What is a Strong Mayor?

Houston has one, but few other cities do.

- Wikipedia: Mayor–council government.

A mayor–council government is a system of local government in which a mayor who is directly elected by the voters acts as chief executive, while a separately elected city council constitutes the legislative body. It is one of the two most common forms of local government in the United States, and is the form most frequently adopted in large cities, although the other common form, council–manager government, is the local government form of more municipalities.

The form may be categorized into two main variations depending on the relative power of the mayor compared to the council. In a typical strong-mayor system, the elected mayor is granted almost total administrative authority with the power to appoint and dismiss department heads. In such a system, the mayor's administrative staff prepares the city budget, although that budget usually must be approved by the council.

- Ballotpedia: Mayor-Council Government. 

Mayor-council government is one of the five major types of municipal government found in cities and towns throughout the United States. The other four are council-manager, commission, town meeting, and representative town meeting.

Mayor-council governments generally feature an elected executive officer called a mayor and an elected legislative body that is most often known as the city council. Depending on a city’s history or its relationship with the surrounding county, however, the legislative body might go by another name such as an urban-county council, a common council, a board of supervisors or a metro council. Similarly, the number of city council members varies widely. The Madison Common Council, for example, consists of 20 members, while the New York City City Council consists of 51 members.

In a mayor-council government, the mayor and city council work together to balance and pass a budget, draft and enforce legislation, and oversee city departments and appoint departmental heads. The dynamics of how the mayor and city council work together depend on the type of mayor-council government that a city uses.

For more:

- New Houston City Council powers are shifting the dynamic of the city's 'strong mayor' system.

- COUNCIL-MANAGER OR “STRONG MAYOR”

- The Houston mayor is a ‘strong mayor’ who will soon face a new limitation.

- How much power does Houston’s mayor have at City Hall? Maybe more than you think.