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Comments on How to intuit that if you destroy someone else's lottery ticket, you didn't deprive her of a chance of winning the lottery?

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How to intuit that if you destroy someone else's lottery ticket, you didn't deprive her of a chance of winning the lottery?

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Despite perusing the following at least 20 times, I'm still tempted (in dereliction of the authors' advice to resist this temptation) to answer $\color{red}{\text{"Yes – though it was a very small chance"}}$ to the question whether Friend deprived Ungrateful of a chance of winning the National Lottery, when Friend ripped Ungrateful's ticket up?

I'm tempted in this manner probably because of footnote 70. Because '[t]he chance that Friend actually came up with the winning numbers for the weekend National Lottery draw was 1 in 14 million', hence the answer is "Yes – though it was a very small chance."

Kindly expound this reasoning more intuitively, or in another way? How can I overcome this temptation? Please correct my intuition?

A. Proof

In the case where Applicant is applying for a job as a skiing instructor, it is easy to see why we might say that Applicant has a chance of getting the job. The reason is that whether she gets the job or not is down to the decision of the employer, and human beings enjoy free will. There is always a chance that the decision could go your way when you apply for a job.
          In the case where a claimant wants to sue for damages for the loss of a chance of avoiding a physical injury, it is much more difficult for the claimant to show that the defendant’s tort deprived her of a genuine chance of avoiding that injury. This is an obstacle the claimant in Hotson [v East Berkshire Health Authority [1987] AC 750] was not able to overcome. In that case, it will be recalled, the claimant fell

N.J. McBride and R. Bagshaw, Tort Law, 6th edn (2018), page 279.

out of a tree and suffered a hip fracture which resulted in him eventually becoming permanently disabled. The House of Lords found that it was 75 per cent likely that when the claimant fell out of the tree, he damaged so many blood vessels in his hip that he was doomed to become disabled, no matter how well he was treated by the defendant. But this not only means it was more likely than not that the defendant’s failure to treat him properly did not make any difference to his becoming disabled. It also means that it was more likely than not the defendant’s failure to treat the claimant properly did not even deprive him of a chance of avoiding disability: it was more likely than not that the claimant had no chance of avoiding disability when he was first seen by the defendant.
          Students who have trouble appreciating this point should consider the Lottery Ticket Problem:

Friend went to a birthday party for Ungrateful at her house and included inside her birthday card a ticket for the National Lottery® draw that was due to take the place the same evening as Ungrateful’s party. Friend could not remember what numbers he had picked for the ticket. Ungrateful accepted the card and saw the ticket (without noting the numbers), but quickly put both the card and ticket aside and did not even bother to watch the National Lottery draw being made to see if she had won. Friend was so angry that Ungrateful did not seem at all excited by his present that, when her back was turned, he ripped up the ticket and threw the pieces of the ticket away. Due to a computer breakdown, there is no record of where the winning tickets for the draw on the evening of Ungrateful’s birthday were bought, and indeed there is no record of whether there was any winning ticket for that draw.

Did Friend deprive Ungrateful of a chance of winning the National Lottery when he ripped her ticket up? $\color{red}{\text{Most students will be tempted to say ‘Yes – though it was a very small chance.’ The temptation should be resisted.}}$ [color and emphasis added] Either Friend picked the winning numbers or he did not. If he did, Ungrateful won the Lottery. If he did not, Ungrateful could not have won the Lottery with the ticket Friend gave her. Which is it – was Ungrateful a winner, or a loser? The only way of resolving that question is through consulting the balance of probabilities. And when we do this, we will obviously conclude that it is more likely than not that Ungrateful could not have won the National Lottery with the ticket Friend gave her.70
          It was the same with the claimant in Hotson. He could not prove, on the balance of probabilities, that when he was wheeled into the defendant’s hospital, that he had any chance of avoiding permanent disability. As a result, it was simply not possible to make a claim for damages for loss of a chance of avoiding disability in Hotson.71 However, there do seem to be cases where the courts are willing to accept that Nature gives everyone a

70 The chance that Friend actually came up with the winning numbers for the weekend National Lottery draw was 1 in 14 million.
71 I presented this in this post.

Page 280

genuine chance of avoiding harm. For example, if A negligently dislocates B’s knee, the courts recognise that in such a case we can say B has a chance, but no more than a chance, of developing arthritis in his knee in the future as a result of what A has done. The courts do not approach that kind of case on the basis that B is either inevitably doomed to develop arthritis, or is inevitably fated to get better with proper treatment – and ask B to establish, on the balance of probabilities, which it is going to be in his case.

Page 281

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2 comment threads

x-post https://math.stackexchange.com/questions/4693955/how-to-intuit-that-if-you-destroy-someones-lo... (1 comment)
This seems like more of a legal question than a mathematical one. (3 comments)
x-post https://math.stackexchange.com/questions/4693955/how-to-intuit-that-if-you-destroy-someones-lo...