30% probability might be around the point where we start to call things ludicrous. If you talk seriously about things that you think have a 10% chance of happening, you will be beyond the point where most people call it ludicrous, or even crazy; they simply will not understand or believe that that’s what you mean.
This comment provides more confirmation for a view I’ve held for a long time, and which was particularly reinforced by some of the reactions to (the first version of) my Amanda Knox post.
People have trouble distinguishing appropriately among degrees of improbability. This generalizes both underconfidence and overconfidence, and is part of what I regard as a cluster of related errors, including underestimating the size of hypothesis space and failing to judge the strength of evidence properly. (These problems are the reason that judicial systems can’t trust people to decide cases without all kinds of artificial-seeming procedures and rules about what kind of evidence is “allowed”.)
The reality is that given all the numerous events and decisions we experience on a daily basis and throughout our lives, something with a 10% chance of happening or being true is something that we need to take quite seriously indeed. 10% is, easily, planning-level probability; it should attract a significant amount of our attention. By the same token, something which isn’t worth seriously planning on shouldn’t be getting more than single digits of probability-percentage, if that.
There is a vast, huge spectrum of degrees of improbability below 1% (never mind 10% or 30%) that careful thinking can allow us to distinguish, even if our evolved intuitions don’t. Consider for instance the following ten propositions:
(1) The Republicans will win control of both houses of Congress in the 2010
elections.
(2) It will snow in Los Angeles this winter.
(3) There will be a draft in the U.S. by 2020.
(4) I will be dead in a month.
(5) Amanda Knox (or Raffaele Sollecito) was involved in Meredith Kercher’s death.
(6) A U.S. state will make a serious attempt to secede by 2020.
(7) The Copenhagen interpretation of quantum mechanics, as opposed to the many-worlds interpretation, is correct.
(8) A marble statue has waved or will wave at someone due to quantum tunneling.
(9) Jesus of Nazareth rose from the dead.
(10) Christianity is true.
I listed these in (approximately) order of improbability, from most probable to least probable. Now, all of them would be described in ordinary conversation as “extremely improbable”. But there are enormous differences in the degrees of improbability among them, and moreover, we have the ability to distinguish these degrees, to a significant extent.
The 10%-30% range is for propositions like (1) ; the 1%-10% range for things like (2) (the last time it snowed in LA was in the 1960s). Around 1% is about right for (3). Propositions (4), (5), and (6) occupy something like the interval from 0.01% to 1% (I find it hard to discriminate in this range, and in particular to judge these three against each other). Propositions (8), (9), and (10), however, are in a completely different category of improbability: double-digit negative exponents, if you’re being conservative. We could argue about (7), but it probably belongs somewhere in between (4)-(6) and (8)-(10); maybe around 10^(-10), if you account for post-QM theories somehow turning Copenhagen into something more mundane than it seems now.
So the point is, we, right here, have the tools to make estimates that are a lot more meaningful than “probably yes” or “probably no”. I remember reading that we tend to be overconfident on hard things and underconfident on easy things; I think we can afford to be a little more bold on the no-brainers.
Propositions (8), (9), and (10), however, are in a completely different category of improbability: double-digit negative exponents, if you’re being conservative.
It would of course be sacrilegious to place (8) below (9) and (10). Nevertheless even in the case of apparently overwhelming evidence, if you disagree with a mainstream belief 10^(-20) times you will be wrong rather a lot more than once.
Meanwhile, quantum tunnelling is a specific phenomenon which, if possible (very likely) gives fairly clear bounds on just how ridiculously improbable it is for a marble statue to wave. Even possible improbable worlds which make quantum tunnelling more likely still leave (8) less probable than (9) (but perhaps not 10).
I personally place (10) at no less than 10^(-5) and would be comfortable accusing anyone going below 10^(-7) of being confused about probabilities (at least as related to human beliefs).
Nevertheless even in the case of apparently overwhelming evidence, if you disagree with a mainstream belief 10^(-20) times you will be wrong rather a lot more than once.
Like most majoritarian arguments, this throws away information: the relevant reference class is “mainstream beliefs you think are that improbable”. (edit: no, I didn’t read the whole sentence) In that class, it’s not obvious to me that one would certainly be wrong more than once, if one could come up with 10^20 independent mainstream propositions that unlikely and seriously consider them all while never going completely insane. Going completely insane in the time required to consider one proposition seems far more likely than 10^-20, but also seems to cancel out of any decision, so it makes sense to implicitly condition everything on basic sanity.
Meanwhile, quantum tunnelling is a specific phenomenon which, if possible (very likely) gives fairly clear bounds on just how ridiculously improbable it is for a marble statue to wave. Even possible improbable worlds which make quantum tunnelling more likely still leave (8) less probable than (9) (but perhaps not 10).
(9), and (10) for some definitions of “Christianity”, being more likely than (8) seems conceivable due to interventionist simulators (something I really have no idea how to reason about), but not for any other object-level reason I can think of. Can you think of others?
I personally place (10) at no less than 10^(-5) and would be comfortable accusing anyone going below 10^(-7) of being confused about probabilities (at least as related to human beliefs).
I’d be inclined to accuse anyone going above… something below 10^-7… of being far too modest.
Like most majoritarian arguments, this throws away information: the relevant reference class is “mainstream beliefs you think are that improbable”.
No, that is the reference class intended and described (“apparently overwhelming evidence”).
In that class, it’s not obvious to me that one would certainly be wrong more than once, if one could come up with 10^20 independent mainstream propositions that unlikely and seriously consider them all while never going completely insane.
Your prior is wrong (that is, it does not reflect the information that is freely available to you).
