The physics of an election — how VoteScope Labs works

1 · The starting point

Rolling the dice 50,000 times

Most election forecasts, our reference forecast included, work like a casino. You imagine the election tens of thousands of times, randomly drawing the possible polling errors, then you count: in how many of those universes does a given party win?

It is simple, robust and remarkably effective. But it is an approximation: even with 50,000 draws, some noise remains. Above all, it says nothing about the shape of opinion itself. Orbit asks a different question: what if we could compute directly instead of drawing lots?

2 · The shape of opinion

An electorate is a point on a sphere

Take voting intentions: 40% for one party, 35% for another, 25% for the rest. Those three numbers always add up to 100%. You could draw them as a point in a triangle. Orbit does something odd: it takes the square root of each share. Suddenly the triangle becomes a piece of a sphere, like an orange peel.

Why? Because on that sphere, a poll’s uncertainty has the same size in every direction. On an ordinary triangle, a party at 3% and a party at 40% do not “wobble” the same way from one poll to the next. On the sphere, they do. A single setting therefore describes the error of every party, big and small.

Another consequence: a 2-point move does not mean the same thing everywhere. Going from 2% to 4% is doubling; going from 40% to 42% is a detail. The sphere knows this by instinct: the distance between two electorates measures how well polls could tell them apart.

Two parties: vote shares live on the straight line; their square roots live on a quarter circle. Near the edges (a party that is almost absent), a small step along the circle means very few points of vote.

3 · Curvature

Carrying an arrow across a curved world

A thought experiment. Standing on the equator, you hold an arrow pointing north. You walk to the North Pole without ever turning the arrow, walk back down along another meridian, and return to your starting point along the equator. Surprise: your arrow has rotated, even though you never turned it. That is the signature of curvature.

Orbit faces the same problem. The province-wide polling movement is an arrow: this party rises, that one falls. To know what that movement means in one specific riding, the arrow has to be carried there, across the sphere, without distortion. This is called parallel transport.

The result is neither a uniform swing (the same points everywhere) nor a proportional swing: geometry decides. A party gains or loses more points where it is strong; a new party can appear where it did not exist.

An arrow carried without ever turning around a triangle drawn on a sphere comes back rotated: that is curvature. Orbit carries the province-wide movement to each riding the same way.

4 · Tracking opinion day by day

Navigating like Apollo

Polls arrive one by one, each with its margin of error and its pollster’s habits. To extract the most likely position of the electorate, Orbit uses a Kalman filter adapted to the sphere: with each new poll, it corrects its estimated position, weighing how reliable the measurement is and how much time has passed.

It also removes each pollster’s own lean, and it does not let a pollster that publishes every day dictate the average on its own. The settings are not picked by hand: they are estimated from the polls themselves. One lesson emerged: opinion has no momentum. A one-week trend does not carry itself forward.

5 · Polls as measurements

The Born rule

In quantum physics, a system is described by “amplitudes”, and the probability of an outcome is the square of its amplitude. That is the Born rule. The square roots on the sphere in section 2 are exactly that: amplitudes whose squares give back the vote shares.

So Orbit treats each poll as a measurement of the state of the electorate. Pooling all the polls gives what physicists call a density matrix. If every pollster said the same thing, it would be “pure”. The more they contradict each other, the more mixed it becomes, and the von Neumann entropy measures that disagreement.

And on election night, the electorate “collapses” onto an outcome. In nine Canadian elections since 2015, the party leading in the polls always did better on the night, and smaller parties did worse. Orbit builds this in with a single number, estimated from past elections only: at the moment of measurement, shares concentrate slightly toward the dominant parties.

6 · Counting seats

Qubits instead of dice

Each riding becomes a small register, like a qubit: its amplitudes give each party’s chances of winning there. The whole province is the assembly of all those registers, and a party’s seat count is read on a counter wired to each of them.

A quantum computer would “measure” that counter to get the seat distribution. We do not need one: the structure of the problem lets us do exactly the same calculation on an ordinary computer, riding by riding. We checked: a real quantum circuit, simulated with IBM’s qiskit library, gives the same distribution to the billionth.

The result: no randomness at all in the seat count, and a complete calculation in seconds. Only the large common shocks, such as a nationwide error by every pollster, are walked through on a regular grid rather than drawn at random.

Each riding is a register whose amplitudes give each side’s chances. The seat counter is obtained exactly, without a single random draw.

7 · The map

Geographic nesting dolls

Pollsters often publish results by region, each in their own way: one firm’s “Montreal” is the metropolitan area, another’s includes all the suburbs, a third publishes the island alone. Orbit cuts Quebec into thirteen elementary pieces (the island, Laval, the suburban rings, the Quebec City area…) and rebuilds each pollster’s region as an assembly of those pieces.

The pieces nest like Russian dolls: each belongs to a block, each block to a large zone. When a piece is rarely measured, it borrows information from its block and its zone. And each poll is compared with itself: what it says about a region, versus what its own province-wide numbers predicted. Its pollster habits cancel out; only the geography remains.

What this is not

Voters are not quantum particles, and an election has nothing to do with gravity. Orbit borrows mathematics, not laws of nature: it turns out that the tools invented for curved space and the quantum world are also the natural tools of probability.

Orbit is not yet better than our reference forecast: replayed the day before the vote, past elections show comparable errors, sometimes favouring one, sometimes the other. That is exactly why it runs alongside, every night, on the same polls. When the two engines agree, the signal is solid. When they diverge, that is where to look.

See what Orbit projects →