Prioritization (It really is just a numbered list)
I'm not sure how we got to the state that we need direction on how to number our priorities, but here we are. There really can only be ONE number 1 priority. What is the context for this discussion? How does this apply to Software Delivery? Simple, the People making the software need to know what is the highest priority thing so that we can maintain a deadline for delivery. Confusion on the priorities can make deciding when to delay work difficult.
You may say, "We have more than one team so we can have more than One number 1". I politely call B.S. Every company, the complete set of people, need to have a priority list to work off of. Yes, each team may have their highest priority item in the backlog, but that does not mean it is higher than the company's number 1. This will be better with some examples.
Ok, I have created a prioritized list of items. Let's say you have 2 teams, Team A and Team B. Team A takes number 1 and Team B takes number 2. Everything is going as planned. But, we find out that it will add extra time for the expedite feature to include the new language pack, German. What do we do? Should we delay our highest priority item for our second most priority? If we do, then I believe have decided that number 1 was really number 2. When we make the priority decisions, we have to always ask ourselves "If I could only deliver one, which one would I deliver?".
It doesn't matter how many projects or teams you have, just have an ordered list of items. Make sure everyone is committed to the order. Try to keep the numbers consistent long enough to deliver something. If you find that these items are taking so long that priorities change, then I suggest you figure out how to do incremental delivery. You can take the time to break things down and set scope smaller to allow for more fluidity with priorities. The changing of priorities, scope, etc. is one of the main drivers of moving towards scrum. Scrum gives you a timebox such as 2 weeks as a minimum time that the priorities should be stable. Just be wary of making progress on a large set of things instead of delivering on your list.