[luckylion]

That was my point regarding it not being a linear relationship and only working on somewhat rational actors (not on somebody that is on drugs and completely out of their mind for example). Getting caught is irrelevant if it has no consequence at all. If there is zero punishment (meaning no negative consequences and you get to keep the loot), but you are 100% sure to get caught, you have incentive to commit e.g. robbery, but zero incentive not to. If the punishment isn't negative (i.e. "you get $1000 for getting caught"), getting caught is also irrelevant. Getting caught only becomes relevant when it has consequences you'd prefer to avoid: punishment.

The point isn't that punishment isn't a deterrent, it's the only external deterrent (and you could argue that a bad conscience is self-punishment). It's that the likelihood of getting caught is a very important factor, not so much the severity of the punishment.

In RTS games, there's the idea of overkill: a unit (or set of units) does so much damage that it would kill the attacked unit multiple times. That's a problem, because you waste a lot of the damage, it's generally more efficient to do less damage more often for the same DPS (damage per second). I believe that you can think about punishment in a similar way. With the likelihood of punishment staying the same (for example: 10%), a hike of "somebody stares angrily at you" to "you spend 10 years in prison" very much acts as a deterrent. You get barely any more value out of that being 20 years though, because of "over-deterrence". Here as well, the same punishment with more frequency (=likelihood of punishment) would be more efficient.