Economist Michael Davis has some interesting thoughts on the recent Olympic vote (my thoughts on the vote here). He demonstrates that with some fairly general assumptions about voters’ preferences that Chicago may have been barely defeated. In fact, just making it to the second round might have been able to propel it to victory in a head-to-head contest with Rio.
The key to all of the above possibilities is that they are consistent with the revealed preferences of the voters (with the exception of the three voters whose votes are changed from Tokyo to Chicago). It is also consistent with the geographical solidarity that the voters seem to exhibit.
The scenarios where Chicago ultimately succeeds are probably not the most likely, as there seems to have been a lot of sentimental support for Rio. Scenario 4 seems the most likely to me, but a variation of scenario where Chicago barely beats Rio in the final round certainly seem plausible to me.
The problems with voting and cycling of outcomes in democracy have been studied for some time by economists. If you are interested in some of the analysis, I suggest starting with the work of Kenneth Arrow and Duncan Black.