And how do you know the result isn't rigged? People who resist vaccine don't trust the government, and they won't trust the result is going to be fair.

I just hope that the government won't get butthurt by how little this lottery affects people's decision, and then start door-to-door forced vaccination.
Those people who do not trust the government are not the target audience for such actions. They are trying to lure those who are hesitant or just lazy to get vaccinated. Based on the example of my country, I can say that the effect of such actions is about zero, and maybe even negative - all people understand that free cheese is only in a mousetrap.