…statistics.

Or at least percentages.

The area where I live has a District Council by-election coming up due to the mid-term resignation of a councillor. The candidate for the Red party (see UK General Election 2015 ‘North/South Divide’ to understand why I use colours instead of names of political parties) published an election leaflet which claimed that his party was the only choice to beat the majority Blue party and that people who had previously supported other parties should instead back him (so-called tactical voting). In the actual words used in the leaflet he used an old and widely considered derogatory term for the Blue party instead of its common name.

A significant claim in the leaflet (the claim occupied around one quarter of the space) was that his party had achieved an increase of 110% in votes in the 2017 General (parliamentary) Election as compared with their 2015 General Election vote; it also mentioned that the Orange, Purple and Green parties had all lost votes - and gave the percentages.

Here’s the claim:

2017 General Election votes in {my parliamentary constituency}

Impressive?

Well, no - and here’s why not.

• It’s selective reporting of the data. They have not given all the data gathered in that they have not mentioned the Blue party’s results or the new entrant in the 2017 election standing as an independent - for whom I will arbitrarily assign the colour Pink.

• The actual calculation they used was not declared on the leaflet but I was able to work out that they have used this formula.

  ((votes cast in 2017)-(votes cast in 2015))/(votes cast in 2015).

  The calculation of the precentages is mathematically accurate to 0 decimal places but it is a ridiculous formula to apply. Would it be more impressive if a party had achieved a 200% increase in votes? Say from 10 votes to 30? Of course not. It’s how popular a candidate is relative to others across the whole poll that gets them elected.

  In words the claim could be phrased as ‘for every 100 votes last time we got 110 more votes this time’.

• The leaflet reports the percentage increase in votes for the selected parties but not the overall number of votes cast for all parties. It only selects 4 out of the 6 candidates to report on. The 4 selected parties commanded 49.3% of the votes cast and 34.0% of the electorate in 2015 and 43.9% of the votes cast and 31.3% of the electorate in 2017. A significant decrease from 2015 to 2017.

• Elections in the UK are run on a ‘first past the post’ basis. To understand whether one group has a chance of beating another by encouraging tactical voting we need to see the whole picture.

• The data given refer to the two most recent General Elections - not to District Council elections. I don’t think voting patterns are comparable. For one thing, the local District Council constituency is a very small subset of the parliamentary constituency.

• The above table is just as mathematically accurate and is apparently even more impressive - it uses this formula:

  (votes cast in 2017)/(votes cast in 2015)

  I’ve no idea why dividing the 2017 vote by the 2015 vote should be a particularly useful thing to do. At best you could say that ‘for every 100 votes we got last time we got 210 votes this time’ which at least saves the reader from struggling to work out what 110 more than 100 is. I certainly wouldn’t base any claim to skill in government office or public finance acumen on such arithmetic.

So here are the numbers in full with headings and (perhaps) more interesting calculations added.

Things to note:

• The data and calculation result given in the leaflet have been highlighted. I’ve used higher precision for additional percentage calculations (1 decimal place). See how much more useful the whole table is. Though perhaps it does not tell the story that the Red candidate wanted.

• 2,231 (3%) more voters were registered and 3,324 (6%) more votes were cast in 2017 than in 2015. A greater proportion of voters (2.2% more) bothered to use used their votes in 2017 than in 2015 - this is a Very Good Thing. Unfortunately a turnout of 71.2% of the electorate in 2017 still means that 28.8% of them (more than 1 in 4) did not vote.

• Since the leaflet appeals for voters to help the Reds beat the Blues it may be worth looking at the ‘anti-Blue vote’. From the data we can calculate that in 2015 27,336 non-Blue votes were cast; in 2017 there were 26,430 non-Blue votes. Using the same calculation and precision as in the leaflet that’s a decrease of 3% in non-Blue votes. Again, that’s probably not the message the Red candidate was hoping to deliver.

• In aplying the same arithmetic as the leaflet the Pink candidate’s performance is the most impressive. He had an infinite increase in the percentage of votes cast. This is a strong example why the formula used is inappropriate.

• Although the data does not (and we should not be able to) track which individuals changed allegiance from one party to another I think it is probably significant that the Purple party had 9,629 fewer votes and that the Red party had 9,226 more votes in 2017 than in 2015. It seems reasonable to me that many former Purple voters of 2015 switched to Red in 2017.

• Looking at the % shares of the votes cast it appears to me that voters polarised around the Blue and Red parties and withdrew support from the other parties - particularly the Purple party.

Of course, the turnout (the number of votes cast as a percentage of the electorate) does not affect the result. It does not matter how many are in the electorate; if they don’t vote then their numbers are not counted in an election.

In my opinion, offering himself as the ‘only choice to beat the Blue party’ encourages polarisation of the voters. It reinforces the idea of an anti-Blue coalition - of ‘them’ vs ‘us’. Given that the Blue party had more than half of the votes cast the Red party needs either to attract voters from the Blue party (rather than alienate them; and to do that it probably needs policies that appeal to these voters), or persuade the 28.8% of people who did not vote in 2017 to do so in future - and to vote for them, but not for anyone else.

I’m not suggesting that appeals to vote ‘to stop the XYZ party’ should be banned - I really dislike banning things even if I think they’re rubbish ideas. But if voters want such an ability at the polls they should vote at the general elections for parties which have policies that include electoral reform to the Alternative Vote or some form of Proportional Representation. Instead of this we get appeals to polarise our district politics to the same level as our national politics.

One last point for now: With 3 weeks to go to the election, the Red party is so far the only party to have bothered to deliver delivered a leaflet. I wonder what dodgy statistics the other parties will offer?

Update 19-Aug-2017: Only the Orange and Red parties bothered to deliver delivered a leaflet about this by-election. The Orange party leaflet avoided any misuse of statistics by not including any at all.

I know I said above that ‘the turnout does not affect the result’ - but the turnout for this by-election was only 13.1% - appalling; almost 7 out of every 8 people didn’t vote. Here are the results of the 2017 district councillor by-election in my ward:

By the look of it, the Orange candidate came closest to beating the Blue.