A computer-implemented method comprising: performing, by a first server of a secure multi-party computation "MPC"system in collaboration with one or more second servers of the secure MPC system, a selection process to select a digital component based in part on a selection value for each digital component in the selection process, the performing comprising determining a first secret share of a winner parameter for each digital component in the selection process, wherein the winner parameter indicates whether the respective digital component is the winner of the selection process; determining, for each given digital component in the selection process and in collaboration with the one or more second servers, a highest other selection value that corresponds to a different digital component that is different from the given digital component, the determining, for each given digital component, comprising: determining a first secret share of a highest selection value among the selection values for the digital components in the selection process; determining a first secret share of a second highest selection value among the selection values for the digital components in the selection process; for each given digital component in the selection process, determining a first secret share of the highest other selection value based at least in part on the first secret share of the highest selection value, the first secret share of the second highest selection value, and the first secret share of the winner parameter for the given digital component; and providing (610, 612) the highest other selection value for each given digital component to an owner of the given digital component. performing, by a first server of a secure multi-party computation "MPC"system in collaboration with one or more second servers of the secure MPC system, a selection process to select a digital component based in part on a selection value for each digital component in the selection process, the performing comprising determining a first secret share of a winner parameter for each digital component in the selection process, wherein the winner parameter indicates whether the respective digital component is the winner of the selection process; determining, for each given digital component in the selection process and in collaboration with the one or more second servers, a highest other selection value that corresponds to a different digital component that is different from the given digital component, the determining, for each given digital component, comprising: determining a first secret share of a highest selection value among the selection values for the digital components in the selection process; determining a first secret share of a second highest selection value among the selection values for the digital components in the selection process; for each given digital component in the selection process, determining a first secret share of the highest other selection value based at least in part on the first secret share of the highest selection value, the first secret share of the second highest selection value, and the first secret share of the winner parameter for the given digital component; and determining a first secret share of a highest selection value among the selection values for the digital components in the selection process; determining a first secret share of a second highest selection value among the selection values for the digital components in the selection process; for each given digital component in the selection process, determining a first secret share of the highest other selection value based at least in part on the first secret share of the highest selection value, the first secret share of the second highest selection value, and the first secret share of the winner parameter for the given digital component; and providing (610, 612) the highest other selection value for each given digital component to an owner of the given digital component.