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Comments on 2 construals "of 100 patients presenting with a lump like the claimant’s in Gregg v Scott, 42 will be ‘cured’ if they are treated immediately."

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2 construals "of 100 patients presenting with a lump like the claimant’s in Gregg v Scott, 42 will be ‘cured’ if they are treated immediately."

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Are there official terms for these 2 different interpretations of the same statistic?

Lord Hoffmann and Baroness Hale advanced the following arguments against awarding damages for the pure loss of a chance of being cured:

(1) The Hotson82 problem. In cases such as Gregg v Scott, it may well be that the claimant never had a chance of being cured, and if this is the case it would be inappropriate to award him damages on the basis that his doctor’s negligence deprived him of a chance of being ‘cured’.83 The statisticians tell us that of 100 patients presenting with a lump like the claimant’s in Gregg v Scott, 42 will be ‘cured’ if they are treated immediately. [emphasis mine] One way of interpreting this statistic is to say that each of those 100 patients has a 42 per cent chance of being ‘cured’. If this is right, then it would be correct to say that the claimant in Gregg v Scott had a 42 per cent chance of being ‘cured’ when he saw the defendant doctor. But there is a different way of reading the statistics. It may be that of 100 patients presenting with a lump like the claimant’s in Gregg v Scott, the varying genetic make-ups of the 100 patients mean that 42 of them are certain to be ‘cured’ so long as the lump is treated immediately, and 58 of them have no chance of being ‘cured’ no matter how much treatment they receive. If this is right, then it was more likely than not that the claimant in Gregg v Scott had no chance of being ‘cured’ and it would therefore be inappropriate to award him damages on the basis that he did have a chance of being cured.

82 See above, § 8.6.
83 Gregg, at [79]–[81] (per Lord Hoffmann).

N.J. McBride and R. Bagshaw, Tort Law, 6th edn (2018), page 285.

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This is a mathematics site, not a law site. (2 comments)
This is a mathematics site, not a law site.
Peter Taylor‭ wrote 12 months ago

The first question is borderline mathematical. The second question is not, so I'm going to edit to remove it.

Tim Pederick‭ wrote 11 months ago · edited 11 months ago

Even the mathematical part of the question is really about a legal principle—the “balance of probabilities”—much like another of the asker’s questions. I doubt there are “official terms” (OP’s request) in mathematics, but there may be in law.

To my understanding (but I am not a lawyer and this is not an answer), the issue is that the law does not allow expected value as a way to handle uncertain facts. If we blame each other in court for a loss of £100 each, and the court determines that there’s a 60% chance I’m to blame versus a 40% chance you’re to blame, it won’t award you £60 and me £40.† It will take the more likely scenario as 100% factual and award you £100. The “Hotson problem” seems to be whether this principle precludes damages for uncertain health outcomes.

† On the other hand, if it determines that it’s most likely that we’re both to blame, but that I bear more of the blame, it can and will award proportional damages.