Ann likes oranges and dislikes apples; Bob likes apples and dislikes oranges. Tomorrow they will receive one fruit that will be an orange or an apple with equal probability 0.5. Giving to each half of that fruit is fair for each realisation of the fruit ; but agreeing that whatever fruit appears will go to the agent who likes it more gives a higher expected utility to each agent and is fair in the average sense: in expectation, each agent prefers his allocation to the equal division of the object, he gets a Fair Share . We turn this familiar observation into an economic design problem: upon drawing a random object (the fruit), we learn the realised utility of each agent and can compare it to the mean of his distribution of utilities; no other statistical information about the distribution is available. We fully characterize the division rules that use only this sparse information in the most efficient possible way, while giving everyone a Fair Share . Although the probability distribution of individual utilities is arbitrary and mostly unknown to the designer , these rules perform in the same range as the best fair rule having full knowledge of this distribution.
Ann likes oranges much more than apples; Bob likes apples much more than oranges. Tomorrow they will receive one fruit that will be an orange or an apple with equal probability . Giving one half to each agent is fair for each realization of the fruit . However, agreeing that whatever fruit appears will go to the agent who likes it more gives a higher expected utility to each agent and is fair in the average sense: in expectation, each agent prefers his allocation to the equal division of the fruit, i.e., he gets a fair share . We turn this familiar observation into an economic design problem: upon drawing a random object (the fruit), we learn the realized utility of each agent and can compare it to the mean of his distribution of utilities; no other statistical information about the distribution is available. We fully characterize the division rules using only this sparse information in the most efficient possible way, while giving everyone a fair share . Although the probability distribution of individual utilities is arbitrary and mostly unknown to the manager , these rules perform in the same range as the best rule when the manager has full access to this distribution.
R
and dislikes
much more than
R
and dislikes
much more than
R
0.5. Giving to each half of that fruit
. Giving one half to each agent
R
realisation
realization
R
; but
. However,
R
object,
fruit, i.e.,
R
Fair Share
fair share
R
realised
realized
R
that use
using
R
Fair Share
fair share
R
designer
manager
R
fair rule having full knowledge of
rule when the manager has full access to