Final answer:
A broad community development program is most effectively supported by a block grant, which provides local governments with greater flexibility and discretion in use, as opposed to categorical grants, unfunded mandates, or cooperative agreements.
Step-by-step explanation:
A broad program for community development would most likely be supported through a block grant. A block grant is a type of funding provided by the federal government with fewer restrictions and gives local governments more discretion on how to use the funds for various projects. If the intention is to offer flexibility and allow local communities to assess their own needs and decide how to allocate resources effectively, block grants are the preferred type of grant.
Categorical grants, on the other hand, are federal transfers formulated to limit recipients' discretion in the use of funds and come with strict administrative criteria. While they are more common and often allow sponsoring elected officials to take credit for positive outcomes, they do not offer the flexibility necessary for broad, community-directed development initiatives.
In contrast, unfunded mandates impose requirements without providing funding, which would not be supportive of development projects that require financial resources. Cooperative agreements involve shared responsibilities and resources, but they are not as open-ended as block grants and are typically project-specific collaborations rather than sources of general funding. Thus, the nature of the program and its need for flexible allocation of funds align most closely with the less restrictive and more broadly purposed block grants.