I describe the more formal definition in the post:

‘Actions (or more generally ‘computations’) get an x-ness rating. We define the x shard’s expected utility conditional on a candidate action *a* as the sum of two utility functions: a bounded utility function on the x-ness of *a* and a more tightly bounded utility function on the expected aggregate x-ness of the agent’s future actions conditional on *a*. (So the shard will choose an action with mildly suboptimal x-ness if it gives a big boost to expected aggregate future x-ness, but refuse certain large sacrifices of present x-ness for big boosts to expected aggregate future x-ness.)′

And as I say in the post, we should expect decision-influences matching this definition to be natural and robust only in cases where x is a ‘self-promoting’ property. A property x is ‘self-promoting’ if it is reliably the case that performing an action with a higher x-ness rating increases the expected aggregate x-ness of future actions.

Possibly relevant?