BUT THEREIN LIES a significant, and usually expensive, conundrum: If the Olympics are coveted, as they clearly are now, getting selected to be the host city requires one-upping your competition by laying down the kind of cash required to put on a grand spectacle. That, of course, means it’s impossible to replicate the “low cost, use what you have and reap the profits” example of L.A. “Chicago can’t bid for the Games and use Dyche Stadium up at Northwestern University and use the existing Soldier Field and United Center,” points out Matheson. “What you have to do to win the Games now is build the Bird’s Nest and the Water Cube.”

Recent history has, by and large, shown how difficult it can be to put on a memorable, spectacular, and profitable Olympics. The Athens Games in 2004, for example, ended up costing more than twice their original budget -- in fact, the security costs ($1.6 billion) were more than the entire tab was for the L.A. Olympics. The CEO of the state-run company charged with running the Greek Olympic facilities after the Games was even quoted as saying, “Financially, the Games were a disaster.” In Lillehammer, Norway, host of the 1994 Winter Olympics, the postevent tourism boom never materialized, and hotels built for the occasion were auctioned off for just a dollar. Already, the budget for the 2012 London Olympics has ballooned to more than twice its original estimate.

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There’s a fairly persuasive argument, however, that it is fl awed, or at least shortsighted, to think that revenue generated from visitors, sponsorships, TV deals, and the like doesn’t cover the cost of building stadiums and hosting the Games. Bruce Kidd, a professor and the dean of the faculty of physical education and health at the University of Toronto, contends that most of the Games over the past two decades have, in fact, made a profit on operations -- their huge deficits come as a result of capital costs. But much of the infrastructure that goes hand in hand with putting on the Olympics, Kidd argues, actually provides long-term economic and cultural benefits to the host city. He even points to the much-maligned Montreal Games, which took decades to pay off, as being beneficial to Montreal. “The Olympics can accelerate long-planned infrastructure developments. The Montreal Olympics accelerated the extension of mass transport, their metro system,” he says. “The need to have a facility to get people to the Olympic park accelerated a project that would have come about eventually but would have taken another 10 years.”

Mackay says he witnessed a similar dynamic in Athens. Before the Games there, he says, the city had a terrible airport and no subway. “You go back now and they have one of the top three airports in Western Europe; they have a fast highway you can take from the airport and a state-of-the-art metro system. None of that would have happened without the Olympics,” he says. Mackay says London is doing much of the same by focusing a good deal of its Olympics-based infrastructure development in East London, an area of the city that has largely been ignored since World War II.

There will obviously be a lot of disappointed folks once the big announcement is made in Copenhagen. But among fans and visitors, there will clearly be no losers: All four bidders are magnificent global cities, places so rich in culture and history that they warrant a visit or two or three, even if they don’t manage to land the Games. Here’s a brief look at the 2016 contenders, why they think they deserve to host the Olympics, and a few reasons why people will continue to love and visit each of them, win or lose.