Fair Car Pooling

cavedave

I am trying to figure out which way of splitting a shared resource people think is fair. I would like your opinions on what scheme makes sense to you.

Say three people commute to town everyday. Person1 costs 10 a week, Person 2 20 and Person3 30. They live something like below



Person 3 says how about I collect you in the morning and we share the cost of the petrol? What sharing scheme would you go for?

1. Share when you are in the car. The first is to split the cost evenly amongst everyone sharing the car while they share it. So the first person would pay 10/3=3.33. the second would pay this and the 10 extra divided between two people = 5, a total of 8.33. The third would pay this much and the last 10 by themselves. THis is the Shapley value and this solution comes from the airport problem

So sharing scheme would cost 3.33, 8.33, 18.33 each.

2. Divide the Savings. The other way is to divide the savings proportionately amongst the sharers. So the total taken in would be 60. The cost is 30, so 30 is saved. the first person gets 10/60 of this back so they pay 5. The second gets 20/60 so they pay 10. And the third gets 30/60 of the savings back so they pay 15.

In the proportional savings scheme the three pay 5, 10 and 15.

There are other ways of splitting using the Nash bargaining strategy for example. But I think these are too complicated for people to understand.

I have built a calculator here for the sharing scheme. But what I am trying to figure out here is which scheme people actually think is fairer.

Rightwing

cavedave wrote: »

I am trying to figure out which way of splitting a shared resource people think is fair. I would like your opinions on what scheme makes sense to you.

Say three people commute to town everyday. Person1 costs 10 a week, Person 2 20 and Person3 30. They live something like below



Person 3 says how about I collect you in the morning and we share the cost of the petrol? What sharing scheme would you go for?

1. Share when you are in the car. The first is to split the cost evenly amongst everyone sharing the car while they share it. So the first person would pay 10/3=3.33. the second would pay this and the 10 extra divided between two people = 5, a total of 8.33. The third would pay this much and the last 10 by themselves. THis is the Shapley value and this solution comes from the airport problem

So sharing scheme would cost 3.33, 8.33, 18.33 each.

2. Divide the Savings. The other way is to divide the savings proportionately amongst the sharers. So the total taken in would be 60. The cost is 30, so 30 is saved. the first person gets 10/60 of this back so they pay 5. The second gets 20/60 so they pay 10. And the third gets 30/60 of the savings back so they pay 15.

In the proportional savings scheme the three pay 5, 10 and 15.

There are other ways of splitting using the Nash bargaining strategy for example. But I think these are too complicated for people to understand.

I have built a calculator here for the sharing scheme. But what I am trying to figure out here is which scheme people actually think is fairer.

J Nash didn't win the Nobel Laureate for nothing. The above example is perfect for the Nash equilibrium, it eliminates variables such as time spent in the taxi.

cavedave

Rightwing
J Nash didn't win the Nobel Laureate for nothing.

Neither did Llyod Shapley

The above example is perfect for the Nash equilibrium, it eliminates variables such as time spent in the taxi.

In the 10,20,30 case the 30 savings would be split equally using the Nash bargaining strategy giving a cost to each of 0,10,20. I think that for person 1 would be a bit like offering 0.01 in the divide the dollar game. The others should logically accept it but they won't to save face and enforce social norms of cooperation.

Thanks for the reply. It is really interesting to hear other peoples views on this.

Rightwing

cavedave wrote: »

Neither did Llyod Shapley


In the 10,20,30 case the 30 savings would be split equally using the Nash bargaining strategy giving a cost to each of 0,10,20. I think that for person 1 would be a bit like offering 0.01 in the divide the dollar game. The others should logically accept it but they won't to save face and enforce social norms of cooperation.

Thanks for the reply. It is really interesting to hear other peoples views on this.

It's nice to see genuine economic questions/problems posted as opposed to exam questions.