Your percentage calculations (multiplying the three probabilities together to get the probability of all 3 happening) only make sense if the probabilities are all independent of one another. It's not at all obvious to me that they are.
Sorry I missed your comment. Yes, you're right. They are, as the textbooks say, for illustration purposes only. (Even this idea of three, entirely independent rolls of the dice diminishing the final probability rapidly, which is as simple as problems come, is alien to most. Which goes a long way to explaining why most people continue to handle probability so poorly.)
Thanks Dan. I appreciate your reply. However, I think your correction is still incorrect. High dependency between the 3 "die rolls" raises the overall chance of success for Putin. I believe we would agree that a Putin-friendly outcome on any of the 3 "rolls" makes Putin-friendliness on the other "rolls" more likely. This means those other "rolls" have less probabilistic power to diminish Putin's overall chances of success. And overall chance of Putin success ("the probability of nailing all three") is the value you focus on in the post.
What about your logic that "a strong Ukrainian military response is likely to encourage to strong Western sanctions response" so that variable dependence will be *bad* for Putin? The overall story here - again, if we agree that Putin-friendly outcomes make other Putin-friendly outcomes more likely - is polarized outcomes. If Putin succeeds on 1 or 2 outcomes, he's more likely to sweep the rest, but if he fails on 1 or 2, he's more likely to lose on the remaining outcomes. To put it in intuitive terms, victory in war begets more victory, while defeats beget further defeats. Variable dependence increases both Putin's chances of a sweep on all 3 points and his chances of losing all 3. But it was his chances of that successful sweep that you focus on in the post, and variable dependence is good for Putin's chances there.
The one way variable dependence would be *bad* for Putin's chances for success is if success on one outcome *reduced* the chances of success on another. For instance, perhaps swift removal of the Ukrainian government is a paradoxical success that only makes the Ukrainian military and populace fight even harder. In that case, dependence can reduce Putin's overall odds of success. I just don't get the impression that you believe in that kind of probabilistic relationship between any of the three points.
Sorry for the length of this reply. Hopefully it is helpful or at least not too annoying.
Dependent probabilities only help Putin when they are above 50%. It says the impact of prior military training and equipment is significant if it is sufficient to make weak resistance unlikely.
I think you could model this by saying the 3 results depend on the results on the previous day. So you end up with a Markov model. But it means at any time including before the invasion the results multiply as independent probabilities and the simple model of independent risks works. Each is actually the weighted sum of all possible interactions over time that could happen.
It is why it makes sense for Ukraine to fight a superior foe. A good result or the perception of one on a Tuesday effects the other two items probabilities on the Wednesday.
Your percentage calculations (multiplying the three probabilities together to get the probability of all 3 happening) only make sense if the probabilities are all independent of one another. It's not at all obvious to me that they are.
Sorry I missed your comment. Yes, you're right. They are, as the textbooks say, for illustration purposes only. (Even this idea of three, entirely independent rolls of the dice diminishing the final probability rapidly, which is as simple as problems come, is alien to most. Which goes a long way to explaining why most people continue to handle probability so poorly.)
Thanks Dan. I appreciate your reply. However, I think your correction is still incorrect. High dependency between the 3 "die rolls" raises the overall chance of success for Putin. I believe we would agree that a Putin-friendly outcome on any of the 3 "rolls" makes Putin-friendliness on the other "rolls" more likely. This means those other "rolls" have less probabilistic power to diminish Putin's overall chances of success. And overall chance of Putin success ("the probability of nailing all three") is the value you focus on in the post.
What about your logic that "a strong Ukrainian military response is likely to encourage to strong Western sanctions response" so that variable dependence will be *bad* for Putin? The overall story here - again, if we agree that Putin-friendly outcomes make other Putin-friendly outcomes more likely - is polarized outcomes. If Putin succeeds on 1 or 2 outcomes, he's more likely to sweep the rest, but if he fails on 1 or 2, he's more likely to lose on the remaining outcomes. To put it in intuitive terms, victory in war begets more victory, while defeats beget further defeats. Variable dependence increases both Putin's chances of a sweep on all 3 points and his chances of losing all 3. But it was his chances of that successful sweep that you focus on in the post, and variable dependence is good for Putin's chances there.
The one way variable dependence would be *bad* for Putin's chances for success is if success on one outcome *reduced* the chances of success on another. For instance, perhaps swift removal of the Ukrainian government is a paradoxical success that only makes the Ukrainian military and populace fight even harder. In that case, dependence can reduce Putin's overall odds of success. I just don't get the impression that you believe in that kind of probabilistic relationship between any of the three points.
Sorry for the length of this reply. Hopefully it is helpful or at least not too annoying.
Dependent probabilities only help Putin when they are above 50%. It says the impact of prior military training and equipment is significant if it is sufficient to make weak resistance unlikely.
I think you could model this by saying the 3 results depend on the results on the previous day. So you end up with a Markov model. But it means at any time including before the invasion the results multiply as independent probabilities and the simple model of independent risks works. Each is actually the weighted sum of all possible interactions over time that could happen.
It is why it makes sense for Ukraine to fight a superior foe. A good result or the perception of one on a Tuesday effects the other two items probabilities on the Wednesday.