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Suppose I am given a lottery ticket. This ticket has a 1 in 1000 chance of winning me one million dollars, and will otherwise be worth nothing.

Before I can see whether I've won, some guy comes along and destroys the ticket. There is no way to buy a replacement, and no way of knowing whether the ticket would have paid out or not.

The expected value of the ticket is clearly 1e6/1e3 = one thousand dollars. My question is, would the court do that math and award me one thousand dollars? It's extremely unlikely that I've suffered any actual loss, so obviously I can't recover a million bucks in speculative damages from the guy; and yet $0 in damages hardly seems fair.

In other words: If the actual value of my loss cannot be determined with certainty, yet the statistically expected value of the loss can be, can I recover the expected damages?

Bonus question: Suppose instead of the ticket being a gift, I had paid $500 for it, or $2000. (Remember, I can't buy another one.) Would either situation change the result?

Sneftel
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  • If I were you, I'd try to recover the purchase price of the ticket. Lotteries only make money because product of the expected payout and the odds of winning is lower than the purchase price. – phoog Jun 15 '15 at 22:18
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    @phoog sure, but in the main question, the ticket was a gift and had no explicit price. In any case, the question is about the damages, not the lottery. – Sneftel Jun 15 '15 at 22:32
  • Of course. That's why I commented rather than answering. Still, for most lotteries, even if they roll the jackpot over when no one wins, it's really not worth it. The largest payout in the US, at least, was $474MM (https://en.wikipedia.org/wiki/Lottery_jackpot_records); multiplying by odds of 1:175,711,536 (https://en.wikipedia.org/wiki/Mega_Millions#Versions_of_.28The_Big_Game.29_Mega_Millions) gives $2.70 a ticket. But oh, the prize was split among 3 people: The odds of hitting the jackpot are not the same as those of winning the entire jackpot; they depend on the number of tickets sold. – phoog Jun 15 '15 at 22:50
  • Still I am interested in the answers your question might elicit as the principle might be more significant in other circumstances. So +1 from me. – phoog Jun 15 '15 at 22:51
  • In the UK, you can for example bet whether a football team will win the championship. If this all happens two weeks before the end of the season, a ticket originally purchased for £10 might have a 35% chance of winning £10,000. If this goes to court after the season is offer, do I get (a) £10, (b) £3,500 or (c) nothing or £10,000 depending on whether the team wins or not? – gnasher729 Jul 17 '16 at 14:13
  • Your expected value calculation is slightly off, assuming the ticket cost you $1. To calculate the expected value, at least in the statistical sense of the word, you need to know how much the ticket cost. If the ticket cost you $1.00, then the expected value would be 0.001 x $1,000,000 - 0.999 x 1 = $999.001. If the ticket cost you $1,000, the expected value would only be $1. – StatsStudent Jul 25 '16 at 05:15
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    @StatsStudent That's how you would calculate the expected value of the game, not the expected value of the ticket. (Well, mostly. Your calculation is slightly wrong: Since the ticket price isn't refunded if you win, there's no need to multiply the $1 by 0.999.) – Sneftel Jul 25 '16 at 11:23
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    @Sneftel, Ahhh! I missed the small detail of game vs. ticket. We, as statisticians rarely calculate the former (game) so I just umped in with my two cents. Thanks for pointing this out. – StatsStudent Jul 25 '16 at 12:52

1 Answers1

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Sort of.

In this instance, it doesn't seem that the damages awarded (if any) would be compensatory damages, but speculative damages. A good definition is

Possible financial loss or expenses claimed by a plaintiff that are contingent upon a future occurrence, purely conjectural, or highly improbable. These damages should not be awarded. For example, a plaintiff may claim that in ten years, as he ages, he may begin to feel pain from a healed fracture caused by a defendant (even though no doctor has testified this is likely to happen), and should therefore recover money from the defendant now.

In order to be awarded compensation, a plaintiff must prove that there is a high likelihood that the future event would occur. The required likelihood may be subjective, in part because it is hard to estimate the odds of many claims. In the situation given here, there is a 0.1% chance of a payoff. That is most likely far too low to be considered likely.

Now, if the plaintiff argued for compensatory damages, then s/he might receive an amount of money equivalent to the price of one lottery ticket - or the same ticket back. Assuming the original ticket is destroyed, the odds are the same (and even if it is not destroyed, the odds change by only a tiny amount); the same thing happens if the original ticket is returned, instead. The plaintiff has not lost any chance to win the million dollars.

Bonus question: If you paid $500 or $2,000 dollars and wanted to be awarded compensatory damages, you might receive those sums of money. If you wanted to be awarded speculative damages, you would most likely receive nothing, because the odds are the same.

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