Do not know really what to say about this.
Do we really have so little trust in science?
I totally get where you are coming from with this, but in Massachusetts, that's not the issue. Our actual vaccine hesitance rates are
ludicrously low - on the order of only 5%. About two-thirds of our population is at least partially vaccinated. And our rate for people completing the course and getting the second shot is over 95% as well.
Instead, we have two other basic problems about getting to that final third:
1) Folks who are elderly, don't have cars, have to work several jobs or long hours, etc, are hard to get to come in for vaccines. The state is working on this issue by slowly shutting down the big centralized mass-vaccination centers (that were very efficient, but you had to drive to), and putting the resources towards getting vaccines into local areas - into pharmacies, doctor's offices, running mobile vaccine clinics, and so on, to make it
convenient, targeting those communities with lower vaccination rates.
2) Getting some of these people off their butts. Especially men, aged 20-40. They look at the world, see case rates plummeting, see restrictions lifting, think they are macho, and decide that they don't need to bother.
The lottery is mostly about the second issue - folks who just need that little bit more motivation. Apparently in Ohio, their lottery did a good job motivating just that demographic.