Least-occurrence order on cardinal properties (${<}_1$)

For cardinal properties $\Phi$ and $\Psi$ that occur, let ${\iota }_{\Phi }$ and ${\iota }_{\Psi }$ be their least witnesses. Define $\Phi {<}_1\Psi$ whenThis relation need not be transitive, because the two implications can be proved under different joint existence assumptions.

Let $I,W,M$ mean inaccessible, weakly compact, and measurable, and defineThen $I{<}_{1}W$ and $W{<}_1\Theta$. Subject to the consistency of an inaccessible without a weakly compact cardinal, there is also a model in which $\Theta =I$, so $I/{<}_1\Theta$.