The "proof" of inconsistency is unclear. What we should do is this: If you prefer A over B, and your preferences are given by expected utility, then U(1m) > 0.1 U(5m) + 0.89 U(1m) + 0.01 U(0) Subtract 0.89 U(1m) from both sides: 0.11 U(1m) > 0.1 U(5m) + 0.01 U(0) Now add 0.89 U(0) to both sides: 0.11 U(1m) + 0.89 U(0) > 0.1 U(5m) + 0.9 U(0) The left-hand side is the expected utility of C, the right-hand side of D So if you prefer A over C and you follow exp. utility, you MUST prefer C over D That's the contradiction. So "real" people can't be following expected utility when making their choices.
please fix this: if someone chooses d over c they are presumably maxim izing expected value and if someone chooses a over b they are presumably maximizing expected value
How can you honestly cancel the .89 chance of $1m?? The C/D gamble is based on a 0 bankroll (more utility) and the A/B gamble is based on a 89% likely $1m bankroll (less utility)... unless you're going around polling millionaires.
Thank you sir, I love you. I've spent 4 hours myself but couldn't get it and you did it for me in 11 minutes
The "proof" of inconsistency is unclear. What we should do is this:
If you prefer A over B, and your preferences are given by expected utility, then
U(1m) > 0.1 U(5m) + 0.89 U(1m) + 0.01 U(0)
Subtract 0.89 U(1m) from both sides:
0.11 U(1m) > 0.1 U(5m) + 0.01 U(0)
Now add 0.89 U(0) to both sides:
0.11 U(1m) + 0.89 U(0) > 0.1 U(5m) + 0.9 U(0)
The left-hand side is the expected utility of C, the right-hand side of D
So if you prefer A over C and you follow exp. utility, you MUST prefer C over D
That's the contradiction. So "real" people can't be following expected utility when making their choices.
Why do you choose 0.89 u(1) and 0.89 u(0)? Are we trying to reduce one gamble to the other? Is that the aim?
Thank you for your videos Ronald.
please fix this: if someone chooses d over c they are presumably maxim
izing expected value and if someone chooses a over b they are presumably maximizing expected value
What can be unknown events for gambles with ticket draw of 1 to 100 when applying STP?
How can you honestly cancel the .89 chance of $1m?? The C/D gamble is based on a 0 bankroll (more utility) and the A/B gamble is based on a 89% likely $1m bankroll (less utility)... unless you're going around polling millionaires.
if they pick a over b we can presume they do not do math
Perfect explanation. Really thank you, from Italy. :)
thanks! Very clear explanation.
why can you rearrange it, because you always would get 100% chance of 1million just doesnt make sense