From CNN:
Sprinters Allyson Felix and Jeneba Tarmoh threw their bodies across the finish line so evenly matched that cameras recording 3,000 frames a second couldn’t tell who beat whom.
Both runners recorded precisely the same finishing time, down to thousandths of a second: 11.068 seconds.
Two women beat Felix and Tarmoh: Carmelita Jeter and Tianna Madison. Their first and second place finishes on Saturday give them the chance to represent the United States at the Olympics in London this summer.
But the photo finish leaves USA Track & Field with a dilemma: Who gets the third slot?
There appears to be no precedent for a dead heat at U.S. Olympic Team track and field trials, prompting the U.S. Olympic Committee to announce new rules Sunday.
One of the runners can give up her claim to a spot on the Olympic team.
If neither one takes that unlikely option, they’ll be asked if they want to run a tie-breaking race or flip a coin.
If they choose the same option, the committee will respect their wishes.
If they disagree, they’ll have to race for it.
And if both athletes refuse to declare a preference, officials will flip a coin — a U.S. quarter to be exact.
They certainly have given it some thought but they may want to consult the previous literature as it seems they might be slightly off track:
Leaving nothing to chance, other than the flip itself, the rules also detail who gets to pick heads or tails and how the coin should be flipped.
“The USATF representative shall bend his or her index finger at a 90-degree angle to his or her thumb, allowing the coin to rest on his or her thumb,” the rules say.
Cheap Talk 
3 comments
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June 25, 2012 at 10:14 pm
Mild Speculation
A related question: is there a threshold for competitiveness after which the U.S.A. or any given country is disadvantaged? That is, can 4 athletes competing for 3 spots be worse than 3? Athletes who are clear favorites can plan their training so that they peak at the Olympics, but in events where there are no clear favorites, athletes must peak for the Olympic Trials, which is suboptimal for Olympic performance (the degree to which is it is suboptimal depends on the sport).
How could an athlete’s skill be modeled by a few parameters, and how might one express preferences over menus of athletes? Can these preferences be represented by a utility function?
June 26, 2012 at 5:08 am
Anonymous
I do not see how it relates to King Solomon’s dilemma. Do the runners know something that the judge(s) do not know?
June 26, 2012 at 7:01 am
Daniel
I believe runners know whether their time was better or worse than their expected performance. If AF thinks she is worth 11 flat and Jeneba thinks she is worth 11.1, then Jeneba would go for Coin-toss while AF would go for run-off. Since the USATF has commitment, that is incentive compatible, but the USATF is not using that information (they should send AF to the Olympics in that case). What is not the case is that it is common knowledge among them who is better (which is the case in the Solomon’s Dilemma). I guess that they only know whether their time was above or below their expected performance and their expectation over their rival’s performance is exactly their time.