The sensorimotor theory of perception considers that to perceive is to understand the effect of active movements on sensory signals. Gibson’s ecological theory also places an emphasis on movements: information about the visual world is obtained by producing movements and registering how the visual field changes in lawful ways. Poincaré also defined the notion of space in terms of the movements required to reach an object or compensate for movements of an object.
Information about the world is contained in the sensorimotor “contingencies” or “invariants”, but why should it be important that actions are voluntary? Indeed, one could see movements as another kind of sensory information (e.g. proprioceptive information, or “efferent copy”), and a sensorimotor law is then just a law defined on the entire set of accessible signals. I will propose two answers below. I only address the computational problem (why it is useful), not the problem of consciousness.
Why would it make a difference that action is voluntary? The first answer I will give comes from ideas discussed in robotics and machine learning, and known as active learning, curiosity or optimal experiment design. Gibson makes this remark that the term “information” is misleading when talking about the sensory inputs. Senses cannot be seen as a communication channel, because the world does not send messages to be decoded by the organism. In fact rather the opposite is true: the organism actively seeks information about the world by making specific actions that improve its knowledge. A good analogy is the game “20 questions”. One participant thinks of an object or person. The other tries to discover it by asking questions that can only be answered by yes or no. She wins if she can guess the object with fewer than 20 questions. Clearly it is very difficult to guess using the answer to a random question. But by asking smart questions, one can quickly narrow the search to the right object. In fact with 20 questions, one can discover up to 220 = a million objects. Thus voluntary action is useful for efficiently exploring the world. Here by “voluntary” it is simply meant that action is a decision based on previous knowledge, which is intended to maximally increase future knowledge.
I can see another way in which voluntary action is useful, by drawing an analogy with philosophy of science. If perception is about inferring sensory or sensorimotor laws, then it raises an issue common to the development of science, which is how to infer universal laws from a finite set of observations. Indeed there are an infinite number of universal laws that are consistent with any finite set of observations – this is the problem of inductivism. Karl Popper argued that science progresses not by inferring laws, but by postulating falsifiable theories and testing them with critical experiments. Thus action can be seen as the test of a perceptual hypothesis. Perception without action is like science based on inductivism. Action can decide between several consistent hypotheses, and the fact that it is voluntary is what makes it possible to distinguish between causality and correlation (a fundamental problem raised by Hume). Here “voluntary” means that the action could have been different.
In summary, voluntary action can be understood as the test of a perceptual hypothesis, and it is useful both in establishing causal relationships and in efficiently exploring relevant hypotheses.