Person who win the jackpot in lottery will not go to work.
If everybody wins the jackpot, nobody will go to work.
If nobody goes to work, the society cannot function.
Therefore, the government should not allow any lottery game.
I think the main problem is that winning jackpot is not easy, but this argument assume it is very common.
If this is a fallacy, is there a name for it?
The error can't be seen unless we add the missing false premise.
(1) Everyone wins the jackpot.
(2) Person who win the jackpot in lottery will not go to work.
(3) If everybody wins the jackpot, nobody will go to work.
(4) If nobody goes to work, the society cannot function.
(5) Therefore, the government should not allow any lottery game.
Validity and Soundness
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.
A deductive argument is sound if and only if it is both valid, and all of its premises are actually true. Otherwise, a deductive argument is unsound. https://www.iep.utm.edu/val-snd/
When we add the missing premise we can see that the argument is unsound.
The second premise is not needed.
The logical conclusion is that the government shouldn’t allow a lottery where everyone wins the jackpot. That’s a valid conclusion from the data given and makes sense. Without the “everyone wins the jackpot” it’s not a valid conclusion.
I wouldn’t say it’s a fallacy, just a mistake in the argument.
There is an element of false dichotomy. The conclusion, that lotteries should be banned, ignores that the current solution (lotteries where only a rare few win) is very effective at avoiding the downfall of society.
...but this seems more like a mask of arguments against things like welfare, universal basic income, and similar ideas. The problem with those arguments is that the first two premises are false, and the third is an assumption rather than a fact.
Correctly built or not, your argument seems to be using the slippery slope fallacy, aka number 15 on this page.
