First, let's look at the wrong approach - the direct cascade. Key results at "higher up the hierarchy" should become Objectives for the teams below. This approach violates the basic tenet of OKRs: Objectives are qualitative, and Key Results are quantitative. It cannot be both!
It is also not thought-provoking and deepens the hierarchy in the organization.
The cascade paradigm is a holdover from the Command and Control philosophy, in which decisions flow downward. In the OKR setting, this creates an enormous time sink.
OKRs can be linked both horizontally and vertically (strategic). The latter is less complicated but still challenging.
We encourage managers and their teams to have thoughtful conversations to ensure that the OKRs chosen align with the organization's goals.
OKRs should be established through a bottom-up and top-down process in which teams identify OKRs aligned with the organization's objectives and validated by management.
The company's OKRs can provide teams with direction and help them understand how they can contribute to achieving those OKRs.
It is okay if teams create some guild-flavored goals, but they must not in any shape or form support or even widen the gaps between organizational units. As used above, the word "team" means "people from the same department".
Agile Tools product goes a long way to break bad habits and offer better, more progressive approaches. Teams are a separate concept as organizational units with employees. Cross-functional teams are much less likely to produce siloed goals.
But, even if you choose the classic approach and create OKRs for a department, there is a mechanic to connect (horizontally) with another department by having two Key Result caretakers, each from a different org unit.
The alignment techniques vary greatly based on culture, OKR "maturity", organization size, product or project-oriented mindset, and many other factors.
A rule of thumb suggests that more than half of the OKRs should be drafted bottom-up, with managers focusing on the Objective and team members on the Key Results. This is only possible if the foundation is sound, well-defined, and properly communicated. That means a Mission and Vision are there, Values are known, and top OKRs are published.
Make a "dry run" with a pilot group to get some experience and make adjustments to "aligning rules" before you go all-in.