Not the best idea. By decision, I mean a specific situation where individual people made a conscious choice.
I think, strictly speaking, this is unknowable. But philosophically this type of question is very useful to ask, because it forces us to truly examine the idea of consequentiality of decisions. It is one of the best ways to improve decision-making skills.
Since there are already many interesting answers here, I'll offer a meta-answer and a way to make sense of the candidates.
What Sorts of Answers are More "Correct"?
Practically, my guess is that Lee Semel's answer is the closest to the type of answer that is likely correct. But curiously, I don't think Brandon Tung's seemingly similar answer is as close. A presidential decision is far more robust/less sensitive to noise than that of a lower-level influencer along a path. One piece of evidence is that another American President (Kennedy) pulled back from the brink as well. I recently visited the Minuteman missile national monument in South Dakota, and got a sense of what it takes to pull the nuclear trigger, and the process seemed a lot more delicate at the "false alarm" level than at the Presidential authority level. This was partly a consequence of deliberate injection of calibrated amounts of instability/snowball dynamics in the process (due to the doctrine of brinkmanship).
Answers like Lucretia M Pruitt's about Newton, are much less likely to be correct. Informally, the reason is that Leibniz invented calculus too, and the climate was such that it was highly likely that somebody else (or some group of others) would have discovered things that Newton did. This is a well-documented phenomenon: when a paradigm shift is nearing, a lot of people may make nearly the same discoveries at the same time. Kuhn's paradigm shift process is overall a lot more robust than the individual domino-fall patterns within it.
Answers like Fahd Butt's about Hitler are somewhere in between. He was a crazed psycho, and did not have a clearly substitutable role in the drama. But then, the German people were smarting with resentment over Versailles anyway, and it is not clear whether or not a different psycho (or even non-psycho) might have triggered a rearmament and world war. This type of answer has actually been beautifully explored in science fiction. Asimov's Foundation novels involve a Hitler-like mutant psycho in one part, who deeply upsets the predictability of Hari Seldon's psychohistory model. Weird inputs from critically-positioned Black Swan type individual decision-makers can have huge effects on the course of history.
Daniel Ahn's answer is intriguing. My guess is that it is like the Newton answer (the Europe/Islam dynamic would have played out the same way anyway, but with a much bigger transient perturbation to the course of history).
Does the Question Actually Make Sense?
But these are merely the practical, phenomenological considerations (i.e. things like whether the time is/is not "ripe" for something, to what extent historicist models of history (i.e. that history has certain stable-attractor trajectories that are hard to perturb in the large) are justified, etc.
At its heart, this is a metaphysics question. In rare cases, you have empirical evidence (for example, the invention of zero appears to have happened in two and possibly three isolated historical streams, so that's empirical evidence that no single invention event was critical), but mostly, reasoning about what might/might not have happened is in the realm of the unfalsifiable.
But that doesn't mean it is useless, or that it cannot be done systematically to get to useful insight.
This is what is known in philosophy and physics as a question about possible worlds. The reasoning involved is counterfactual reasoning. Or "what-if" reasoning. Technically, this is called modal logic. It is very tough indeed (good news for fiction writers).
For the question to make sense, you have to strengthen its philosophical foundations.
Assumptions You Need
First pass, assume that a decision is important in proportion to how differently the course of events would probably have flowed, had it been made differently. I think this is how most people are interpreting the question.
What do we mean by "different?" If Newton hadn't existed and Leibniz had been a true-redundant Newton by also developing the laws of motion and gravity, how different would history have been?
This is extremely tricky. Perhaps it was Newton's role in the history of the British Treasury, or as a client of a particular barber that was more sensitive historically. This sort of what-if naturally leads to the path-instability idea: that maybe the most consequential decision ever was some random guy choosing to drink a second cup of coffee one morning. This is the stuff of sci-fi time-travel perturbation theory. It is the chaos-theory butterfly effect applied continuously to a time trajectory.
It completely messes up and ruins this question, so let us make the BIG assumption:
History is not sensitively-dependent on path conditions.
or if you prefer, the weaker version:
The actual sensitivity of history to path conditions is correlated to the observed sensitivity.
This assumption (weaker or stronger) is almost certainly not true (for the same sorts of mathematical reasons why "future is like the past" assumptions are wrong in the Black Swan sense), but without it, this question is uninteresting. And the thing is, even if it is not strictly true, it doesn't matter, so long as it is at least ROUGHLY true. Even 10% true.
Think of events and their impact on history in terms of a 2x2 diagram: controllable/uncontrollab
The only part worth talking about is the controllable/observable quadrant. To the extent that we feel that we do shape history through our deliberate and intentional actions that have forseeable consequences, this what-if question about big decisions is a useful one. Sure, it might turn out that history is mostly driven by unobservable/uncontrollab
If we further assume that of the controllable/observable events, total causal impact is in proportion to intended causal impact (i.e. you get more unintended consequences with more intended consequences) then we can say that "big" decisions will cause overall big perturbations. I'd measure "intended causal impact" by the product of the energy unleashed by a decision (megatons for a big nuclear bomb or a few calories for a paper read out to the Royal Society) and the information content behind the decision (measured in compressed bits, for example).
Is the Question Useful?
Sure it is fun to play this game, merely as an excuse to share our favorite nuggets of history, engage in what-if one-upmanship, or messing with people's sense of what is/was important.
But is it useful beyond that? Yes.
IF you agree with all this philosophical scaffolding then the question makes sense and you have the tools to make both sense of and use of the answer. The answers ARE useful. They tell you where to strengthen crucial decision-making processes. What we are doing here is an informal/crowdsourced version of virtual-perturbation analysis to test the stability of our collective sense of history.
