decision Analysis You have won a prize You get a free lotter

You have won a prize! You get a free lottery ticket to one of the following lotteries. 1/10 chance of winning: A 5 year lease on a Porsche, plus a trip to Disney w world three days plus $1000. 1/12 chance of winning: A 3 year lease on an Audi, plus a trip to Fiji for 1 month, plus $10000. 1/15 chance of winning: A one year lease on a used car, plus a trip to Europe for a week, plus $ 100000. You cannot turn in your free ticket for cash and none of the prizes can be cashed out, sold or transferred. Assuming you prefer more money to less, Porsche over Audi and Audi over used car, and prefer Fiji to Europe and Europe to Disney, elicit your utility function and determine which lottery ticket you would prefer.

Solution

Preference - Porsche over Audi over used car

Fiji to Europe over Disney

Probability of winning a 5 year lease on a Porsche plus a trip to Disney + $1000= 1/10

Probability of winning a 3 year lease on a Audi plus a trip to Fiji + $10,000 = 1/12

Probability of winning a 1 year lease on a Used car plus a trip to Europe + $1,00,000 = 1/15

Let utility of places be defined in the following order 0.5x , 0.3x and 0.2x in order of preference

So, for the first option - Porsche - 1st preference , Disney - 3rd preference and $1,000 - 3rd preference

1/10 * (0.5*x + 0.2x + 0.2x) = 0.09x

Second option -  Audi - 2nd preference , Fiji - 1st preference and $10,000 - 2nd preference

1/12 * (0.3*x + 0.5x + 0.3x) = 0.092x

Third option -  USed car - 3rd preference , Europe - 2nd preference and $100,000 - 1st preference

1/15 * (0.2*x + 0.3x + 0.5x) = 0.006x

Hence go with the second option