No, in accordance with whatchamacallit's law.
If you end up with complex probabilities, you won't be able to plug them into an expected utility formula to get a preference ordering. This has always been the knockdown argument for quantitatively scaled real-number subjective probabilities in my book. Even if underlying physics turns out to use complex-numbered reality fluid, I don't see how I can make choices if my degree of anticipation for something happening to me is not a real number - I don't know of any complex analogue of the von Neumann-Morgenstern theorem which yields actual decision outputs.
After the first dozen responses, I'm currently thinking of writing something along the lines: "While the unusual math of noncommutative probabilities allows for complex probabilities, which have applications in quantum superpositions and eigenstates, there is little likelihood of any practical application involving (the protocol). A (protocol) statement may be written with a complex number for its confidence, but a (protocol) reader or interpreter need only concern itself with the real portion of that number."
Either that, or just stating 'real nu...
It's well-established that 0 decibans means 1:1 odds or 50% confidence; that 10 decibans means 10:1 odds; that -10 decibans means 1:10 odds; and that fractional numbers of decibans have similar meaning.
Does it make sense to talk about "i decibans", or "10 + 20i decibans"? If so, what does that actually mean?
I'm currently roughing out what may eventually become a formal specification for a protocol. It includes a numerical field for a level of confidence, measured in decibans. I'd like to know if I should simply define the spec as only allowing real numbers, or if there could be some purpose in allowing for complex numbers, as well.