How to express a self-diminishing recursive property. Elegantly

Question

In the following, I can't find the right way to express my meaning for the part in bold:

Studies show that high IQ individuals are more susceptible to drug addiction than the general population, meaning there is a cognition-dependent aspect to substance abuse. While mainstream drug treatment programs are notoriously ineffective in general, with recidivism rates reaching 80 percent or higher, many people believe that for high IQ individuals those programs are even less effective than they are for the general population. Tragically, when an attempt to overcome drug addiction ends in failure, the negative light in which the addict saw himself in the world that made him vulnerable to addiction in the first place is intensified, reducing his value in his own eyes and, consequently, diminishing the incentive to try again. This recursive property makes traditional treatment programs for some addicts outright harmful.

I want to express the meaning that entering a drug treatment program, then failing (leaving the program unfinished or getting high one night with a friend, for example), makes it more likely one will slip back into full blown addiction, while simultaneously making it less likely they will seek help, and even if they do seek help, more likely they will fail again, which, of course, not only repeats the pattern (the recursive part), but intensifies it.

None of these seems exactly right, let alone elegant:

• negative recursive
• negative self-intensifier
• recursively diminishing
• lethal feedback loop

Interestingly, I found the question discussed mathematically here on StackExchange, but still wasn't able to come up with a way to express the idea in English.

Answer 1

You’ll have to let me know if you agree, but I’m fairly confident the phrase you’re looking for is a “vicious cycle” or sometimes called a “vicious circle”. This describes the kind of feedback loop you mentioned where the situation only becomes worse with each repetition. The converse would be a virtuous cycle.

https://wikipedia.org/wiki/Virtuous_circle_and_vicious_circle

Answer 2

It's a downward-spiral.

From wiktionary:

A series of thoughts or actions which feeds back into itself, causing a situation to become progressively worse. It is worse than a vicious circle, which is self-sustaining in its current state.

Or maybe amplification through recursion (which isn't a standard phrase as far as I can find, but it describes your effect). The negative effect grows as the cycle continues/repeats.

Answer 3

It would be a bit visual, but you could use Feedback or Feedback Loop.

From Wikipedia:

Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to feed back into itself.

Answer 4

I agree with "vicious cycle":

• a situation in which an attempt to resolve one problem creates new problems that lead back to the original situation
• A vicious circle is a problem or difficult situation that has the effect of creating new problems which then cause the original problem or situation to occur again.

A "vicious cycle" is a result of or example of "positive feedback" (e.g. "the weaker it is, the more it moves ... and the more it moves, the weaker it gets").

An example of "negative" feedback (a.k.a. "virtuous cycle") would be, for example:

1. Get addicted
2. Negative consequences (criticism from society, worse health, less money, less enjoyment)
3. Seek to reverse to addiction (because of the negative consequences)

The way in which the question is phrased might cause you to disagree with the answer, but I think the phrasing of the question is wrong or nonstandard -- i.e. instead of saying that it's "self-diminishing", note that (according to what you quoted) the vulnerability is intensified by continued exposure and/or by the intended treatment, and therefore spirals out of control.

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A similar process (i.e. "positive feedback" plus "the attempted cure made things worse") happened at Chernobyl:

Because of the positive void coefficient of the RBMK reactor at low reactor power levels, it was now primed to embark on a positive feedback loop, in which the formation of steam voids reduced the ability of the liquid water coolant to absorb neutrons, which in turn increased the reactor's power output. This caused yet more water to flash into steam, giving a further power increase.

... and later ...

A bigger problem was the design of the RBMK control rods, each of which had a graphite neutron moderator rod attached to the end to boost reactor output by displacing water when the control rod section had been fully withdrawn from the reactor. Thus, when a control rod was at maximum extraction, a neutron-moderating graphite extension was centered in the core with a 1.25 m column of water above and below it. Therefore, injecting a control rod downward into the reactor during a SCRAM initially displaced (neutron-absorbing) water in the lower portion of the reactor with (neutron-moderating) graphite on its way out of the core. As a result, an emergency SCRAM initially increased the reaction rate in the lower part of the core as the graphite section of rods moving out of the reactor displaced water coolant.