Bermuda.
The article doesn’t seem to present any sort of actual design, it just lists off things that would be “cool”. As such, it’s a bit impossible to opine on the practicality of it.
Personal guess would be that there is no design, that the 600 people who signed on are idiots, and that the most that will happen is that they blow a lot of money on 30 separate designs from 10 different companies, be unable to decide on any one design because they don’t believe in social hierarchies nor have any profit motive to drive them through to the end.
I was doing some research on this when I come across “Pneumatic Floating Platform” and these guys were talking about building some floating airport.
Despite their size, wouldn’t these floating cities be legally considered ships? I thought it was an international convention that all ships at sea had to be registered to some sovereign nation as having jurisdiction. A floating city that claimed it’s own sovereignty would be either ignored, have it’s inhabitants be considered stateless refugees, or be declared pirates.
In other words, you’re a nation when other other nations call you a nation.
It depends on how important you are, too. If Sealand is any indication, if you’re a nobody and not interfering with anybody else, no one cares. But if you’re a trading quasi-state like Taiwan, suddenly people start harassing you. I suppose a huge ship would fall somewhere between the two, and whether other nations decide to intervene would probably depend on the ship’s activities and influence. In the Freedom Ship’s case, they said:
So looks like sovereignty isn’t a goal at all.
Though I have to say that it’d be AWESOME if they armed every passenger with RPGs or whatnot and had them defend themselves against pirates and enemy states. Imagine a broadside volley from a ship that size 
I haven’t seen anywhere how these “platforms” would be powered. I would assume nuclear, but wouldn’t that be expensive? And difficult?
Why? Are we out of land? Plenty of land out in the Midwest or Siberia.
It’s not so much that there is a shortage of land. It’s that there is a shortage of usable land where people need or want to be. IOW, building a man-made island in the middle of the ocean or giant roving ship is useless as anything but a giant resort for rich folk. In an urban area, however, it would be a similar concept to building on landfill or piers.
Ding ding! We have a winner! Now imagine being (relatively) out of the long arm of the law most of the year, potentially having your own security force, little unwanted scrutiny from the local onboard government, questionable taxable status (for non-US citizens), mysterious under-reported man-overboard incidents… plus you get to travel the world all the friggin’ time!
Not to mention (literally) off-shore accounts. You could set the place up as the double-secret banking capital of the world.
Dramamine! 
But not, as I said, in Japan. Or in some other countries. Somehow I don’t think that a Japanese proposal to annex a chunk of the Midwest and put it under Japanese law would go over well.
Japan trying to get more land? Pfft. They’d never do that!
The CNN article wouldn’t load for me, but it seems the most likely configurations for a ‘floating city’ would be derived from large oilfield structures and thus would consist of either a ship-shaped hull along the lines of a Floating Production, Storage and Offloading facility (FPSO), such as the Cossack Pioneer, off Australia, or a semisubmersible production platform, such as BP’s Thunder Horse Production, Drilling and Quarters (PDQ) in the Gulf of Mexico.
FPSOs tend to be used in regions where waters are more or less calm at all times. Semisubs are intended for more variable sea states; they are more stable in large seas because, like an iceberg, much of the vessel’s mass is below the water line. The tradeoff is additional complexity, as semis need a ballast control system to ride the swells evenly, and slower transit times when moving from one location to another, due to the vessel shape. Although most semis are used for drilling and/or production, there are a few used as pure accomodation units, or so-called ‘floatels’.
In either case, if the water depth were less than about, say, 3000 feet, the structures would normally be moored via anchors and lines more or less permanantly; if the water were deeper, either type of vessel would require a dynamic positioning system with hull-mounted directional thrusters to maintain station. If it were desired to move to another location, the thrusters could be used as a propulsion system, although generally when this is done, tow vessels are used as well.
Either type would be best operated where the chances of a violent storms are low. Although semis in particular are usually designed for fairly large waves and high wind loads on the structure, it would be foolhardy indeed for our hypothetical seagoing poulation to try to ride out a hurricane aboard one, especially a Cat 3 or higher. In oilfield operations, semis usually are evacuated completely or moved out of the way of hurricanes, while FPSOs simply aren’t used in hurricane zones due their length and the way they are moored.
Typical practical lifespan of one of these structures is a mere 15-30 years, although chances are this could be stretched due to the lack of loads from drilling and production equipment, or the need for as much oil tankage. Like any vessel, however, they would have to somehow put for refitting and structural repairs every few years.
I’ll leave the working out of how many people could be accomodated, and the logistics of food qnd fuel supply, for someone else. Cheers.
Missed the edit window…
A floating building anchored in Tokyo bay makes some sort of sense, because real estate in the city of Tokyo is the most expensive in the world. A floating building or city-ship in the middle of the pacific ocean doesn’t make any sense, because there are plenty of random uninhabited places all over the world.
About floating houses: yesterday evening, BBC World News, Earth Report showed a report about the Netherlands dealing with rising water (both sealevel and more frequent floods). The Youtube is here. They recounted how the Netherlands, after the tragic flood of 1953 that killed about 2 000 people, spent decades and money on building incredible strong seawalls, but are now rethinking their whole concept of building higher and higher dykes and sewalls to keep the water out to instead accepting that the water will come and how to go along with it, e.g. giving up parts of farmland to serve as reserve area when the River Maas floods.
They also talked with a Dutch architect and his floating homes. (the youtube won’t load for me, so I can’t tell you the time stamp when he appears - it was at least a third of the way through). They have been built for several years now, and interestingly enough, the problem is not designing them, but finding a place to put them. Of course the architect complains that the bureaucrats are holding things up by not granting permission, while the city officals say that floating homes would be a solution for only a small part of people, and they are thinking of solutions for the large part of population.
That is where they could host the United Nations. Then it would be on neutral “ground”.
Only if they move to international waters - where the sea is rougher than in a bay.
Would waves really affect such a ship? Looking at the pictures linked to in this thread, I’d think it would be many times the size of the largest waves in the ocean, and thus hardly pushed around.
I’m going to interject a bit of reality into the discussion now.
You may recall that ships routinely sank in storms in the past. The main reason that modern ships tend to not sink in storms is simple–weather forecasting and weather satellites.
Modern ships can see storms coming, and they change their track to avoid them.
Major storms occur on the open ocean all the time–I’ve experienced a few. In one case, I was on board a submarine in the North Atlantic. There was a major storm going on, and we could feel the waves, even though we were deeper than 250 feet below the surface. We were supposed to go to periscope depth for communications purposes during the storm. As we ascended to 150 feet, we were doing 15 degree rolls–at which point we called things off and went deep. The sonarmen estimated the sea state for that storm to be 8-9. Sea state 9 consists of “phenomenal” waves greater than 14 meters in height. This was a storm capable of sinking vessels.
Picture the storm depicted in the movie “The Perfect Storm.” Anything floating has to be capable of avoiding such storms.
Obviously, small vessels can be capsized by storms. While large vessels can also be capsized in a large enough storm, there is the additional danger with large vessels (or floating structures), that they can find themselves suspended on the peaks of adjacent waves, with a trough in the middle. The vessel can then collapse into the trough as its keel breaks.
In short, there is no surface vessel that people have ever built that is immune to large enough storms.