A computer-implemented method comprising: receiving, by a first server of a secure multi-party computation, MPC, system and from a client device, a digital component request; identifying, for each digital component in a set of digital components, a selection value for the digital component and a priority tier for the digital component; for each of a plurality of priority tiers: performing, using a secure MPC process in collaboration with one or more second servers of the secure MPC system, a selection process to select a digital component, the performing comprising: determining, for each digital component in the priority tier, a first secret share of a candidate parameter that indicates whether the digital component is a candidate for selection; and determining a first secret share of the winner parameter for each digital component in the priority tier based on: the first secret share of a value of the candidate parameter for each digital component in the priority tier; one or more second secret shares of the candidate parameter for each digital component in the priority tier; and the selection value for each digital component in the priority tier; identifying a highest tier of the plurality of tiers for which a given digital component has a winner parameter that indicates that the given digital component is a winning digital component for the tier; and providing, to the client device, a first secret share of a selection result identifying the given digital component. receiving, by a first server of a secure multi-party computation, MPC, system and from a client device, a digital component request; identifying, for each digital component in a set of digital components, a selection value for the digital component and a priority tier for the digital component; for each of a plurality of priority tiers: performing, using a secure MPC process in collaboration with one or more second servers of the secure MPC system, a selection process to select a digital component, the performing comprising: determining, for each digital component in the priority tier, a first secret share of a candidate parameter that indicates whether the digital component is a candidate for selection; and determining a first secret share of the winner parameter for each digital component in the priority tier based on: the first secret share of a value of the candidate parameter for each digital component in the priority tier; one or more second secret shares of the candidate parameter for each digital component in the priority tier; and the selection value for each digital component in the priority tier; determining, for each digital component in the priority tier, a first secret share of a candidate parameter that indicates whether the digital component is a candidate for selection; and determining a first secret share of the winner parameter for each digital component in the priority tier based on: the first secret share of a value of the candidate parameter for each digital component in the priority tier; one or more second secret shares of the candidate parameter for each digital component in the priority tier; and the selection value for each digital component in the priority tier; the first secret share of a value of the candidate parameter for each digital component in the priority tier; one or more second secret shares of the candidate parameter for each digital component in the priority tier; and the selection value for each digital component in the priority tier; identifying a highest tier of the plurality of tiers for which a given digital component has a winner parameter that indicates that the given digital component is a winning digital component for the tier; and providing, to the client device, a first secret share of a selection result identifying the given digital component.