A Public Incubator is similar to a Business Incubator

Business incubator

Business incubators are programs designed to accelerate the successful development of entrepreneurial companies through an array of business support resources and services, developed and orchestrated by incubator management and offered both in the incubator and through its network of contacts...

, though it's intent is to accelerate the development of ideas for the benefit of the public good. Many Universities and non-profit organization succeed in a goal of public good, though few if any provide a democratic process of refinement. A Public Incubator incorporates a process of citizenry, measurement, and refinement to culture community ideas.