A critical-path component is at risk of delay because two developers are in continuous disagreement. The team cannot resolve this personality-related conflict. What should the project manager do?

The correct answer is to log the issue and escalate to HR. The project manager's role includes facilitating conflict resolution, but when a personality-based conflict directly impacts a critical path component and the team cannot resolve it, it becomes an interpersonal issue requiring specialized intervention. HR is equipped to handle such personnel matters, potentially through mediation, counseling, or other appropriate actions. Logging the issue is always a good practice for tracking and transparency. Delaying the component is a consequence, not a solution. Asking the team to vote on a personality conflict is inappropriate and unlikely to resolve the underlying issue. Letting the developers resolve it themselves has already proven ineffective, as stated in the scenario.