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An Honest Lottery


James Adrian

      There are many millions of people who bet on a lottery. It is not hard to imagine how they could be better served. The following is a description of a lottery that has some unusual, and possibly some interesting properties.

      It is a lottery for gamblers who hold a debit card, and are willing to bet one dollar per month. This one dollar bet would be automatically deducted, once per month, from the checking account associated with the debit card that they hold.

      The manager of the lottery would cause a random drawing to take place once per month to select a winner. The winnings would be automatically deposited in the winner's checking account without ceremony. There would be one and only one winner.

      The amount of the winnings awarded each month would be the largest possible fraction the total of the one-dollar bets, or 25% of the current median income, which ever is less.

      If the lottery becomes popular, the amount of money collected but not awarded will grow. When it grows beyond half of the median income, another winner is selected at random before the end of the month. If the lottery continues to collect more than it awards, it would continue to increase the number of selected winners per month. Under no circumstances does an award increase beyond 25% of the median income.

      If you are one of the lucky winners, it is unlikely that you will quit your job. It is also unlikely that you will need to fight off long lost acquaintances eager to reestablish contact. You might fix a broken refrigerator or a damaged roof. You just might save your house from foreclosure, or pay your overdue bills.

      What would be the largest possible fraction of the total of the one-dollar bets if the money collected by the lottery is too small to pay out 25% of the median income? If the lottery is popular, what fraction of the collected money would be paid out in awards to winners?

      To pay out the most possible to the gamblers, the cost of managing the lottery must be as small as possible. Since there are no envelopes, stamps, ceremonies, advertisements, contributions to education, government sharing, etc., the cost would be that of the extra computing required by the bank. Computing is quite automatic these days. It might cost only pennies.

      I am reminded of a joker who got ahold of the ship's microphone and shouted "Liberty! Liberty!" and a couple of seconds later said "This is a drill."

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