[EDIT] I'm leaving my original comment as-is, but noting that I wrote it having completely misread the original comment by @inphiknit. We are in agreement.
Original, dumb reply that I made:
Um, what? Think that through and try again.
Suppose there are 100 people in on it, and 1 would benefit by leaking. Then they add another 100 faithful people. The 1 who would benefit by leaking is still there! He would still benefit by leaking! But by adding 100 more people the conspirators now have to worry about twice as many people flipping on them.
No, if you think about it critically, I'm sure that smaller conspiracies are more stable.
I think I'm missing something, or there is confusion because of how I phrased it with a negative and a positive... I agree and am certain smaller conspiracies are more stable too, which is what my initial statement indicates. Chance of success decreases by half when you double the population. But I seem to recall an old formula that precisely defines the rule. But since I can't recall the name, I can't find it. I learned it when listening to a lecture about "Applewhite Theorem," (about that cult in California a decade or so ago.)
Regarding your adding 100 "faithful" people, that's just the thing, we can't ever really say that, and people change. So for every doubling in the following, the chances of a leak double too. Isn't that so regardless of that specific guy who might benefit? (And now there may be 2 of them too.)
I'm not being argumentative, I just think the likelihood of a (successful) FE conspiracy to be extremely, extremely low. Maybe I got the exact formula wrong, but we agree on the principle I think. So aside from perhaps partially misremembering the it, I don't understand where I have missed thinking critically. (But am open to an education^^)
Ach, sorry. I totally misread your original comment. I'm editing my reply to fix it.
I was in "disagree with everybody" mode and didn't give your comment the thought it deserved. :)
That sounds pretty interesting - I'll check it out.
Disagree with everybody mode.
You seriously think this is an acceptable or productive mindset to enter into a debate with? The context of your previous comments make a lot more sense after reading this.
Thanks for the edit, I appreciate it and know exactly what you mean when you say you were in "disagree with everybody mode!" I get ridiculous when like that... Lol!
Sorry I can't recall the name of the formula. I did a quick search and haven't found it yet, so please let me know if you do! It was in some lecture on youtube, so my google search isn't helping much so far...
I think you should read the parent comment again, it says that the probability the conspirary succeeds goes down (by half) as the number involved increases (by two times).
Yep, you're correct. I read it too quickly and let myself misread "decrease" as "increase." Thanks!