It's an interesting question. You also have to consider the properties of the games as well as the number of players, and all kinds of other imponderables. For example in the swimming competitions, it was very clear that a lot of both individual and team strategy was involved in deciding which events to compete in and how hard to try in each event in view of the schedule of events and outcomes so far. Michael Phelps dropped some events he had been scheduled to compete in, in order to be rested for others. In one team of the relay events a completely disjoint set of swimmers were in the final than in the qualifying rounds. Just as in voting systems, I suspect it's not possible to devise systems without paradoxes or undesirable outcomes.