# Are lotteries auctions?

I heard one professor of my university say that "lottery is a kind of auction. So we can predict it! Then we could get a lot of money!"

Since he is in the mathematics department, and I know little about that matter, I couldn't answer to my gut feeling which told me that he was wrong.

So, from the Economist's perspective, is it true? Is a lottery some kind of an auction?

Generally, and surprisingly, yes, lotteries are similar to auctions. What do I mean by that?

In an auction, you increase the likelihood of winning by increasing your bid. In many auctions, if you increase the bid sufficiently much, that probability will go to one.

A similar thing is true for lotteries: the more tickets you buy, the higher is the likelihood of success. It is not a one-for-one correspondence, but it holds. And again, by predicting other people's actions (are they more likely to bid/gamble on week days or week ends), you can increase your chances of winning the lottery.

However, this means that you can increase your chances of winning, not that you will make a net surplus ("get a lot of money"). In the same way as sometimes, you can bid "too high" and make a net loss in an auction, you can pay a too high price for the (expected) win. In a lottery, this is quite often the case.

• Indeed, most lotteries are designed so that you always make an expected net loss, i.e. the optimal bid (assuming non-convex utility) would be zero. In some cases this is guaranteed by design; in other cases (e.g. raffles) the organizers simply expect that people will overbid as a matter of course (which they'll usually do, not least because optimizing the expected return would require knowing how many tickets have been / will be sold, which is rarely openly advertised). Commented Aug 29, 2015 at 19:49

No. The winner of an auction is the highest bidder, while the winner of a lottery is chosen at random. Even if you buy more tickets than anyone else, you are not guaranteed to win.

An auction is a price discovery mechanism. You can get useful information from the result of an auction, e.g. how much a similar item might be worth.

The value of the prize of a lottery is usually known upfront, and anyway no information is gained by rolling dice.

• "The winner of an auction is the highest bidder" is often true in practice, but not by definition. Commented Jan 29, 2016 at 17:06