A system and method for fair dynamic priority conflict resolution in a multi-processor computer system having shared resources wherein each multi-processor seeking access to said shared resource possesses a common priority level. In the occurrence of a priority tie or when a single port is active, a typical dynamic conflict resolution scheme is altered to ensure fair resolution of the conflict or tie. Upon determination that a priority conflict tie exists, one of the processor elements is selected based on a predetermined priority level. The identity of the selected processor element and the configuration of the conflict priority tie is stored. Upon a subsequent conflict priority tie having the same configuration as a previous priority conflict tie, the processor elements selected in previous ties are prevented from being selected in subsequent priority conflict ties until all of the processor elements in a particular priority tie configuration have been selected. In situations involving a single active port, established dynamic conflict resolution schemes are modified to provide fair access and reduce priority tie conflicts.