The Conservatives have just won the UK general election convincingly. The people have spoken, we are told. They want to get Brexit done, and done it will be (though it will take a lot longer than the Tories are letting on).

But have the people delivered this message? Well, not really – not if you add up the popular vote.

It wasn’t just the Sun wot won it, or dislike of Jeremy Corbyn, or years of neglect of our post-industrial heartlands (who have just voted in large numbers for the party that has just presided over nine years of austerity – weird!) or even that desire to get Brexit done. It was the voting system.

First past the post (FPTP). Winner takes all in each constituency. Dead simple, keeps local connections, tried and tested. Perfect for a two party world, which characterised most of the UK until the 1980s. Terrible for a more variegated electorate, in which issues like Brexit divide in a different way to tradition. And grossly unfair to smaller parties and their voters. They are left behind.

To demonstrate this, let’s take the vote in this election, and see what would have happened under proportional representation. I’m taking a pure nationwide form here, which exists in very few countries. Most PR systems attempt to retain some local element, so don’t perfectly divide the seats by the number of votes. But they get close. And this example is just illustrative. I’ve rounded up where there is a fraction in seats under PR (this particularly benefits the Tories, DUP and Plaid Cymru, where the fraction is below 0.5). They don’t add up to 650 because of all the other candidates who have won votes, but it doesn’t detract from the overall findings.

Data is from the BBC website, except the right hand column, which is my calculation.

Party              Seats actually won              % of popular vote             Seats under PR

Cons               365                                        43.6                                     284

Lab                 203                                        32.1                                     209

Lib Dem        11                                           11.5                                        75

SNP               48                                          3.9                                         25

Green            1                                             2.7                                         18

Brexit            0                                            2.0                                         13

Plaid              4                                            0.5                                           4

DUP               8                                            0.8                                          6

SF                   7                                            0.6                                           4

SDLP             2                                            0.4                                           3

Alliance         1                                            0.4                                           3

Under this PR system, the Conservatives win 81 fewer seats. Eighty-one! The SNP loses half its seats, because its vote is concentrated in Scotland, which greatly benefits it under FPTP (as it did Labour in the past). Labour stays about the same, but the big winners are the Lib Dems, who have 75 seats rather than a measly 11. The Greens and the Brexit party also get a decent number of seats.

So let’s fantasise about a progressive alliance forming, comprising Labour, Lib Dems, SNP, Greens, Plaid Cymru, the SDLP and the Alliance Party. It wins 337 seats and forms a government with a 31 seat working majority (ie, in a 643 seat parliament as Sinn Fein doesn’t take its seats).  It would be a nightmare to keep together, but it would be worth a go. The point is that we do have, even now, a progressive majority of voters in this country. It’s just that it is split many ways, which is fatal under FPTP. We have just seen quite a few Labour and Lib Dems candidates lose in this election, because of the votes that the weaker of the two has taken away from the stronger. Some key Tory figures, like Dominic Raab and Ian Duncan-Smith, have been able to breathe a sigh of relief because of this.

The other interesting counterfactual is if we try to brigade these figures into a Leave/Remain split. There are two big assumptions here: Labour is a Remain party, and the Conservatives are all Leavers. This covers 94.6% of those who voted – the sum of the popular vote percentages in the above table.

REMAIN: Labour, Lib Dem, SNP, Green, Plaid Cymru, Sinn Fein, SDLP, Alliance = 51%

LEAVE: Conservative, Brexit, DUP = 49%

Close! But Remain has the majority.

Unfortunately it reinforces the notion that we are just a very divided country. Thanks for letting us know, David Cameron.

Now, these are all just counterfactuals – what-ifs. In the real world the Tories have a majority of 80 (more if you take out Sinn Fein). So they can do what they like in the next five years.

Be very afraid.