Ideological divide within the cabinet and public spending

A budget, i.e., spending by category, is prepared by the cabinet of (three key) ministers. The finance minister wants to minimize total spending, while the rest have single-peaked preferences over budgets and each views his own spending as relatively more important. The goal is to understand effects of polarization in spending priorities, - or divergence of the ideal points, - on the budget under two typical budgeting procedures. If the procedure is "fragmented," i.e., the finance minister just passively compiles spending requests, then the divergence of the ideal budgets increases total spending. If the procedure is more centralized, i.e., challenging the initial proposal of the finance minister is costly, and it also requires support of another minister, then polarization may lead to a tighter budget, as it enlarges the set of the unchallenged proposals, provided the ideals of the spending ministers are sufficiently far apart.