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Are some constituencies "prone" to by-elections?

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Brock
1381299.  Tue May 11, 2021 11:40 am Reply with quote

Last week there was a Parliamentary by-election in Hartlepool, and I noted that there had previously been a by-election in 2004. Now, following the election of Tracy Brabin as Mayor of West Yorkshire, there will be a by-election in the constituency of Batley & Spen. She became the constituency's MP in 2016 as the result of another by-election, after the murder of Jo Cox - so this will be the second by-election within five years.

I've noticed on several occasions during my life that by-elections seem to crop up in the same constituencies more often than one might expect, and I'm starting to wonder if it's just a statistical fluke, or if there's some other underlying reason.

By my reckoning, there have been 231 by-elections since the June 1970 general election (including the ones still pending). The number of constituencies is variable but has always been around the current total of 650, which means that most constituencies wouldn't expect to have had a by-election at all during that period. Yet there are a surprising number that have had two, or (in one instance) even three. Boundary changes sometimes make it difficult to ascertain what is and isn't the "same" constituency, but this is my list of constituencies that have had more than one by-election during that period:

Greenwich - 8/7/71, 26/2/87
Uxbridge - 7/12/72, 31/7/97
Glasgow Govan - 8/11/73, 10/11/88
Wirral/Wirral South - 11/3/76, 27/2/97
Hamilton/Hamilton South - 31/5/78, 23/9/99
Fermanagh & South Tyrone** - 9/4/81, 20/8/81, 23/1/86*
Belfast South - 4/3/82, 23/1/86*
Brecon & Radnor(shire) - 4/7/85, 1/8/19
North Down - 23/1/86*, 15/6/95
Upper Bann - 23/1/86*, 17/5/90
Kensington/Kensington & Chelsea - 14/7/88, 25/11/99
Bootle - 24/5/90, 8/11/90
Hemsworth - 7/11/91, 1/2/96
Rotherham - 5/5/94, 29/11/12
Eastleigh - 9/6/94, 28/2/13
Littleborough & Saddleworth/Oldham East & Saddleworth - 27/7/95, 13/1/11
Hartlepool - 30/9/04, 6/5/21
Batley & Spen - 20/10/16, TBA (2021)

*Fifteen by-elections were held simultaneously in Northern Ireland on this date as the result of the mass resignation of Unionist MPs over the Anglo-Irish Agreement, so these may perhaps be discounted as irregular.

**The election on 20/8/81 was due to the death of the IRA hunger striker Bobby Sands, who was elected on 9/4/81, so this may be seen as special circumstances.

Notwithstanding the above comments, is something odd happening here?

 
suze
1381302.  Tue May 11, 2021 12:20 pm Reply with quote

Without carrying out any research, here's one possibility.

I'd imagine that most by-elections are precipitated by the incumbent MP dying. For an MP to be murdered is fortunately a rare event, so cet par an MP who dies is probably on the older side.

Do some ridings have a tendency to choose candidates who are on the older side, and therefore more likely to die? In the case of a safe seat, might this in turn suggest that a riding which is unusually prone to by-elections ought perhaps to get someone closer to the 21st century involved in choosing the candidates?

One riding that I know a little bit about is Maidstone and the Weald. When Ann Widdecombe decided to retire (for the first time), the local association was very keen not to replace her with another person of advancing years who was still living in the 1930s. With that in mind, it called in Ian Hislop to help it select the candidate - and Mr Hislop was reportedly rather sharp with some committee members who sought to present the successful applicant's youth and ethnicity (black) as making her unsuitable.

It may be that some ridings are less enlightened, and associations continue to choose "one of us" - even if "one of us" is necessarily older than is ideal.

 
Brock
1381313.  Tue May 11, 2021 1:05 pm Reply with quote

suze wrote:
Without carrying out any research, here's one possibility.

I'd imagine that most by-elections are precipitated by the incumbent MP dying. For an MP to be murdered is fortunately a rare event, so cet par an MP who dies is probably on the older side.

Do some ridings have a tendency to choose candidates who are on the older side, and therefore more likely to die?


That's an interesting thought, but (from memory) quite a few of the by-elections I listed above were caused by something other than the death of the incumbent. For example, the 2004 Hartlepool by-election was caused by the appointment of Peter Mandelson as a European Commissioner, and the 2021 by-election was caused by the resignation of Mike Hill following allegations of sexual harassment and victimisation.

Even when they were due to death, the deaths were sometimes unexpected. The first Bootle by-election in 1990 was caused by the death of Allan Roberts at the age of 46, and the second was caused by the death of Mike Carr at the age of 43, just 57 days after his election.

If I've got a few moments I'll go through the rest of the list to find out the reasons for the by-elections. There are one or two decidedly odd ones in there.

 
Numerophile
1381320.  Tue May 11, 2021 2:19 pm Reply with quote

Doesn't look odd to me.

If your figures are right, and there have been 231 by-elections in 650 constituencies in 51 years, that suggests that the probability of a by-election in any given constituency in any given year is approximately .007 (ignoring awkward questions about whether these probabilities are independent and identically distributed!).

If that is so, you would expect that out of 650 constituencies, 455 would have no by-elections in 51 years, 163 would have one, 29 would have 2, and 3 would have three. Your figures are 438, 194, 17, and 1 respectively. So if anything, the surprise is that there aren't more constituencies with multiple by-elections!

 
Brock
1381321.  Tue May 11, 2021 2:30 pm Reply with quote

Numerophile wrote:

If that is so, you would expect that out of 650 constituencies, 455 would have no by-elections in 51 years, 163 would have one, 29 would have 2, and 3 would have three. Your figures are 438, 194, 17, and 1 respectively. So if anything, the surprise is that there aren't more constituencies with multiple by-elections!


Yes indeed - I just did the same calculation myself. It's a Poisson distribution, isn't it? (Haven't really studied this stuff properly since school.)

Perhaps it's one of those things like the "birthday paradox", where the statistically expected result appears counter-intuitive.

 
suze
1381331.  Tue May 11, 2021 5:22 pm Reply with quote

Ooh, now then. Once upon a time, I knew enough about the Poisson distribution to know that you can do a χ test to see whether a set of observations fit a Poisson distribution. The good husband once knew that too, and he has a spreadsheet which can do the necessary sums.

That spreadsheet shows that the incidence of by-elections does not follow a Poisson distribution, but it's not a million miles away. The reason it's not a Poisson distribution is probably that by-elections are not independent. There were multiple by-elections caused by the Good Friday Agreement as already noted, there were multiple by-elections over fiddlage of expenses, and so on.

But take those out, and the good man is reasonably confident that the incidence of by-elections more or less fits a Poisson distribution - as you'd expect it to. So there may not actually be much to see here.

Oh well, it gave me something to do that wasn't marking!

 
tetsabb
1381340.  Wed May 12, 2021 3:38 am Reply with quote

This distribution all sounds a bit fishy to me.

Well, someone was bound to say it...

 
PDR
1381342.  Wed May 12, 2021 4:40 am Reply with quote

It suppose could be normal - your gauss is as good as mine.

PDR

 

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