I agree that the betting approach is better at clarification, but the problem is that it’s often too much better. For example, if I say, I’ll bet $10 at 80% odds that the weather tomorrow will be sunny, the discussion rapidly devolves into the definitional question of what is a sunny day, exactly? Do I win if I see the sun at any point in the day? Is there a certain amount of cloud cover at which point the day no longer counts as sunny? Where is the cloud cover measured from? If the sky starts out with < 5% clouds, clouds over to > 50%, but then the clouds clear later in the day, does the day still count as “sunny”? Etc.
Sometimes I want to make a certain probability judgement about an outcome defined by a colloquially understood category (such as “sunny day”) without having to precisely specify all of my definitions exactly.
Well, I’m not sure how you can have both well-defined propositional probabilities AND undefined, “colloquial” inexact meanings.
if I say, I’ll bet $10 at 80% odds that the weather tomorrow will be sunny, the discussion rapidly devolves into the definitional question of what is a sunny day, exactly?
I think I’d use the word “progresses” rather than “devolves”. This is necessary to clarify what you actually assign 80% chance to happening.
Sometimes I want to make a certain probability judgement about an outcome defined by a colloquially understood category (such as “sunny day”) without having to precisely specify all of my definitions exactly.
You can absolutely do so, but you need to recognize that the uncertainty makes your prediction a lot less valuable to others. “80% chance that it might conceivably be considered sunny” is just less precise than “80% chance that the weather app at noon will report sunny”.
If someone disagrees, and you care about it, you’ll need to define what you’re disagreeing on. If nobody cares, then hand-waving is fine.
If someone disagrees, and you care about it, you’ll need to define what you’re disagreeing on. If nobody cares, then hand-waving is fine.
That’s what I’ve also thought was the norm this whole time without being consciously aware of it. So I appreciate it being spelled out, but I’m now surprised that the opposite norm could even be taken seriously.
(Though perhaps its more of a pretend-to-care about each other’s vague probability numbers to signal desirable things dynamic and not literally believing in them as reliable estimates.)
I agree that the betting approach is better at clarification, but the problem is that it’s often too much better. For example, if I say, I’ll bet $10 at 80% odds that the weather tomorrow will be sunny, the discussion rapidly devolves into the definitional question of what is a sunny day, exactly? Do I win if I see the sun at any point in the day? Is there a certain amount of cloud cover at which point the day no longer counts as sunny? Where is the cloud cover measured from? If the sky starts out with < 5% clouds, clouds over to > 50%, but then the clouds clear later in the day, does the day still count as “sunny”? Etc.
Sometimes I want to make a certain probability judgement about an outcome defined by a colloquially understood category (such as “sunny day”) without having to precisely specify all of my definitions exactly.
Well, I’m not sure how you can have both well-defined propositional probabilities AND undefined, “colloquial” inexact meanings.
I think I’d use the word “progresses” rather than “devolves”. This is necessary to clarify what you actually assign 80% chance to happening.
You can absolutely do so, but you need to recognize that the uncertainty makes your prediction a lot less valuable to others. “80% chance that it might conceivably be considered sunny” is just less precise than “80% chance that the weather app at noon will report sunny”.
If someone disagrees, and you care about it, you’ll need to define what you’re disagreeing on. If nobody cares, then hand-waving is fine.
That’s what I’ve also thought was the norm this whole time without being consciously aware of it. So I appreciate it being spelled out, but I’m now surprised that the opposite norm could even be taken seriously.
(Though perhaps its more of a pretend-to-care about each other’s vague probability numbers to signal desirable things dynamic and not literally believing in them as reliable estimates.)
For sunny days you can just get a reliable reporter to tell you whether its sunny.