Now that I’ve think about it more, even if we have the symmetric assumption (each person gets the same share), the pie share is not necessarily 1/n in that the utility of each person is different given a certain amount of pie.
for person 1 is not hungry at all, the pie is worth nothing to her and if she were to get 1⁄3 of the pie, she would not really even enjoy the consumption of it. Thus if person 1 were to get a tiny slice of pie, it could also be consider fair if we look at the symmetry in terms of utility instead of object. Well to achieve this, we can use a bidding system in which people bid for each infinitesimal part of the pie.
Either way, I believe that the argument that “each person gets 1/n of the pie is fair” is not sound because the worth of the pie is different for each person.
Now that I’ve think about it more, even if we have the symmetric assumption (each person gets the same share), the pie share is not necessarily 1/n in that the utility of each person is different given a certain amount of pie.
for person 1 is not hungry at all, the pie is worth nothing to her and if she were to get 1⁄3 of the pie, she would not really even enjoy the consumption of it. Thus if person 1 were to get a tiny slice of pie, it could also be consider fair if we look at the symmetry in terms of utility instead of object. Well to achieve this, we can use a bidding system in which people bid for each infinitesimal part of the pie.
Either way, I believe that the argument that “each person gets 1/n of the pie is fair” is not sound because the worth of the pie is different for each person.