Kalinowski et al[4] show that, when there are two agents with a Borda scoring function, and each ranking is equally probable, the "round robin" sequence (ABABAB...) attains the maximal expected sum-of-utilities.
If agents have complete information on each other's preferences (as is common among parties), it may not be rational for them to choose truthfully; it may be better for them to make sophisticated (strategic) choices.
Thus, the picking sequence induces a sequential game and it is interesting to analyze its subgame-perfect equilibrium.
Brams[5]: 202–206 suggests to use divisor methods, similar to the ones used for apportionment of congress seats among states.
Both methods start in the same way: Picking sequences can be used to find allocations that satisfy a strong fairness and efficiency condition called competitive equilibrium.