The Quantum Mechanics of Voting
Now that I’ve finished a marathon session of report-writing I thought I’d take a few minutes out this Friday afternoon, have a cup of tea and pass on a rather silly thought I had the other day about the relationship between Quantum Mechanics (and specifically the behaviour of spin therein) and voting behaviour in elections and referendums.
For a start here’s a brief summary of the usual quantum-mechanical context as it relates to, e.g., electrons (rather than elections). Being fermions, electrons possess half-integer spin. This attribute has the property that a measurement of its component in any direction has only two possible values, ±½ in units of Planck’s constant. In the Stern-Gerlach experiment illustrated above, which measures the spin in the vertical direction of silver atoms emerging from a source, the outcome is either “up” or “down”, not some spread of values in between. Silver has a single unpaired electron which is why its atoms behave in this respect in the same way as an individual electron.
The way this is often described in physics textbooks is to say that the operator corresponding to spin in the z-direction has only two eigenstates (call these ↑ and ↓) ; the act of measurement has to select one of them, not some intermediate state. If the source is thermal then the spins of individual atoms have no preferred direction so 50% turn out to be ↑ and 50% to be ↓ as shown in the cartoon.
Once such measurement has been made, a given particle remains in the same eigenstate, which means that if it is passed through another similar measuring device it will always turn out to have spin pointing in the same direction. If you like, the particle has been `prepared’ in a given state by the act of measurement.
This applies as long as no attempt is made to make a measurement of the spin in a different direction, which is when the fun starts. If we start with a particle in the ↑ state and then pass it through an experiment that measures spin (say) with respect to the x-axis instead of the z-axis then the two allowed eigenstates are then not ↑ and ↓ but ← and →. A particle that was definitely spin-up would then be forced to decide between spin-left and spin-right (each would have a 50% probability).
Suppose now we took our long-suffering particle that began with spin ↑ after a measurement in the z-direction, then turned out to be spin → when we measured it in the x-direction. What would happen if we repeated the z-measurement? The answer is that “preparing” the particle in the → state destroys the information about the fact that it was previously prepared in the ↑ state – the outcome of this second z-measurement is that the particle that was previously definitely ↑ now has a 50% chance of being either ↑ or ↓.
So what does all this have to do with voting? It is clear than an election (or a referendum) is very far from a simple act of measurement. During the campaign the various sides of the debate make attempts to prepare a given voter in a given state. In the case of last year’s EU referendum the choice of eigenstates was `Leave’ or `Remain’; no other possibilities were allowed. The referendum then `prepared’ each voter in one or other of these possibilities.
If voters behaved quantum mechanically each would stay in their chosen state until some other measurement were attempted. But that’s exactly what did happen. Earlier this month there was a General Election. More than two parties were represented, but let’s simplify and assume there were only two options, `Labour’ and `Conservative’.
Now it is true that the `Leave’ camp was dominated by the right wing of the Conservative party, and the majority of Labour voters voted `Remain’, but there were a significant number of Labour Leave voters and a significant number of Tories voted Remain. While these pairs of states are therefore not exactly orthogonal, they are clearly not measuring the same thing so the situation is somewhat analogous to the spin measurement problem.
So along came the General Election result which `prepared’ voters in a state of `Labour’ or `Conservative’, with a slight preference for the latter whereas the earlier referendum had prepared a them in a state of `Leave’ versus `Remain’ with a slight preference for the former. From a quantum mechanical perspective, however, you can further argue that the General Election prepared the voters in such a way that should have erased memories of their vote in the referendum so the previous BrExit vote is now invalid.
There’s only one way to test this quantum-mechanical interpretation of voting patterns, and that is by repeating the EU Referendum…
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June 23, 2017 at 5:38 pm
Putin would still find a way to hack it and change the result!
June 23, 2017 at 5:56 pm
But not by analogising this…
https://en.wikipedia.org/wiki/Elitzur%E2%80%93Vaidman_bomb_tester
June 24, 2017 at 10:24 am
Given the level of misunderstanding of quantum mechanics among some people without a specialist physics background, it might be important to point out here that this post is humorous: it is meant as a joke.
(If anything, the post makes a little fun of those people who think, wrongly, that quantum processes apply to macroscopic systems, such as people or society in general.)
June 24, 2017 at 10:26 am
Perhaps I should try to get this idea published in a sociology journal?
June 24, 2017 at 11:00 am
I’m sure you could. Perhaps the Journal of Applied Sophistry, if such a thing exists (and it probably does exist).
June 24, 2017 at 12:12 pm
Stop misleading people Bryn. I appreciate your sense of humour but the post is entirely serious, of course.
June 24, 2017 at 2:57 pm
Of course.
June 24, 2017 at 4:20 pm
There’s an element of irony in that. The idea of applying quantum mechanics to this brexit / general election voter system is obviously silly but, to the detriment of the joke, it’s not quite so obvious that the idea of applying quantum theory* to it is silly. There’s enough of a prima facie possibility of an appropriate description of it by noncommuting observables to spoil the joke for me at least.
Unfortunately, most people with a physics background aren’t even taught a proper understanding and interpretation of classical probability theory. Then QM is mostly taught as though it’s some weird new kind of mechanics instead of as a natural generalisation of probability theory applied to mechanics. So when QT is applied elsewhere it’s often mistaken for a silly application of QM (and there are plenty of those of course).
* Or maybe some ‘nearly quantum’ theory.
June 24, 2017 at 5:19 pm
I do a lot of my work at home. Does that mean I am noncommuting?
June 24, 2017 at 5:31 pm
Depends. You might be telecommuting.
June 24, 2017 at 5:33 pm
At least you’re not anticommuting..
June 24, 2017 at 5:37 pm
You anticommute if you live in London and work outside it.
June 25, 2017 at 9:35 am
If the outcome is a quantum probability function, does that mean my vote is imaginary?
June 25, 2017 at 2:40 pm
Aye aye?
June 26, 2017 at 9:55 am
Only in safe seats!
June 26, 2017 at 1:44 pm
In some places you are not even trying if the vote does not exceed 100% of the electorate…
June 26, 2017 at 2:59 pm
I voted three times in the recent General Election…
March 3, 2018 at 8:40 am
[…] psi-epistemic* relatives interpret QM as (generalised) probability theory applied to mechanics: https://telescoper.wordpress.com/2017/06/23/the-quantum-mech… It’s hardly a cop-out. See e.g. Rovelli’s take on what the ontological ramifications […]