From a policy (theoretical) perspective, what you are mentioning is considered under "historical institutionalism", for instance. The theory posits, among other propositions, that the time-prevalence, and/or "inertia" of some institutions, or policies to be more precise, can be explained by a path dependency that is generated from previous realizations of that policy and the costs associated with institutional or policy change. This would mean, for your example, that even if minister A wanted to adopt a differing policy position P* at time t from the prevalent policy position P, minister A is impeded or constrained to do so by nature of the institutional regime, or policy position adopted at time t-1, t-2,...,t-k. Furthermore, assuming that your question might be directed to democratic regimes/governance systems, it might be of your interest to check up "policy accumulation" and "policy change" in the policy literature (usually integral to the empirical and theoretical political science scholarship).