I’ve been promoting stapling a lottery ticket to every vaccination card for some time, so it was good to see Ohio followed by New York, Maryland and Oregon introduce vaccine lotteries. Moreover, the program appears to be working as noted by Philip Bump in the Washington Post:
The seven-day average number of Ohioans getting their first shots increased the day after DeWine’s announcement and continued heading up through Sunday. It’s worth noting that this happened while the number of vaccinations nationally remained flat, suggesting that the trend in Ohio was driven by something different. It’s also worth pointing out that the number of Ohioans completing their vaccinations continued to slip lower, again reinforcing that these were people newly seeking out the vaccine. (In two or three weeks it will be interesting to see if more people are completing their vaccinations.)
Sadly, some politicians are now introducing legislation in Ohio to stop the program. Thus, it’s worthwhile recapping why we expect a lottery program to work. Most people think first about behavioral or psychological explanations. A vaccination is all about immediate costs and future benefits and it’s more difficult to act on future benefits than immediate costs, ala hyperbolic discounting. A free beer, donut, or lottery ticket provides an immediate benefit to offset the immediate cost and so may encourage vaccination, especially for those who are very present oriented. Note, however, that a lottery ticket might be expected to be less beneficial than an equivalent-cost donut because the donut is truly immediate while the lottery ticket is not. On the other hand, if vaccine hesitancy is driven by over-estimated fear of rare side-effects then perhaps a lottery ticket balances with an over-estimated hope of rare-benefits.
Even within a risk-neutral, rational model, however, there are good reasons to tie public goods to lotteries (ungated). Charities, for example, often use lotteries or raffles to fund public goods. Why? The reason is that a lottery is a natural counter to free-riding. Imagine that there is a public good but no one contributes because they each hope to free ride off other people’s contributions. As a result, the public good is not provided. Now introduce a fixed prize lottery. If no one else contributes then a contributor wins the lottery for certain so it can’t be an equilibrium for everyone to free ride (reminiscent of my dominant assurance contract mechanism for producing public goods). Note that the lottery in this model can’t just be a regular lottery ticket where you have to match X numbers to win. It has to be a raffle where the probability of winning is 1/N where N is the number of contributors. Thus, the Maryland and Ohio vaccine lotteries, which draw winners from the vaccinated, are much better than New York version which just hands out free lottery tickets. Thus, I expect the Ohio and Maryland versions to be more successful than the New York version.
Hat tip: Casey Mulligan for reference to the Morgan paper.