So, the case is closed, the verdict is in writing – only the referee has slipped up and written the result down wrong. It’s a simple case of correcting the mistake, right? Ah – not so fast.

It was the sort of mistake any QS could make. There were perfectly good claims by one side that came to £386 542; this went into the account for the M&E contractor, Dahl-Jensen. Then there were perfectly good claims by the other side that came to £178 801; this went into the account for the main contractor, Bouygues. If you take one figure from the other, you’re left with the balance of about £207 741 that Bouygues should pay to Dahl-Jensen, right? Well, actually, no, it is not quite right. In fact, it has all ended in tears.

This is the story of a very recent adjudication, Bouygues UK Limited vs Dahl-Jensen UK Limited.1 Let me tell you what happened. Bouygues was main contractor for building work at King’s College, part of the University of London. It placed the M&E subcontract with Dahl-Jensen, and work began last April. Within two months, Bouygues determined the contract. Dahl-Jensen upped and left. By now, about £7m had been forked out on interim payments. Dahl-Jensen said it was not in default and began adjudication for money it said was due.

Bouygues admitted cash was due, then started its own adjudication against Dahl-Jensen. Its counterblast came to more than £5m. The same adjudicator accepted both adjudications and made his headlong dash to decide who gets what. He gave Dahl-Jensen its cash, and gave Bouygues £178 801, and it looked right.

But the two sides' calculations were not like for like. One party had done its calculation inclusive of retention. So, the adjudicator ordered Bouygues to pay Dahl-Jensen £207 741 when it should have ordered Dahl-Jensen to pay Bouygues £141 254. It’s rather like the referee in the England vs Scotland rugby international writing down that Scotland won with 80 000 spectators knowing it hadn't.

I guess Bouygues refused to honour the adjudicator's decision – after all, the adjudicator had plainly made a mistake. Dahl-Jensen now sued for its money. It went to the High Court.

Mr Justice Dyson saw that the adjudicator had got the arithmetic wrong. And now, dear reader, you will expect the judge to get to grips with putting things right. Oh dear, how do I put this? He can't. The judge has to apply the rules set out in the Construction Act. These say the decision of the adjudicator is binding until finally decided in litigation or arbitration. So, if that is cast in parliamentary stone, that is what goes. If the adjudicator referee writes the wrong score down, that's that.

If the referee has a right to be on the pitch, what happens if he makes wrong decisions?

I know all that sounds as though the law is an ass. Let's see if that is correct. If the adjudicator is put in place by an appointing body, the right to do the job arises out of something called jurisdiction. So, if the work is construction operations in a construction contract in writing after 1 May 1998, not within set exemptions in the act, the referee has this so-called jurisdiction. Further, the referee's job will be set out in second level jurisdiction being the exact questions they are required to decide on. If the referee goes outside general jurisdiction, or answers questions not specifically referred to him, he was not playing the right game, and his decisions are void.

Lawyers say the referee acted ultra vires. But if he does have authority to be on the pitch, what happens if he makes wrong decisions? Say he gets the score wrong. Tough. Say he acts unfairly by listening to the arguments of one side but not the other. Tough again. The judges in English and Welsh courts say that if the referee has a right to be there, he has a right to make mistakes.

So, does an obvious and fundamental mistake stick? Seems so. But hang on – one of the senior Scottish judges isn't convinced. Lord Macfayden, as I discussed last week, is hesitant about keeping his hands off decisions unfairly reached or decisions plainly and fundamentally wrong. Lord Macfayden hints that the right approach for any tribunal is in a case called Anisminic in 1969 when the House of Lords explained that seriously wrong decisions were so flawed as to not count. But how flawed does a decision within jurisdiction have to be before it is set aside?

The Scottish judge will have their own ideas where the threshold is. But the English judge won't trouble to even ask. It stands. And it will continue to stand, says the rule, until corrected by a trial in court or arbitration.

There are now four arbitrators in the wings, ready and willing to correct fundamental errors of adjudication: a surveyor, an architect, an engineer and a lawyer. Each acts as the umpire in the stand. We can't have the referee on the pitch getting things so wrong that he ends up with the wrong score, now, can we?