughts on politics and life from a liberal perspective

Saturday 16 May 2009

Has our electoral system contributed to the MPs expenses scandal?

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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:

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.


Alix said...

Marvellous! I was way too slow. I'm not a statistician at all and was trying in a way too complicated way.

I reckon The Party should look at this, before they lose the moment.

dazmando said...

I agree, I think this is very important and a link should be sned to the party

Anonymous said...

Interesting analysis, good post. Although my personal interpretation is that this correlation might have more to do with the journalistic bias of the good men and women at the Daily Telegraph: papers will sell more copy if they get bigger scalps (i.e ministers, important aides) and the more important you are in your party the more likely you are to be given a safe seat. The information we're getting about expenses is being filtered by journos. This analysis would only really work with the (more) complete data of all MPs.

Anonymous said...

I am not a statistician either, but I wonder whether the real reason might not be with the size of an MP's majority, but with the length of time an MP has been in Parliament picking up bad habits. I would expect these to be correlated.

Also there is a potential reporting bias from the Telegraph --- it may be more likely to report on slighty dodgy expense claims if they are from a better known MP, which would tend to mean MPs who have been in Parliament longer, with larger majorities.

Mark Thompson said...

Alix/dazmando - Chris Huhne is aware of this now (in case you aren't aware he is Chair of Make Votes Count) so hopefully he can help take this forward.

Anons - yes it is possible that these issues have had an effect. We will only know for sure when all the data is released into the public domain. I still feel though that cannot fully explain the results above.

Andy said...

Worth having a look at this with some proper stats tests, I think so we can put a confindence interval on it. Would you mind emailing me the spreadsheet?

Simon Fawthrop said...

Intersting analysi,s but not sure that it is FPTP issue. Any other system will generate a number of people who always appear at the top of any list and will be almost guaranteed to maintain their position in parliament.

What it does point to is that we should have term limits. The problem then would be stability, but that's another debate.

Mark Thompson said...

The Great Simpleton - What you say here is not right if we use STV. Some forms of PR use list systems but the Single Transferable Vote (which is the system I support) does not. The party does select a number of candidates but it is the voters who decide which of them gets elected by listing preferences on the ballot paper. In this situation if a party had a bad apple, the electorate within the constituency could simply not vote for them but if they still wanted to support the same party could instead vote for a different candidate of that party. It empowers the voters in a way that the current system does not.

Please see the Electoral Reform Society for more information on this.

Anonymous said...

We need to let rank-and-file voters have a choice of candidates WITHIN a party as well as between parties. STV allows this (unlike the closed-list system used in EU elections which the Commons fought the Lords over).

Open primaries also allow this, somewhat. The Lib Dems can actually start using open primaries (while STV is an impossible hurdle at the moment) - it's up to the party to do so. We have the power. And we should start using them in a transparent manner, not like the scams the Tories have pulled off as 'open primaries'.

Anonymous said...

This is a great post. Firstly, because you've done a great job on the stats alone.

Secondly, because it proves that blogs can be more than mere "echo chambers" for "proper journalism".

Good work!

Mark Thompson said...

Thanks badconscience.

I am hoping that other bloggers take this on and bat it around to see how well it stands up and to provoke a debate that moves things onto the electoral system itself. I do think that I might be onto something and any changes to the system need to encompass a more widespread approach and not just focus on expenses.

Andy, from the comments above has done some more proper detailed analyses on the data I collated for this which have yielded some encouraging results about the statistical significance. I plan to post about this tomorrow.

Ed said...

The first past the post system in our country is pretty objectionable in the first place anyway.
A system that lets thousands of votes go to waste...? Very democratic...
Lets face it though its not going to change. It has kept New Labour and the Tories in majority for years so I doubt they'll be too willing to give it up just yet.

Mark Thompson said...

Ed - I know Labour and the Tories do not want to change the electoral system. But if what I seem to have discovered here is right and it gets reported more widely then a bit like with the MPs having to repay the money (which would have been unthinkable a few weeks ago) and the Speaker going (which looks likely now, but again would have looked very unlikely a few weeks ago) it could take on a life of its own and MPs may be forced to seriously look at it as part of the overall reform package they are going to have to introduce.

skipper said...

Really good bit of thinking I reckon; best possible kind of blogging journalism here. Stats seem OK to me and I'm no staticician either. Maybe 'safe-seaters' get so well entrenched and confident in their longevity they have 'learnt' how to work the system to their advantage. It's a fair point that those we know about about have been mediated by Telegraph journos but nevertheless the correlation is striking: 34 MPs involved in top quartile of safest seats. Excellent!

skipper said...

bugger, sorry, spelt 'statistician' wrong!

Simon Fawthrop said...


Thanks for the clarification.

Another point to add to your analysis - those MP's in the safest seats end up on committees like the Members' Estimates Committee, due to their longevity, which sets expenses policy and manages the fees office.

Having been out of the "real world" the longest they are more susceptible to believing their own PR about their entitlement.

Mark Wadsworth said...

Good work.

If you enjoy doing this sort of thing, there is also a list of total expenses claimed by each MP, you could enter for each MP the size of their majority and then do an X-Y scatter graph.

Doubting Richard said...

I'm usual;ly with Iain, but knowing a little about statistics I would agree with your initial instinct to discard the odd cases. There is good, solid reason to do so, you are not distorting the stats to do so. Good analysis, a little over-simplified but nothing wrong statistically that I can see.

However there are very good reasons for keeping FPTP, so these facts should be used in that context.

Mark Thompson said...

Richard - I did both in the end so that everyone else could decide themselves.

What do you see as the advantages for FPTP?

Anonymous said...

Sorry, but I think your analysis is flawed. You've eliminated all MPs who have not been implicated. You need to consider logistic regression (probability of being implicated) using seat majority as a covariate. Only focussing on those who have been implicated ignores those who have not been implicated and have large majorities.

David Bouvier said...

All for using data; others have pointed out some of the limitations of the analyis (exclusion of non-mentioned for example).

More importantly, correlation is not proof of cause. For example high majorities are presumably more prevalent among Labour MPs by virtue of winning the last GE (not for long, boys!).

As for the electoral system impact - I think there is agreement that immunity from public discontent is an issue, which should be the end of list based systems. The only serious discussion should be of ways of choosing one or more MPs from a geographic patch.

FPTP has a good record for "kicking the bastards out"; it is not clear to me that STV etc would provide what you hope so clearly, and churning for the sake of it is not a benefit either.