A raffle, like a tournament or a dollar auction, is a system designed to sell things for more than they are worth, manipulating the buyers by setting their incremental incentives against them. But the raffle tickets must have some price set on them — if the number of tickets is fixed, then this price could be set too high (reducing the total price paid by selling too few tickets) or too low (reducing the total price paid by selling out at too low a price). Making the raffle open-ended does not eliminate this problem, although it does reduce it.
It occurred to me that a Dutch auction for the raffle tickets might be a useful variant — all of the tickets are sold at the lowest price that sells all of them. This provides an incentive to buyers to reveal their true value.
An open-ended alternative would sell a previously undetermined number of tickets at the price that generates the largest amount of revenue. For example, given bids for 10 tickets at $10, 20 tickets at $20, 20 tickets at $30, 10 tickets at $40, and 1 ticket at $60, you could sell 61 tickets at $10, 51 tickets at $20, 31 tickets at $30, 11 tickets at $40, or 1 ticket at $60, with revenues respectively of $610, $1020, $930, $440, and $60. So selling 51 tickets at $20 is the best option, leaving out those who would only have bid $10, giving all others equal winning chances of 1.96%.
I’m not sure what the incentive landscape looks like for buyers. Suppose the raffled good is worth $1000 to you, and there’s a closed-end Dutch auction for 100 raffle tickets. If you’re risk-neutral, you should be willing to buy all 100 at any price up to $10 each, but none at any higher price. If it’s worth $1100 to another risk-neutral rational actor, they would bid $11 each for all 100; according to the rules of Dutch auctions, this results in them getting all 100 tickets at $10 and you getting nothing. So far so good, since you also paid nothing.
But, if you’re truly risk-neutral, you should be just as happy to pay $500 for a 50% chance of acquiring it as to pay $1000 for a 100% chance, so all numbers of tickets are equally good to you, regardless of whether your true value is $1000 or $1100 or $2000 or what.
All of this seems okay so far, except that it doesn’t have the intended perverse incentive of inducing buyers to pay more than they get in return, as I think raffles are observed to do in the real world.
We could attempt to explain this by supposing that some buyers are risk-positive, so that a 50% chance of acquiring a $1000 good is worth more than $500 to them. But there are a large variety of different ways that someone could be risk-positive.