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The whole talk about N+1 gives the same probability as N is not right.
Earlier quoted context omitted.
The parent comment talks about scaling back the amount of rock climbing they do in order to reduce risk.. And now you are saying that they should go one more time, because a single climb is low risk?
Yes. I am saying their analysis of risk is incorrect, and therefore if that's the only reason they aren't climbing then they should climb more often.
None of this intended to cast aspersions on rock climbing in particular, just pointing out that a reasonable person, understanding independence of events and not falling prey to any fallacy, could reasonably make this decision based on their personal risk tolerance
This story reminded me of a story written by a Czech biologist who studied animals in Papua-New Guinea and went to a hunt with a group of local tribesmen. The dusk was approaching, they were still in the forest and he proposed that they could sleep under a tree. The hunters were adamant in their refusal: no, this is dangerous, a tree might fall on you in your sleep and kill you . He relented, but silently considered…
Earlier quoted context omitted.
Is 1:5000 an actually good assessment? I'd suspect it's very much not, especially if you avoid obviously dead trees and maybe move if a storm comes.
1:5000 would suggest an average lifetime of 13.7 years for a grown tree (i.e. not counting the years where it's too young to sleep under), and that's before the ability to avoid trees that look more likely to fallover. I don't know anything about trees around there, maybe they're really short-lived? For forests around here, it's a gross overestimate.
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The "slippery slope" principle applies here though: N+1 enables N+2, which enables N+3 and so on.
Slippery slope is a fallacy, not a principle. Just because you took N steps, that doesn't necessarily mean you will take N+1 steps. It's a convincing fallacy because sometimes you do take N+1 steps. But just like in the article, heuristics aren't always right.
The argument can certainly be used in a fallacious manner (e.g. by greatly exaggerating the probability of the further steps, saying they are inevitable if the first step is taken, etc.). It's logically valid to say that the first step enables subsequent steps to be taken.
Edit: I'd say that the slippery slope is perfectly valid rule of thumb in a lot of 'adversarial' situations. Once one side makes an error or fails somehow, the balance between the two sides can be disrupted leading to one 'side' gaining momentum. Just as between people, a similar 'adversarial' process can occur within the minds of individuals: between two ideas or patterns of thought/behaviour, one idea can gain momentum after a decision has been reached. Precedence is a strong force.
Earlier quoted context omitted.
Is 1:5000 an actually good assessment? I'd suspect it's very much not, especially if you avoid obviously dead trees and maybe move if a storm comes.
1:5000 would suggest an average lifetime of 13.7 years for a grown tree (i.e. not counting the years where it's too young to sleep under), and that's before the ability to avoid trees that look more likely to fallover. I don't know anything about trees around there, maybe they're really short-lived? For forests around here, it's a gross overestimate.
I would still guess that the number is wrong, I suspect that trees have a longer life on average from becoming what we would consider "big" until they fall over. But it's still an important detail.
Earlier quoted context omitted.
The parent comment talks about scaling back the amount of rock climbing they do in order to reduce risk.. And now you are saying that they should go one more time, because a single climb is low risk?
Yes. I am saying their analysis of risk is incorrect, and therefore if that's the only reason they aren't climbing then they should climb more often.
If your tolerance is X% death/life, you can calculate the climbing frequency that falls below the threshold.
On the plus side, if you assume the events are independent, you can recalculate and increase the frequency after each climb.
Earlier quoted context omitted.
A coworker and I were once stuck in an office building for an hour or two. We were working as consultants at a client's building and ended up working rather late. Not particularly late by software programmer standards, but clearly exceptionally late by the culture of the client company. At some point in the evening all the exit doors, including the front door, became armed, and this was conspicuously noted as when we…
That security guard was performing the important function of allowing the management to legally tick the "we have a security guard" box on the insurance form.
Earlier quoted context omitted.
The parent comment talks about scaling back the amount of rock climbing they do in order to reduce risk.. And now you are saying that they should go one more time, because a single climb is low risk?
Yes. I am saying their analysis of risk is incorrect, and therefore if that's the only reason they aren't climbing then they should climb more often.
If an individual decides their risk tolerance is that they will not accept a one in a million chance of injury from rock climbing, how is their analysis incorrect?
Additionally, getting the base rate right is important when considering lifetime risk and the costs vs. benefits of taking action or engaging in further screening - e.g. missing two or three cancer patients might be worth the benefits of not subjecting large numbers of patients to secondary screening.