Abstract: We now assume that the manna consists of perfect substitutes goods, so that preferences are represented by additive utilities. Such preferences are realistic when we divide the manna into truly "unrelated" goods such as a computer, a bicycle and a portrait in the family heirlooms, where the pair of matching chandeliers must be counted as one item. The practicality of eliciting additive utilities is illustrated by the success of SPLIDDIT (www.spliddit.org/) designed by Goldman & Procaccia (2014), a user-friendly platform where users report additive utilities by dividing 1000 points over the items.
In the additive domain, the prominent division rule is the Competitive one, obtained by endowing all agents with an equal virtuel budget, and finding the unique price at which competitive demands clear the manna. Interestingly, this rule is deeply connected to a well known solution of the general bargaining problem.
For details on the two problems see Lecture 2 in this file

References
Caragiannis I, Kurokawa D, Moulin H, Procaccia AD, Shah N,Wang J.2016. The Unreasonable Fairness of Maximum Nash Welfare, Proceedings of the 2016 ACM Conference on Economics and Computation, EC .16, 305.22
Chipman JS.1974.Homothetic preferences and aggregation, J. Econ. Theory, 8, 26-38
Cole R, Gkatzelis V.2015. Approximating the Nash Social Welfare with Indivisible Items, Proceedings of the 47th Annual ACM Symposium on Theory of Computing (STOC), 371.80
Cole R, Devanur NR, Gkatzelis V, Jain K, Mai T, Vazirani VV, Yazdanbod S. 2016. Convex Program Duality, Fisher Markets, and Nash Social Welfare, Proceedings of the 2017 ACM Conference on Economics and Computation
Goldman J, Procaccia AD.2014. Spliddit: Unleashing Fair Division Algo- rithms, SIGecom Exchanges, 13(2), 41.6
Kurokawa D, Procaccia AD, Shah N.2015. Leximin Allocations in the Real World, Proceedings of the Sixteenth ACM Conference on Economics and Com- putation EC.15 , 345-362, Portland, Oregon, USA, June 15 - 19, 2015
Kurokawa D, Procaccia AD, Wang J.2016. When can the maximin share guarantee be guaranteed?, Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI),523-9