UK Voting: Lesser of Two Evils?

Proportional Representation: Easier to Rig

A month or so ago, I wrote about the voting science of the EU referendum. Since then, there has been further news about Cambridge Analytica. While none of his is any surprise to me, there is something that has the potential to cause serious concern and most people on the side of election reform have to be mindful of the risks that exist in calling for Proportional Representation or other voting change.


The biggest problem with most constituency voting is it means the winner counts, but the losing votes disappear off the map. So they aren’t represented. This is a factual concern of both the Liberal Democrats and UKIP and the mathematics can stack up. However, we have to be mindful that it is possible for FPTP to result in the dampening of extreme swings. I myself wouldn’t have wanted to see UKIP or worse in government, as they make the Windrush scandal look tame. FPTP has saved us from that in the past more than once. While I agree that people’s voices must be heard, if what they are inciting is genocidal hatred, they have no right to thta voice under international human rights law. There is no incongruity there.

Proportional Representation

Unlike FPTP, different alternative votes (including several forms of PR) mathematically and, from the evidence where they’re used, empirically, cause large swings in results as all votes count. They work very well when democracies are relatively central. However, where such referendum style voting is used and central views are not a majority, this results in difficult coalitions and in some case, breaches of human rights and losses of democracy altogether. It’s the Paradox of Tolerance

However, whether a PR democracy is extremist or central, the threshold is set centrally. Meaning large swings in result occur from a small change across the normally central threshold. The net result can be totally decided in much less than 1% of the vote (1 vote in million can decide it).

It’s why PR has aimed to hold representatives, true to the namesake, but very often, no party achieves a majority.

Interference: Cambridge Analytica, a Case-Study

Under normal FPTP votes, Cambridge Analytica would have had to rig every portion of every constituency. In addition, if their side lost, as with all FPTP elections, the votes they worked for are lost.

Not so in Referendums and Proportional Representation. Since those lost votes count towards the ultimate result, they are oversensitive to malicious agents. In FPTP, any I’ll gotten gains resulting in a 1% change to raise Labour in one area from 32% to 33% of turn out, is lost when Conservatives get 35% of turnout. While in some PR models, they all count. Meaning ill-gotten gains or gerrymandering effects are carried into the ultimatum count.

This is what makes Cambridge Analytica’s position so key. By their own admission, Cambridge Analytica state they can make up to two percentage points difference to a vote. What this actually means is 2% of turnout. This is ideal for close elections.

Magnifying Marginal Effects

If a two option vote requires a 50% threshold, a two percentage point shift in a result which achieves 60% leaves you between 58% and 62% in accuracy. That’s fine. The effect of a 2% malicious agent rate doesn’t change the result.

However, if the result is 51% that means the range is 49% to 53%, which means it could actually have been a minority!

In FPTP by comparison, if 3 constituency results were:

  1. 51% win rogues win 48%
  2. 63% win rogue 22%
  3. 45% win rogue 44%

The result is 3 unequivocal wins for the winners. The rogues have been kept out.

However, if the winners were the rogues, that’s a different story. Since they get hold of the 3 results, but again, with the margin of victory, constituencies 1 and 3 are unsafe with a 2% influence margin.

And There’s More…

Yet, while it seems each presents a scenario in which a rogue influence manages to shift an election, we have to consider the number and rate of swing of elections over time. Since such FPTP encroachment can only happen at constituency level, which limits the damage to those which aren’t strongholds.

In PR, an all or nothing vote at UK level means the lost rogue votes don’t disappear. They carry through and makes the entire UK Parliament a rogue target. It swings 2% and that counts!

Revisiting our example:

  1. 5,100 v 4,800
  2. 1,260 v 440
  3. 4,500 v 4,400

Again, this sis a clear FPTP loss. In PR though, it’s not as clear cut.

With lose swings of

4,600 to 5,000

1,220 to 1,300

4,200 to 4,600

In FPTP, they still lose all 3 cases.

In PR, their range is 10,020 to 10,900 while the winners amassed 10,860, meaning that the winners may not actually have won!

PR has huge potential to be rigged at representative votes. You cannot separate losing voters from losing influenced voters. Like digital encryption, the net result is that PR’s benefits will benefit rogues as well as roses.

Written by

EA, Stats, Math & Code into a fizz of a biz or two. Founder: Automedi & Axelisys. Proud Manc. Citizen of the World. I’ve been busy

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store