Going completely insane in the time required to consider one proposition seems far more likely than 10^-20, but also seems to cancel out of any decision, so it makes sense to implicitly condition everything on basic sanity.
Considering normal levels of sanity are sufficient. Failing to account for the known weaknesses in your reasoning is a failure of rationality.
I’d be inclined to accuse anyone going above… something below 10^-7… of being far too modest.
I am comfortable accusing you of being confused about probabilities as related to human beliefs.
Propositions (4), (5), and (6) occupy something like the interval from 0.01% to 1% (I find it hard to discriminate in this range, and in particular to judge these three against each other).
I’d guess you could estimate (4) to within an order of magnitude or better from an actuarial table.
30% probability might be around the point where we start to call things ludicrous. If you talk seriously about things that you think have a 10% chance of happening, you will be beyond the point where most people call it ludicrous, or even crazy; they simply will not understand or believe that that’s what you mean.
This comment provides more confirmation for a view I’ve held for a long time, and which was particularly reinforced by some of the reactions to (the first version of) my Amanda Knox post.
People have trouble distinguishing appropriately among degrees of improbability. This generalizes both underconfidence and overconfidence, and is part of what I regard as a cluster of related errors, including underestimating the size of hypothesis space and failing to judge the strength of evidence properly. (These problems are the reason that judicial systems can’t trust people to decide cases without all kinds of artificial-seeming procedures and rules about what kind of evidence is “allowed”.)
The reality is that given all the numerous events and decisions we experience on a daily basis and throughout our lives, something with a 10% chance of happening or being true is something that we need to take quite seriously indeed. 10% is, easily, planning-level probability; it should attract a significant amount of our attention. By the same token, something which isn’t worth seriously planning on shouldn’t be getting more than single digits of probability-percentage, if that.
There is a vast, huge spectrum of degrees of improbability below 1% (never mind 10% or 30%) that careful thinking can allow us to distinguish, even if our evolved intuitions don’t. Consider for instance the following ten propositions:
(1) The Republicans will win control of both houses of Congress in the 2010 elections.
(2) It will snow in Los Angeles this winter.
(3) There will be a draft in the U.S. by 2020.
(4) I will be dead in a month.
(5) Amanda Knox (or Raffaele Sollecito) was involved in Meredith Kercher’s death.
(6) A U.S. state will make a serious attempt to secede by 2020.
(7) The Copenhagen interpretation of quantum mechanics, as opposed to the many-worlds interpretation, is correct.
(8) A marble statue has waved or will wave at someone due to quantum tunneling.
(9) Jesus of Nazareth rose from the dead.
(10) Christianity is true.
I listed these in (approximately) order of improbability, from most probable to least probable. Now, all of them would be described in ordinary conversation as “extremely improbable”. But there are enormous differences in the degrees of improbability among them, and moreover, we have the ability to distinguish these degrees, to a significant extent.
The 10%-30% range is for propositions like (1) ; the 1%-10% range for things like (2) (the last time it snowed in LA was in the 1960s). Around 1% is about right for (3). Propositions (4), (5), and (6) occupy something like the interval from 0.01% to 1% (I find it hard to discriminate in this range, and in particular to judge these three against each other). Propositions (8), (9), and (10), however, are in a completely different category of improbability: double-digit negative exponents, if you’re being conservative. We could argue about (7), but it probably belongs somewhere in between (4)-(6) and (8)-(10); maybe around 10^(-10), if you account for post-QM theories somehow turning Copenhagen into something more mundane than it seems now.
So the point is, we, right here, have the tools to make estimates that are a lot more meaningful than “probably yes” or “probably no”. I remember reading that we tend to be overconfident on hard things and underconfident on easy things; I think we can afford to be a little more bold on the no-brainers.
It would of course be sacrilegious to place (8) below (9) and (10). Nevertheless even in the case of apparently overwhelming evidence, if you disagree with a mainstream belief 10^(-20) times you will be wrong rather a lot more than once.
Meanwhile, quantum tunnelling is a specific phenomenon which, if possible (very likely) gives fairly clear bounds on just how ridiculously improbable it is for a marble statue to wave. Even possible improbable worlds which make quantum tunnelling more likely still leave (8) less probable than (9) (but perhaps not 10).
I personally place (10) at no less than 10^(-5) and would be comfortable accusing anyone going below 10^(-7) of being confused about probabilities (at least as related to human beliefs).
Like most majoritarian arguments, this throws away information: the relevant reference class is “mainstream beliefs you think are that improbable”. (edit: no, I didn’t read the whole sentence) In that class, it’s not obvious to me that one would certainly be wrong more than once, if one could come up with 10^20 independent mainstream propositions that unlikely and seriously consider them all while never going completely insane. Going completely insane in the time required to consider one proposition seems far more likely than 10^-20, but also seems to cancel out of any decision, so it makes sense to implicitly condition everything on basic sanity.
(Related: Horrible LHC Inconsistency)
(9), and (10) for some definitions of “Christianity”, being more likely than (8) seems conceivable due to interventionist simulators (something I really have no idea how to reason about), but not for any other object-level reason I can think of. Can you think of others?
I’d be inclined to accuse anyone going above… something below 10^-7… of being far too modest.
No, that is the reference class intended and described (“apparently overwhelming evidence”).
Your prior is wrong (that is, it does not reflect the information that is freely available to you).
Considering normal levels of sanity are sufficient. Failing to account for the known weaknesses in your reasoning is a failure of rationality.
I am comfortable accusing you of being confused about probabilities as related to human beliefs.
I’d guess you could estimate (4) to within an order of magnitude or better from an actuarial table.