One way is as briefly presented in The Sunday Telegraph, www.telegraph.co.uk/education/2018/08/25/million-gcse-exams-could-open-challenge-due-tounreliable-grading/, and as we have discussed before. This idea dispenses with grades altogether, and awards the candidate's 'raw' mark, say, 69 (say, current grade 7). But we know this mark is 'fuzzy', and that another marker might have given 72, or whatever. So the 'fuzziness' is also declared as, say, ± 5. The certificate therefore shows 69 ± 5 (in whatever format is easily meaningful), clearly showing that any mark from 64 to 74 is (as Ofqual would say) "reasonable". So there is no meaningful difference between this candidate, and one whose 'raw' score is 70 (say, current grade 8), also ± 5. Certainly, this new way of presenting assessments needs to be communicated clearly, and understood correctly, but I'm sure that's possible. And the claim that it's not possible should not be accepted as a reason to perpetuate the current injustice of unreliable grades.
There are two further things that need to be considered. Firstly, the ± 5 is a property of the subject exam, not a particular candidate's individual script. So ± 5 applies to all candidates doing, say, geography. For maths, the number might be ± 2; for English Lit, ± 8. To determine this number, once all scripts have been marked, the exam board could take one script marked, say, 62, and give that same script to each of, say, 50 different markers for a fair, 'blind', re-mark. Some of those re-marks will give 50, but others won't. This set if 50 re-marks will form a distribution, from which the 'fuzziness' can be determined. This process can be carried out for as many scripts originally marked 62 as you like, and also for scripts originally marked 40, 90, whatever. This will give a sensible average value for the subject's 'fuzziness'. A professional statistician can get the details of all this right.
The second matter concerns appeals. Suppose that a candidate assessed as 69 ± 5 appeals, and suppose that the fair remark is 71. This is to be expected, for 71 is within the range 69 ± 5. So the original assessment is confirmed. The same applies to all re-marks in the range 64 to 74.That's why this process is robust under appeal.
But if the re-mark is, say, 76, that's outside the range 69 ± 5, and is indicative of a (significant) marking error. So the assessment is changed to 76 ± 5.
Two last points to complete the picture. Any marking error within the ± 5 range is masked by the measure of 'fuzziness', and so is undetectable (unless you specifically look for it, but why would you?). This shouldn't matter.
But the point that does matter is that, if the fair range is 69 ± 5, then it is possible that the first mark might have been 74, implying that the assessment, as shown on the certificate, would be 74 ± 5, which might make a real difference. This is true, but if the measure ± 5 has been determined statistically properly, then the likelihood that this is will be the case can be limited. But it is still possible. In which case the appeals system should pick it up, for if the awarded assessment is 69 ± 5, whereas the "real truth" is 74 ± 5, there is a 50% probability that a fair re-mark would be 75 or greater.
This is not perfect, but no system will ever be totally so.
The key question is "Is this more fair than the status quo?" I think it is.
An assessment awarded as [mark] ± [fuzziness] is one possibility... there are some others...
Does this make sense?