First of all, that is a completely separate argument that does not rescue or excuse your previous invalid argument.
What I was trying to say is that getting any of the factors exponentially wrong greatly affects the outcome and that this can easily occur on account of a hidden conjunction.
Secondly, absent evidence that the overwhelming majority of Fermi calculations have this mistake, you should be pointing to a specific event in a specific Fermi calculation that is assigned too high a probability because it is implicitly a conjunction, not attempting a fully general counterargument against all Fermi calculations.
I was not attempting to give incontrovertible argument; rather I was raising some points for consideration. Nor was I attempting giving a fully general counterargument against all Fermi calculations; as I said above
Note that I'm not casting doubt on the utility of Fermi calculations as a general matter
Most of the probabilities used in Fermi calculations about existential risk are unfalsifiable which makes it difficult to point to an indisputable example of the phenomenon that I have in mind.
Nor was I attempting giving a fully general counterargument against all Fermi calculations
You may not have been attempting to make a fully general counterargument, but you did in fact make an argument against Fermi calculations, without referring to any specific Fermi calculation, that fails to distinguish between good Fermi calculations and bad Fermi calculations.
Over the past six months I've been repeatedly going back and forth on my attitude toward the value of short-term and/or exclusive focus on existential risk. Here I'll offer some reasons why a utilitarian who recognizes the upside of preventing human extinction may refrain from a direct focus on existential risk reduction. I remain undecided on my attitude toward short-term and/or exclusive focus on existential risk - this article is not rhetorical in intent; I'm just throwing some relevant issues out there.
1. On the subject of FAI research, Prase stated that:
The same can be said of much of the speculation concerning existential risk in general, not so much existential risk due to asteroid strike or Venusian global warming but rather with the higher probability but much more amorphous existential risks connected with advanced technologies (general artificial intelligence, whole brain emulation, nano weapons, genetically engineered viruses, etc.).
A principle widely held by many highly educated people is that it's virtually impossible to predict the future more than a few decades out. Now, one can attempt to quantify "virtually impossible" as a small probability that one's model of the future is correct and multiply it by the numbers that emerge as outputs of one's model of the future in Fermi calculations, but the multiplier corresponding to "virtually impossible" may be considerably smaller than one might naively suppose...
2. As AnnaSalamon said in Goals for which Less Wrong does (and doesn't) help,
Assuming that A and B are independent events, the probability of their conjunction is p(A)p(B). So for example, an event that's the conjunction of n independent events each with probability 0.1 occurs with probability 10-n. As humans are systematically biased toward believing that conjunctions are more likely than their conjuncts (at least in certain setting), there's a strong possibility of exponentially overestimating probabilities in the course of Fermi calculations. This is true both of the probability that one's model is correct (given the amount of uncertainty involved in the future as reflected by historical precedent) and of the individual probabilities involved assuming that one's model is correct.
Note that I'm not casting doubt on the utility of Fermi calculations as a general matter - Carl Shulman has been writing an interesting series of posts arguing that one can use Fermi calculations to draw reasonable conclusions about political advocacy as philanthropy. However, Carl's posts have been data-driven in a much stronger sense than Fermi calculations about the probabilities of technologically driven existential risks have been.
3. While the efficient market hypothesis may not hold in the context of philanthropy, it's arguable that the philanthropic world is efficient given the human resources and social institutions that are on the table. Majoritarianism is epistemically wrong, but society is quite rigid and whether or not successful advocacy of a particular cause is tenable depends in some measure on whether society is ready for it. In Public Choice and the Altruist's Burden Roko wrote
Even when epistemically justified in the abstract, focus on fringe causes may take too much of a psychological toll on serious supporters in order for serious supporters to be effective in pursuing their goals. To the extent that focus on existential risk requires radical self sacrificing altruism there are dangers of the type described in a comment by Carl Shulman:
4. Because of the upside of ensuring the survival rate is so huge, there's an implicit world view among certain people on Less Wrong that, e.g. existential risk reduction charities offer the opportunities for optimal philanthropy. I think that existential risk reduction charities may offer opportunities for optimal philanthropy, but that the premise that this is so largely independently of the quality of the work that these charities are doing is essentially parallel to the premise behind Pascal's Wager. In Making your explicit reasoning trustworthy Anna Salamon wrote
I'm not able to offer a strong logical argument against the use of Pascal's wager or infinite ethics but nevertheless feel right to reject them as absurd. Similarly, though I'm unable to offer a strong logical argument for doing so (although I've listed some of the relevant intuitions above), I feel right to restrict support to existential risk reduction opportunities that meet some minimal standard for "sufficiently well-conceived and compelling" well above that of multiplying the value of ensuring human survival by a crude guess as to the probability that a given intervention will succeed.
Intuitively, the position "it doesn't matter how well executed charity X's activities are; since charity X is an existential risk reduction charity, charity X triumphs non-existential risk charities" is for me a reductio ad absurdem for adopting a conscious, explicit, single-minded focus on existential risk reduction.
Disclaimer: I do not intend for my comments about the necessity of meeting a minimal standard to apply specifically to any existential risk reduction charity on the table. I have huge uncertainties as to the significance of most of the points that I make in this post. Depending on one's assessment of their significance one could end up either in favor or against short-term and/or explicit focus on existential risk reduction