This paper studies the properties of some well-known scoring rules (linear scoring, highest bid - lowest bid scoring, and lowest bid scoring), which are applied in public procurement and public-private partnership scoring auctions to award contracts under conditions of low tender competition due to corruption and weak regulatory impact assessment. The proposed modifications to the agency model define a new approach to regulatory impact assessment. In the case of two bidders, the restrictions on criteria number and scoring weights are identified. The paper discusses several reasons to consider the quality of scoring rule as a critical success factor at procurement stage of public-private partnership projects as well for public procurement itself.