In limited ways, you can actually model this sort of thing and do sensitivity/pertubation analyses of decision streams. I've done stuff like that and it is a lot of fun. The key thing to keep in mind is that computer models are closed-world constructs and you can only draw limited inferences from them.
Since there are already many interesting answers here, I'll offer a meta-answer and a way to make sense of the candidates.
What Sorts of Answers are More "Correct"?
Practically, my guess is that Lee Semel's answer is the closest to the type of answer that is likely correct. But curiously, I don't think Brandon Tung's seemingly similar answer is as close. A presidential decision is far more robust/less sensitive to noise than that of a lower-level influencer along a path. One piece of evidence is that another American President (Kennedy) pulled back from the brink as well. I recently visited the Minuteman missile national monument in South Dakota, and got a sense of what it takes to pull the nuclear trigger, and the process seemed a lot more delicate at the "false alarm" level than at the Presidential authority level. This was partly a consequence of deliberate injection of calibrated amounts of instability/snowball dynamics in the process (due to the doctrine of brinkmanship).
Answers like Lucretia M Pruitt's about Newton, are much less likely to be correct. Informally, the reason is that Leibniz invented calculus too, and the climate was such that it was highly likely that somebody else (or some group of others) would have discovered things that Newton did. This is a well-documented phenomenon: when a paradigm shift is nearing, a lot of people may make nearly the same discoveries at the same time. Kuhn's paradigm shift process is overall a lot more robust than the individual domino-fall patterns within it.
Answers like Fahd Butt's about Hitler are somewhere in between. He was a crazed psycho, and did not have a clearly substitutable role in the drama. But then, the German people were smarting with resentment over Versailles anyway, and it is not clear whether or not a different psycho (or even non-psycho) might have triggered a rearmament and world war. This type of answer has actually been beautifully explored in science fiction. Asimov's Foundation novels involve a Hitler-like mutant psycho in one part, who deeply upsets the predictability of Hari Seldon's psychohistory model. Weird inputs from critically-positioned Black Swan type individual decision-makers can have huge effects on the course of history.
Daniel Ahn's answer is intriguing. My guess is that it is like the Newton answer (the Europe/Islam dynamic would have played out the same way anyway, but with a much bigger transient perturbation to the course of history).
Does the Question Actually Make Sense?
But these are merely the practical, phenomenological considerations (i.e. things like whether the time is/is not "ripe" for something, to what extent historicist models of history (i.e. that history has certain stable-attractor trajectories that are hard to perturb in the large) are justified, etc.
At its heart, this is a metaphysics question. In rare cases, you have empirical evidence (for example, the invention of zero appears to have happened in two and possibly three isolated historical streams, so that's empirical evidence that no single invention event was critical), but mostly, reasoning about what might/might not have happened is in the realm of the unfalsifiable.
But that doesn't mean it is useless, or that it cannot be done systematically to get to useful insight.
This is what is known in philosophy and physics as a question about possible worlds. The reasoning involved is counterfactual reasoning. Or "what-if" reasoning. Technically, this is called modal logic. It is very tough indeed (good news for fiction writers).
For the question to make sense, you have to strengthen its philosophical foundations.
Assumptions You Need
First pass, assume that a decision is important in proportion to how differently the course of events would probably have flowed, had it been made differently. I think this is how most people are interpreting the question.
What do we mean by "different?" If Newton hadn't existed and Leibniz had been a true-redundant Newton by also developing the laws of motion and gravity, how different would history have been?
This is extremely tricky. Perhaps it was Newton's role in the history of the British Treasury, or as a client of a particular barber that was more sensitive historically. This sort of what-if naturally leads to the path-instability idea: that maybe the most consequential decision ever was some random guy choosing to drink a second cup of coffee one morning. This is the stuff of sci-fi time-travel perturbation theory. It is the chaos-theory butterfly effect applied continuously to a time trajectory.
It completely messes up and ruins this question, so let us make the BIG assumption:
History is not sensitively-dependent on path conditions.
or if you prefer, the weaker version:
The actual sensitivity of history to path conditions is correlated to the observed sensitivity.
This assumption (weaker or stronger) is almost certainly not true (for the same sorts of mathematical reasons why "future is like the past" assumptions are wrong in the Black Swan sense), but without it, this question is uninteresting. And the thing is, even if it is not strictly true, it doesn't matter, so long as it is at least ROUGHLY true. Even 10% true.
Think of events and their impact on history in terms of a 2x2 diagram: controllable/uncontrollab
The only part worth talking about is the controllable/observable quadrant. To the extent that we feel that we do shape history through our deliberate and intentional actions that have forseeable consequences, this what-if question about big decisions is a useful one. Sure, it might turn out that history is mostly driven by unobservable/uncontrollab
If we further assume that of the controllable/observable events, total causal impact is in proportion to intended causal impact (i.e. you get more unintended consequences with more intended consequences) then we can say that "big" decisions will cause overall big perturbations. I'd measure "intended causal impact" by the product of the energy unleashed by a decision (megatons for a big nuclear bomb or a few calories for a paper read out to the Royal Society) and the information content behind the decision (measured in compressed bits, for example).
Is the Question Useful?
Sure it is fun to play this game, merely as an excuse to share our favorite nuggets of history, engage in what-if one-upmanship, or messing with people's sense of what is/was important.
But is it useful beyond that? Yes.
IF you agree with all this philosophical scaffolding then the question makes sense and you have the tools to make both sense of and use of the answer. The answers ARE useful. They tell you where to strengthen crucial decision-making processes. What we are doing here is an informal/crowdsourced version of virtual-perturbation analysis to test the stability of our collective sense of history.
In limited ways, you can actually model this sort of thing and do sensitivity/pertubation analyses of decision streams. I've done stuff like that and it is a lot of fun. The key thing to keep in mind is that computer models are closed-world constructs and you can only draw limited inferences from them.
