There’s a lot of research into this effect due to it’s application in a frontline in warfare.

Manpower can only travel so far in a rapid response to incidents, which quickly makes distant sections 100% independent. That’s linear scaling.

Again, not the same due to the very low amount of goods that have to be smuggled. I'm aware of the rules of thumb for frontline warfare, those are intended for sizeable or sustained troop movements.

For something like fentanyl where a single success is enough for a single trafficker over a long time, the fact that sections are 100% independent is exactly why scaling is exponential - only one section has to fail for the goal to be achieved.

Try and articulate in what way that meaningfully hampers securing a border such that you’re looking at zero illicit crossings a month.

Driving 1 truck through a brick wall isn’t easier than driving 10, you need to deal with the wall either way.

Same deal with a tunnel, it’s detecting that’s hard. Shipping thousands of tons through a small gap is easy.

If anything length of border gives you economies of scale in terms of specialization equipment.

My model is pretty simple, just like yours we cut up the borders into segments. Certain of these segments will have higher or lower probabilities of interception for various reasons, and drug traffickers are able to estimate this probability somehow. Only one of these segments needs to be vulnerable for the traffickers to succeed, and they will assess essentially the whole length of the border. It's then clearly exponentially more likely for the traffickers to succeed as the border is longer, as the likelihood for at least one segment with acceptable probability increases exponentially with the number of segments.

If you assume that drug traffickers can't estimate the likelihood of success or that every part of the border is consistently just as secure at every point in time as any other then you'd be right, but those aren't reasonable assumptions in my opinion.

You just commented a minor logically fallacy here.

People are unwilling to accept infinite risk and the question of if a segment of broader is secure depends on the risk of crossing that segment.

They might have better targets, but if a given segment isn’t secure that’s an inherent issue even if people happen to choose somewhere else.

In the other direction, if some segment is effectively impossible to cross that’s irrelevant. You don’t need other segments to reach an arbitrarily high standard just high enough to either get people to give up on the idea or fail often enough you’re dealing with the issue. IE one guy with a backpack per decade isn’t failure.

> People are unwilling to accept infinite risk and the question of if a segment of broader is secure depends on the risk of crossing that segment.

People are, in practice, given a commensurate reward, willing to accept arbitrarily high risk, and market dynamics are willing to provide the rewards in this case.