Does the following dialogue disprove VNM and show it’s ignoring the value of information?
“Grandma says that next Spring Break she’ll take either me or sis around the world, but to be fair she’ll flip a coin to choose!”
“That sounds pretty awesome. I hope you win. But wait, do you have a passport?”
“No. But I’ll go start the application tomorrow. It’s only like $100. I would hate to miss out on a trip around the world!”
But now, I’m offered D = (50% chance of A, 50% chance of B) or E = (50% chance of A, 50% chance of C). The VNM independence principle says I should prefer D > E. But doing so, it forgets the cost of information/uncertainty. By choosing E, I’m sure I’ll be offered a trip—I don’t know where, but I know I’ll be offered a trip, not a laptop. By choosing D, I’m no idea on the nature of the present. I’ve much less information on my future—and that lack of information has a cost. If I know I’ll be offered a trip, I can already ask for days off at work, I can go buy a backpack, I can start doing the paperwork to get my passport. And if I know I won’t be offered a laptop, I may decide to buy one, maybe not as great as one I would have been offered, but I can still buy one. But if I chose D, I’ve much less information about my future, and I can’t optimize it as much.
I don’t follow this at all. You seem to be drawing some sort of bright line at ‘certainty’ vs uncertainty which seems entirely arbitrary and unjustified.
If you know that a trip is coming up which you may win but which you need to incur costs in advance, then you weigh your chance of winning and the gain from it, against the costs you incur now to make sure you can take advantage of it. If you’re offered multiple possible outcomes, you do the same thing. This is little different from, say, buying multiple kinds of insurance—except you might think of it as positive insurance.
The line isn’t arbitrary—if you’re told “you’ll receive a gift”, you’re given much less information than if you’re told “you’ll receive a trip as a gift”. The same goes here : in option D (a coin is tossed, heads you’re given a trip to Ecuador, tails you’re given a laptop) you are given much less information than in option E (a coin is tossed, heads you’re given a trip to Ecuador, tails you’re given a trip to Iceland). In option E you know you’ll be given a trip—and you can prepare for a trip. In option D, if you prepare for a trip, you’ve 50% chance of the preparation being wasted.
Now take your grandma dialogue. It needs to be added an additional option to see where it contradicts the VNM independence hypothesis: consider grandma could either offer one of us a trip around the world (T), or offer one of us a driving license (L). I value a trip around the world $2000 (in subjective dollars), and a driving license $1850 (in subjective dollars).
To make the trip around the world, as you said, I’ve to spend $100 in paperwork, but there is no such cost for driving lessons. So the total the gain $1900 if I’m offered a trip around the world, and $1850 if offered a driving lesson, just for me. I prefer T over L.
But if we are in the situation of your dialogue, I’m offered (50% chance of T) but I need to make the paperwork and spend the $100 anyway. So in fact, the total value of that offer is $2000/2-$100 = $900. While if I’m offered (50% chance of L) then the total value of that offer is $1850/2 = $925.
So I prefer T over L, but I prefer 50% chance of L to 50% chance of T. Which violates the independence principle.
It needs to be added an additional option to see where it contradicts the VNM independence hypothesis: consider grandma could either offer one of us a trip around the world (T), or offer one of us a driving license (L). I value a trip around the world $2000 (in subjective dollars), and a driving license $1850 (in subjective dollars). To make the trip around the world, as you said, I’ve to spend $100 in paperwork, but there is no such cost for driving lessons. So the total the gain $1900 if I’m offered a trip around the world, and $1850 if offered a driving lesson, just for me. I prefer T over L. But if we are in the situation of your dialogue, I’m offered (50% chance of T) but I need to make the paperwork and spend the $100 anyway. So in fact, the total value of that offer is $2000/2-$100 = $900. While if I’m offered (50% chance of L) then the total value of that offer is $1850/2 = $925. So I prefer T over L, but I prefer 50% chance of L to 50% chance of T. Which violates the independence principle.
Yeah, I’m going to go with benelliott on this one. You’re inputting the wrong stuff which hasn’t been split up right, and complaining that it doesn’t seem to work.
Does the following dialogue disprove VNM and show it’s ignoring the value of information?
“Grandma says that next Spring Break she’ll take either me or sis around the world, but to be fair she’ll flip a coin to choose!”
“That sounds pretty awesome. I hope you win. But wait, do you have a passport?”
“No. But I’ll go start the application tomorrow. It’s only like $100. I would hate to miss out on a trip around the world!”
I don’t follow this at all. You seem to be drawing some sort of bright line at ‘certainty’ vs uncertainty which seems entirely arbitrary and unjustified.
If you know that a trip is coming up which you may win but which you need to incur costs in advance, then you weigh your chance of winning and the gain from it, against the costs you incur now to make sure you can take advantage of it. If you’re offered multiple possible outcomes, you do the same thing. This is little different from, say, buying multiple kinds of insurance—except you might think of it as positive insurance.
The line isn’t arbitrary—if you’re told “you’ll receive a gift”, you’re given much less information than if you’re told “you’ll receive a trip as a gift”. The same goes here : in option D (a coin is tossed, heads you’re given a trip to Ecuador, tails you’re given a laptop) you are given much less information than in option E (a coin is tossed, heads you’re given a trip to Ecuador, tails you’re given a trip to Iceland). In option E you know you’ll be given a trip—and you can prepare for a trip. In option D, if you prepare for a trip, you’ve 50% chance of the preparation being wasted.
Now take your grandma dialogue. It needs to be added an additional option to see where it contradicts the VNM independence hypothesis: consider grandma could either offer one of us a trip around the world (T), or offer one of us a driving license (L). I value a trip around the world $2000 (in subjective dollars), and a driving license $1850 (in subjective dollars).
To make the trip around the world, as you said, I’ve to spend $100 in paperwork, but there is no such cost for driving lessons. So the total the gain $1900 if I’m offered a trip around the world, and $1850 if offered a driving lesson, just for me. I prefer T over L.
But if we are in the situation of your dialogue, I’m offered (50% chance of T) but I need to make the paperwork and spend the $100 anyway. So in fact, the total value of that offer is $2000/2-$100 = $900. While if I’m offered (50% chance of L) then the total value of that offer is $1850/2 = $925.
So I prefer T over L, but I prefer 50% chance of L to 50% chance of T. Which violates the independence principle.
Yeah, I’m going to go with benelliott on this one. You’re inputting the wrong stuff which hasn’t been split up right, and complaining that it doesn’t seem to work.