Which model allows representatives to act with autonomy and independence when making decisions?

The model is the politico model.

Explanation:

The three main types of representative models are delegate, trustee, and politico.

The delegate model of representation act only as a mouthpiece for the wishes of their constituency and make decisions only for the actual interest of their constituency.

In trustee model, representatives make their political decisions based on the common good which is not necessarily in line with what their constituency want. Trustee representative could make decisions on behalf of his people; but can forego their (constituency's) interest to favor national interest.

In politico model, legislators follow their own judgment until the public come calling about a particular matter. They are autonomous and independent of any constituency influence in making decisions.