Mark Thompson, supported by Andy Hinton, has performed a statistical analysis linking the MPs exposed by the Daily Telegraph for excessive expenses to the size of their majorities. Very interestingly there is a clear positive correlation between the likelihood an MP has been implicated in the scandal and the safeness of their seat (i.e. as one goes up, so does the other).
You can see this correlation in the graph below where MPs have been listed in order of the size of their majority and divided into four quartiles (the largest majorities are in the top quartile). The numbers in the box refer to how many of the MPs featured in the Telegraph fit into each quartile. You can see a clear progression.
Unfortunately, demonstrating the link between size of majority and implication in this scandal is very different from showing a link between majority and propensity to cheat: the use of the Daily Telegraph's list is biased – they had their own reasons for choosing which MPs to expose whereas a fair test would either take the entire group, or a random sample; the group from the Telegraph share characteristics such as prominence which could skew the results; and the analysis can only show correlation – not causation.
Three types of test were used to determine the statistical probability that the results were coincidental. Despite contention over which (if any) of the tools were appropriate to this case, all results were highly significant: the successive results being 1 in 1,000, 3 in 10,000, and 8 in 1,000. The threshold for statistical significance is 5 in 100.
Posts across the blogosphere are already linking this to a failure of the electoral system and calls for reform are getting louder. Whether this analysis turns out to be as profound as it seems isn't actually the question. It is very easy to see how MPs in safe seats could become complacent and unresponsive to their constituents without fearing losing out at the ballot box - even if we can't prove this mathematically. There are many reasons why I would much prefer to have the option of genuinely choosing between candidates other than preventing corruption – punishing it, for example.
Mark Thompson has produced an interesting analysis – but the parameters for which it is true are too narrow to draw any further conclusions. What would be much more telling would be an analysis taking into account every MP (or a random sample). It could also be very interesting to compare different years or parliaments. I hope someone will take up the challenge when the full reports are released, and that even if the results are not as stark as they appear to be here (which they almost certainly wouldn't be) people will recognise them as more robust.
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