In all likelihood your coworker doesn't come to the office looking to pick a fight. Rather, ask yourself a few questions: Do you and your coworker report to the same boss? Are those people communicating a similar message and goals?

In our experience, we find that priority exercises like yours fail when an organization lacks a clear strategy. Different units within a company, institution, or nonprofit develop competing agendas, and individuals and teams within these departments are being held accountable for achieving the goals tied to these agendas.

So instead of continuing this prioritization process in conflict, step back and ask your coworker if you and he-and all the team members you represent-are traveling the same path. Discuss whether or not your organization has a vision that extends beyond the next quarter, and a strategy for achieving its goals. Instead of prioritizing projects, you may be doing everybody a bigger favor by pushing the organization to establish an overarching strategy if there is not one in place currently.

With a clear strategy in place, your organization's members will be able to align their goals and better understand their contributions to a larger purpose. You're not off the hook completely- getting an organization to adopt strategy is one hurdle, not to mention that you still haven't finishing your prioritizing homework. But with a long-term view in place, that assignment will be much easier to finish.