6 ms·

Is it extendable to multidimensional preferences or does it require that whatever is being shared is quantizable with a single variable?

• justinpombrio 8y ago
  It requires is that everyone be able to split the line into segments, such that they think it would be fair for them to receive any of their segments, i.e., such that they would rate all segments as equally valuable. This allows people to have different preferences than each other. But I'm not sure what a multidimensional preference is. If your utility for a set of candy is, say, a pair of real numbers (which I presume is the sort of thing you mean by "multidimensional"?), what does it mean for two sets of candy to have equal value? Would both of the real numbers have to be equal? If so, this method isn't going to work: in general you wouldn't be able to split the line into segments of equal value.
  • zwkrt 8y ago
    A classic 'multidimensional' preference is a set of roommates all of whom have to decide both what space they want to take in an apartment and how much they want to pay for that space. https://www.youtube.com/watch?v=7s-YM-kcKME https://www.youtube.com/watch?v=7s-YM-kcKME
  • Misdicorl 8y ago
    Consider splitting a tract of land into four fair farms. That had two dimensions and a naive extension will clearly fail.