You have an X/Y problem. You can't solve your problem without addressing the underlying political issues. No methodology or portfolio-management practice will help until you address the real problem head-on.
The Y in Your X/Y Problem
In your case, Y is the tool you're hoping will help your group prioritize in the face of absentee management and lack of authority. If solving for Y, you just need to apply any methodology that builds consensus among the stakeholders. You won't get 100% agreement from any committee; just look for sufficient buy-in instead.
One possible tool to create consensus is Theme Scoring. Here is the description:
Theme scoring is a prioritization technique that can be used to prioritize themes (groups of user stories) and epics (large user stories) against one another. It can also be used to prioritize projects or products against one another.
You can also download a short document about prioritizing the Product Backlog, along with some sample templates, directly from Mike Cohn's web site. He covers prioritization options quite well.
Regardless of what technique you use, your goal should be to get the stakeholders to agree on the criteria against which each project will be assessed. If your stakeholders can't agree on the metrics for determining what a successful project looks like, there's no point in looking further into the details of individual projects.
Common criteria often include:
- Capital outlay or projected budget for each project.
- Expected return on investment for each project, in total dollars or as a percentage of the project budget.
- Marketing or strategic considerations.
- Regulatory compliance requirements.
The specific criteria don't really matter from a project management point of view. However, there must be stakeholder consensus; the criteria must matter to each stakeholder personally, as well as to the business at large. Once acceptable criteria have been established, then you can apply your chosen portfolio-selection methodology using the agreed-upon criteria.
With consensus on the criteria, the methodology becomes useful politically. By turning opinions on what matters most into measurable comparisons, you create opportunities for consensus and buy-in that (not coincidentally) also lead to self-evident priorities for each project.
The X in Your X/Y Problem
You suffer from absentee management and lack authority. So, it seems, do the rest of the stakeholders. You say:
- [As the project manager] I will not have any say as to priority.
- [The CFO] has high influence but low engagement.
- The two mid managers...are opposed to setting priorities.
- My two bosses...[are] junior members. In fact one of them reports directly to the two mid managers on the team.
In a nutshell, no one with any authority has the desire to set priorities. Let that sink in for a minute. Assuming that the mid-managers have the authority to make prioritization decisions in the first place--that actually hasn't been established here--you state that they are actively opposed to setting priorities anyway. So, unless your managers are politically savvy enough to be able to manage upwards, you are in an untenable position.
You have no authority. Ultimately, the responsibility for the success or failure of the business lies with the executives. Therefore, your only professional responsibility is to make the costs of indecision visible to the management team, and to use your influence (if any) to suggest a constructive course of action that would mitigate those costs.
If you are able to use your influence to build consensus around some strategic value statements and portfolio-selection criteria, by all means do so. You can then follow-up with a metrics-based, politically-neutral approach to evaluating projects for the portfolio.
Just Say "No" to Accountability Without Authority
Projects require an executive sponsor or project champion for a reason, and your current situation exemplifies the need. If managers and executives with authority do not support the initiative, and you have done your best to provide recommendations on how to move forward, that's the end of your professional responsibility. You are not accountable for business decisions made higher up in the organization, and if you're then held accountable anyway, as a professional you must let the organization face the consequences of its own (in)action.
Sometimes the remaining choices are unpalatable. It may require rejecting the role of facilitator for a broken process and moving on to a different role within the company, or dusting off your resume and looking for a better opportunity.
Accountability without authority is not sustainable, and sometimes a project manager's influence just isn't enough. In the final analysis, once you've done your professional best you must simply decide whether to fish or cut bait.