By-Election Calculations: Sorcery or Science?

Since I’ve started this project, I’ve occasionally had folk say they find my “re-calculation for a single councillor” quite dubious. How can you possibly know? Is it educated guesswork? Do I use some kind of complex statistical model? Have I got a direct line to Professor John Curtice? Do I just make it up for funsies? The short answer is simple: I literally count the ballots again.

STV calculations are complex. Counting up later preferences in full to get the correct fractional transfer is time consuming. That’s why it can take a few days to finalise Assembly elections in Northern Ireland. And in Australia, where there can be dozens upon dozens of candidates on the ballot, it’s not unusual for it to take a month to confirm the Senate’s composition.

Alternatively, you can opt not to do a full count of later preferences, and instead take a sample and apply that. So if you take a small bundle of votes for an eliminated candidate with 2000 votes in total, and 8% of the next preferences go to Jane Bloggs, you just fire over 160 votes. But that’s imprecise and in Ireland it’s not unheard of for candidates in tight races to demand recounts on a different sample.

In Scotland, where we like our election results both quick and perfectly accurate, we decided to ditch hand counts and go for computerisation. That means you usually know the makeup of every council in Scotland within 24 hours of polls closing, with absolute certainty about transfers. But computers have been a great addition for another reason. A really useful side effect of this is that you end up with a wealth of public data that it isn’t feasible to collect for any other election.

For example, anyone can access a complete list of votes broken down by individual ballot box in each ward – which you can then use to identify areas where a given party did particularly well or badly. Another of these documents, the Preference Profile Report, is what I use to do my single councillor re-calcs. Here’s an excerpt from Clackmannanshire South’s;

As you can see in the above image, it’s a mind bendingly dull and at first glance really cryptic document. It’s just a list of numbers; what on earth do they mean? Well, those numbers represent absolutely every single ballot that was counted and the exact order candidates were marked. The first number on each line tells us how many ballots were marked in this order, numbers after are the order candidates were marked, and a 0 means no further preferences.

So the first line tells us that 12 voters decided to only vote for the first candidate on the ballot. Second from bottom tells us 2 voters marked candidates 1, 2, 3 and 7 in that order, then no more. And we can see that 3 voters actually opted to rank candidates as they were on the ballot, 1, 2, 3, 4, 5, 6, 7! This goes on for lines and lines and lines, showing every single ballot.

In other words, you can completely reconstruct previous election results for fewer councillors. No guesswork, no theories, no magic – just counting the ballots as normal. It takes ages, because I haven’t found an easy way of automating so I’m effectively doing a handcount. And because it’s a handcount, there is room for human error. But on the whole, I assure you that you can trust these re-calcs just as if they were declared on the day by the returning officer!

January 2020 Update:

Starting from 2020 entries you may notice that in some re-calculations, where a party has stood multiple candidates, the lower placed candidate(s) are eliminated as a first step even if not being the candidate with the least votes. This is a (mostly in vain) attempt to reduce the number of stages of counts I need to go through to find a winner, given the overwhelming majority of next preferences go to the other candidate(s) from the same party. If that might put them 5% over the quota some point down the line, doing it first might mean I don’t have to eliminate a couple of other candidates that’d contribute less than the 5%.

I only do this where it’s either impossible or, based on two years experience of doing these regularly, clearly unlikely the lower placed candidate(s) will overtake their party colleagues. This has no impact on the overall final result, it just makes the re-calculation process marginally easier for me.

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