Who decides the "centre" of a city?

[mikecurtis]

This is a popular question round these parts.
Two examples:

Do road signs telling the distance to cities..

I contend that the distances are only rough estimates to some reasonably close portion of the city or town. On the interstate that runs through my community, there are two signs for distance to my town. The first says “Swansea 12.” Drive four miles down the road, and the next one says “Swansea 10.” Neither of them are correct. I also noticed on I95 through Connecticut: “New Haven 55.” Drive 8 miles: “New Haven 50” Those signs were close (about 52 and 44 miles), given the distance from the Elm …

What are highway mileage signs based on?

This came up during a conversation at work. Someone said that the mileage signs on highways are based on the distance to the City Post Office. Living in Dallas, I asked, “Which one? What if the Post Office changed location?” The conversation fell apart at that point with too many what ifs. I thought that the signs referred to the distance to the center of the city, but even that is questionable. How is the city center determined? Houston, for example, sprawls unevenly, in multiple directio…