I think we do overestimate short term things and underestimate long term things. However, I think it is important to clarify that it would be a mistake to think of this tendency in a pejorative way. It is, best as I can tell, more correct than the alternative.
Some reasons for that:
- Conjunction of events is less than the probability of its individual constituents and unless the events were certain to occur is always less than the probability that they occurred given that they occurred.
- Making an estimate out of multiple different approximations with unknown error bounds you should have decreasing confidence in your approximation because you have increasing confidence of error in your approximation.
- Modeling with the bellman equations such that overestimation of true utilities in short term and bad underestimation of true utilities in the long term can produce superhuman cognitive abilities in many decision making contexts.
- We ought to see overestimation and underestimation: given a coin that is biased, it does not follow that you bet on that coin with probability proportional to the bias, but rather to the rounding. So we should see actions that correspond with rounding up in the short term which is more likely to be less conjuncted and therefore higher probability and we should see rounding down in the long term wherein there is more conjunction and therefore lower probability.
This all leads me to suspect that a framing around faith being justified, not around whether we overestimate or underestimate, might be a more correct framing. This is actually exceedingly true in the cooperative regime wherein other agents force underestimation of probabilities due to the potential for competition, but in which a cooperative environment supports overestimation.
To get at what I mean by that, consider that no one must teach you proper form such that you do not injure yourself at a gym, so your probability of injury is actually pretty high if you are estimating using only the things you can control, yet in practice you will probably get high quality advice to avoid injury if someone cooperative notices you are likely to hurt yourself - it is not sufficient to point at the ability to learn this information yourself to refute this, because all the information available to you is a function of a cooperative society. So the going to the gym and avoiding injury while doing so should use a non-cooperative creature like an octopus going to an open location and doing exercise there in sight of predators: they don't have access to books to help them, they have access to sharks. As an aside, lots of people are so surrounded by the waters of cooperation they can hardly notice they are swimming, which is kind of interesting to contrast with the octopus with adaptive camouflage that is more prone to death the moment it become visible.
But now we are getting into a defense for bad estimation - because we are starting to get into estimates that are predicated on self-reference: agent one observes agent two and makes a decision based on their policy, but agent one is also making observations of agent two and deciding policy based on that! This is a regime wherein we start getting paradoxes like the halting problem, godel's incompleteness proof, or the linguistic paradox of heterological classification. In other words, we find strong evidence for the need for some other concept than yes or no, something more like the idea of mu or the idea of undecidability.
So here we reach another reason to disagree with the idea: how can an answer which isn't even well defined because it is undedicable be an overestimate or an underestimate?
Some reasons for that:
- Conjunction of events is less than the probability of its individual constituents and unless the events were certain to occur is always less than the probability that they occurred given that they occurred.
- Making an estimate out of multiple different approximations with unknown error bounds you should have decreasing confidence in your approximation because you have increasing confidence of error in your approximation.
- Modeling with the bellman equations such that overestimation of true utilities in short term and bad underestimation of true utilities in the long term can produce superhuman cognitive abilities in many decision making contexts.
- We ought to see overestimation and underestimation: given a coin that is biased, it does not follow that you bet on that coin with probability proportional to the bias, but rather to the rounding. So we should see actions that correspond with rounding up in the short term which is more likely to be less conjuncted and therefore higher probability and we should see rounding down in the long term wherein there is more conjunction and therefore lower probability.
This all leads me to suspect that a framing around faith being justified, not around whether we overestimate or underestimate, might be a more correct framing. This is actually exceedingly true in the cooperative regime wherein other agents force underestimation of probabilities due to the potential for competition, but in which a cooperative environment supports overestimation.
To get at what I mean by that, consider that no one must teach you proper form such that you do not injure yourself at a gym, so your probability of injury is actually pretty high if you are estimating using only the things you can control, yet in practice you will probably get high quality advice to avoid injury if someone cooperative notices you are likely to hurt yourself - it is not sufficient to point at the ability to learn this information yourself to refute this, because all the information available to you is a function of a cooperative society. So the going to the gym and avoiding injury while doing so should use a non-cooperative creature like an octopus going to an open location and doing exercise there in sight of predators: they don't have access to books to help them, they have access to sharks. As an aside, lots of people are so surrounded by the waters of cooperation they can hardly notice they are swimming, which is kind of interesting to contrast with the octopus with adaptive camouflage that is more prone to death the moment it become visible.
But now we are getting into a defense for bad estimation - because we are starting to get into estimates that are predicated on self-reference: agent one observes agent two and makes a decision based on their policy, but agent one is also making observations of agent two and deciding policy based on that! This is a regime wherein we start getting paradoxes like the halting problem, godel's incompleteness proof, or the linguistic paradox of heterological classification. In other words, we find strong evidence for the need for some other concept than yes or no, something more like the idea of mu or the idea of undecidability.
So here we reach another reason to disagree with the idea: how can an answer which isn't even well defined because it is undedicable be an overestimate or an underestimate?