Could Chicago have been close to winning its Olympic bid?

Was Chicago actually fairly close to winning the vote for the 2016 Olympics? Given the discussion of Chicago finishing 4^th, only getting 18 of 94 votes, and being eliminated right off the bat, this would be very much in conflict to conventional wisdom. However, my intention in this post is to show that it is possible that Chicago could have come close to winning or even have won the final vote with just a few more votes in the first round of voting.

To look at whether Chicago may have been close to winning, first we need to look at the voting results:

City	Round 1 Votes	Round 2	Round 3
Rio	26	46	66
Madrid	28	29	32
Tokyo	22	20
Chicago	18

This implies the following revealed preferences of the voters:

Name	# of Voters	1st Choice	2nd Choice	3rd Choice	4th Choice
Rio	26	R	?	?	?
Chicago	18	C	R	?	?
Madrid	28	M	?	?	?
Tokyo	21	T	C/R	C/R/M	C/M

The Tokyo voters preferred Rio to Madrid, but it is not clear where Chicago fell in their rankings. So if Chicago could have survived the first round, even barely, the preferences of the voters are consistent with a possible comeback victory for Chicago.

The second key to victory under this scenario would have been a few voters who could have switched to Chicago in the first round, especially if they switched from Tokyo. There may be some evidence of that possibility:

Some IOC members theorized that a few voters who liked Chicago actually voted for Tokyo in the first round, figuring the American city would get through easily and not wanting the Japanese capital to be embarrassed.

Now this is all speculative, but it is at least possible. I will present four scenarios based on feasible preferences of voters. In each case I will transfer three votes from Tokyo to Chicago to begin with. I will not include any strategic voting, i.e., each voter votes for their highest remaining choice. I will also assume that all voters' preferences remain the same once the voting changes. Lastly, I will also ignore the fact that the vote totals increased after the first round.

Scenario 1: Chicago, 2^nd Choice City (Chicago Ultimately Wins)

Name	# of Voters	1st Choice	2nd Choice	3rd Choice	4th Choice
Rio	26	R	C	M	T
Chicago	21	C	R	M	T
Madrid	28	M	C	R	T
Tokyo1	15	T	C	R	M
Tokyo2	4	T	R	C	M

The original Tokyo voters are broken into two groups based on whether Chicago or Rio is their second choice. Changing the three voters from Tokyo to Chicago eliminates Tokyo in the first round (19 for Tokyo). In the second round Madrid is eliminated (C: 36, R:30, M:28). Finally Chicago ends up winning in the final round over Rio, 58-36. Chicago would beat any of the other cities head-to-head. In this scenario all that would be needed would be to survive the first round.

Scenario 2: Tokyo to Chicago, Madrid to Rio (Chicago Ultimately Wins)

Name	# of Voters	1st Choice	2nd Choice	3rd Choice	4th Choice
Rio	26	R	C	M	T
Chicago	21	C	R	M	T
Madrid	28	M	R	C	T
Tokyo	19	T	C	R	M

The scenario begins the same as Scenario 1, as Tokyo is eliminated in the first round. Under this scenario however, Rio is eliminated in round 2 (C:40, M:28, R:26) as the Tokyo voters all switch to Chicago. In the final round, Chicago wins handily 66-28 as the Rio voters vote for their second choice, Chicago. The interesting aspect of this scenario is that Rio would have beaten Chicago head-to-head, 54-40. So, Rio wins if Chicago cannot survive the first round. Chicago wins if Rio cannot survive the second round. Rio wins if they both make it to the finals.

Scenario 3: Madrid Wins

Name	# of Voters	1st Choice	2nd Choice	3rd Choice	4th Choice
Rio	26	R	M	C	T
Chicago	21	C	R	M	T
Madrid	28	M	C	R	T
Tokyo	23	T	C	R	M

Tokyo is eliminated in the first round and Rio in the second round. In this case however, the Rio voters prefer Madrid to Chicago and Madrid wins the final vote.

Scenario 4: Conventional Wisdom before Voting (Rio Ultimately Wins)

Name	# of Voters	1st Choice	2nd Choice	3rd Choice	4th Choice
Rio	26	R	C	M	T
Chicago	21	C	R	M	T
Madrid1	18	M	C	R	T
Madrid2	10	M	R	C	T
Tokyo1	9	T	C	R	M
Tokyo2	10	T	R	C	M

As in the previous three scenarios, Tokyo is eliminated first. The second round allows Chicago and Rio to advance to the finals (R:36, C:30, M:28). Finally, Rio wins the final vote, 54-40.

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.