"We can't really know" is a ridiculous thing to say about lottery cheating, when often a small investigation will show that yes, someone is definitely cheating. It's practically anti-scientific to phrase it as a shrug of the impossibility of knowing.
It might be safer to say that it's hard to know how much undiscovered cheating there if there is no discovered cheating.
The religion example is even less helpful, as religion isn't evidence-based.
Suppose the lottery system is designed in such a way that it really IS practically impossible to cheat.
The numbers are pulled out of a machine and broadcast live and there are tons of witnesses. Or maybe the numbers are generated as a repeatable function of some publicly known events. And so on.
Suppose the chances of winning this lottery fairly are one in 100,000,000.
Then someone wins 3 times out of 20 tickets.
What would you say?
People try to find the flaw and they can't.
What if you DIDNT know the lottery was designed to be perfect? Are you sure you wouldn't constantly suspect the WRONG choice?
The system that you describe in no way resembles the lottery system as it exists today: it's so far from reality that I'm not quite sure why you're even bringing up this fantasy representation of a lottery.
The real lottery abuse - particularly scratch-offs, which are what is being abused here - is not a match-up between "high probability of not winning" and "unable to cheat". It is between "high probability of not winning" and "multiple fairly obvious avenues for cheating". Among them are the two mentioned prominently in the article: Micro-scratching and taking winning tickets and telling customers that they were losers, then claiming it for yourself. Both of which are avenues easily available to the clerks who have suddenly found themselves to be in this "miraculous" state of repeated wins at very low participation rates.
Why are you bringing up some fantasy straw man version of the lottery to defend it?
Because this is HN and people here are interested in exactly such generalizations.
It's mildly interesting to consider the ways in which scratch-offs can be gamed. One can collude with a shop owner to peer behind the scratch-off material with a machine, for instance. It is about as interesting as figuring out how a biometric ID can be gamed by a simple replay attack, storing all the aspects of your fingerprint and replaying it later.
What's MORE interesting is if the lottery was far far harder to game. The general principle is fascinating. We think we can KNOW the truth but using simple math we can SHOW that when evidence on both sides piles up and yet contradicts the other, you cannot recover and somehow come to KNOW the truth.
Thus you see the situation today when people confidently assert one side or the other, but each side has really strong arguments for its side.
Each side will say the other's arguments are bunk, but rarely actually engages with them in depth.
Winners can be investigated where it may be found out that they colluded with someone in the lottery bureau, used a pin and magnifying glass to peek in scratch offs at the 7/11 they work at, etc. The article enumerates these.
If they didn't cheat at all or just cheated very well, then of course nothing can be determined. Just like any other crime. But that's not very insightful. There are unsolved murder mysteries.
Forget scratch offs. What if I told you that the lottery system was actually not breached. Every time you look for a flaw, the system has all indications of not being susceptible. Understand?
And yet someone won 3 out of 20 times and it multiples to a staggeringly unbelievable probability.
You will keep suspecting that you were wrong, long after you make a conclusion. Do you understand? The stronger the evidence on both sides, the less ability you have to remove doubt, EVER!!!
It might be safer to say that it's hard to know how much undiscovered cheating there if there is no discovered cheating.
The religion example is even less helpful, as religion isn't evidence-based.