A better definition I think is to say an entity or system is conscious to the extent it’s world model is encompassing / “complete” and self-conscious when its world model includes itself and its own internal states. By this definition there are many continuous levels of consciousness and self-consciousness and these are not binary all vs nothing.
There must be some strong correlation there: where a better world-model allows you to be more intelligent. Especially if that world-model contains yourself (e.g. self-consciousness).
I do, however, fundamentally believe that our interior conscious experience IS our world model: e.g. There's some property of the information system we live in* such that any tightly integrated and time-coherent partition of information has an interior experience.
A good question: is it possible to build a system that has a highly sophisticated world model, but minimal intelligence, and vice versa?
I think that highly sophisticated world model / low intelligence is possible (and it would have an amazing interior experience).
A non-existent world model / high intelligence seems impossible, since you likely need a good world model to be able to generally reason.
* Our universe / some exterior reality that's running our universe simulation / something weirder we can't even conceive.
Moreover, for social species that live and evolve in groups, like humans, this world-model must crucially include a model of oneself and other minds. We need to be able to predict how others will think and react to our own behaviors. This is what gives rise to self-consciousness and "theory of mind" - a world-model that is recursive and includes representations of itself.
That said, while our conscious experience seems deeply linked to our world-model, the world-model likely encompasses much more than just conscious awareness. It runs in the background, guiding our reflexes, breathing, balance, and myriad other functions below the level of consciousness. It takes in raw sensory data and interprets it, and uses feelings and emotions as a communication channel to influence conscious thought.
There are known critical developmental windows during which an animal's world-model is shaped by early sensory experiences and social interactions. If key stimuli are missing during these windows, the world-model may remain stunted in certain ways even if the missing stimuli are later provided. The animal may compensate through other means, but its overall intelligence - its ability to model and predict - will be constrained by the limitations of its world-model.
So in that sense, a highly sophisticated but narrowly specialized world-model, as in a mathematical or musical savant, may produce an individual who is brilliant in one domain but quite limited in general intelligence.
Whereas a broad but shallower world-model, as in many animals, can enable robust if limited intelligence that is well-adapted to the animal's ecological niche.
Evolution tends to select for world-models and intelligence that are "just enough" for an animal's lifestyle and no more. The metabolic cost of excess intelligence makes it maladaptive. So we see each species with a world-model and associated intelligence that is tailored to its particular environment and survival needs.
That's not what is most essential to intelligence. What is most characteristic of intelligence is intentionality. From there, we can talk about inference, analysis, and so on, which presuppose intentionality. Whereas most animals maintain only a concrete image of the world they encounter, human beings can abstract from the concrete into the general and the universal, so the paradigmatic example of intelligence, as opposed to what may be considered analogues, is human intelligence.
Predictability is effectively a question of practicality. Intelligence is not the ability to predict, but rather, intelligence entails that ability as a consequence of intentionality and reasoning (by sufficiently comprehending the nature of a thing, you can make predictions about how it will behave under certain conditions, something that goes beyond mere cargo cult statistics and enters the realm of reason, which is to say concern for causality).
