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.
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.