Malebranche, like many other Early Moderns, endorses the understanding/will division of the faculties of the mind. Both faculties are described in terms of what it is they receive:
The mind of man likewise contains two faculties; the first, which is the understanding, is that of receiving various ideas, that is of perceiving various things; the second, which is the will, is that of receiving inclinations, or of willing different things. (p. 8)
Regarding the understanding as passive with respect to the receipt of ideas, Malebranche concludes that "it is the understanding that perceives or knows, since only it receives ideas of objects; for it is the same thing for the soul to perceive an object as to receive the idea that represents that object" (p. 9). Here I want to note that Malebranche might win among the early moderns for giving the best, most succinct statement of a non-inferential version of indirect realism. I don't know nearly enough Malebranche to know if the view stated here is consistently embraced throughout his works, but this is just a really nice statement of the view that perception of objects consists in the mind's interaction with ideas of said objects. This is in contrast to views on which the mind, in the first instance, perceives its own ideas, followed by an act of inference to the existence of the objects of those ideas (often described as "indirect perception"). I think both of the two views merit the title "Indirect Realism", but the view on which the mind's interaction with its ideas is constitutive of perception has some strong advantages over views which require us to infer our way to those objects.
Back to the issue at hand though, you might think that if the understanding is the faculty that perceives or knows then the understanding is also the faculty that judges. But not so for Malebranche. In fact, since everything the understanding does, for Malebranche, is to perceive, Malebranche notes about his own view that "it might fairly be concluded [...] that the understanding never judges since it does nothing but perceive (or that judgments and inferences on the part of the understanding are but pure perceptions)" (p. 13).
The parenthetical at the end there is ambiguous when taken out of context, as it could be taken to suggest that Malebranche just beats Hume to the punch at endorsing the view that "belief is more properly an act of the sensitive, than of the cogitative part of our natures" (T. 1.4.1, p. 183). However, the view in parentheses is not an alternative to the view that "the understanding never judges", rather an explication of what role the understanding plays in judgment. The section in question ends with this:
The understanding, therefore, does nothing but perceive the relations between ideas, whcih relations, when they are clear, are expressed by clear ideas; for the relation of six to three, for example, is equal to two, and is expressed by two. And only the will judges and reasons, by voluntarily remaining with what the understanding represents to it, as has just been said [p. 14, emphasis added]
The following section is titled "That judgments and inferences depend on the will", and describes this situation of voluntarily remaining with the representations of the understanding as a type of assent or consent. So, now we've got the relevant aspects of the view on the table, I want to highlight what I take to be some of the most interesting aspects of the view.
The view, as I understand it, is that judgment consists in voluntarily assenting (or consenting) to a representation provided by the understanding. In particular, this voluntary assent is not a positive act of the mind (i.e. not the mental equivalent of getting out a seal of approval and affixing it to the representation), but instead is a sort of voluntary omission. Suspension of judgment then is the positive act*, and occurs when we continue to investigate the representation, rather than letting the matter stand. A Stalnakerian account of updating the context set is really a sort of striking parallel here. On a standard version of something like Stalnaker's picture of conversational dynamics, propositions that are put forward get added to the context set unless they are challenged, rather than because there is some distinctive response that one issues to allow them in. If we are talking and I say, "the weather was nice yesterday, and I hope it will be tomorrow", you don't need to say, "I agree about the weather yesterday" in order for my claim about the weather to successfully incorporate itself into the context set. Rather, you would need to go our of your way to prevent it from succeeding.
As far as voluntarist views of judgment go, there is something very appealing about the view that judgment involves a voluntary omission. It seems that we can try to explain the intuitions against doxastic voluntarism on a picture like this, by observing that, in cases of judgment, there is a sense in which the will didn't really do anything. Judgment results from a voluntary failure to resist the representation, in the same way that we might think that my failure to act when I witness a harm I could have prevented is a voluntary omission.
Returning for a moment to the comparison with Hume's views, it is worth noting that there is a certain sense in which we can take Hume and Malebranche to be closer together in their views than I indicated before. Setting aside a major component of Hume's view (according to which judgments do not require multiple ideas), the "intrinsic" composition of the mental state that is a judgment is basically the same for Hume and for Malebranch. All the "ingredients" come from the understanding. The difference lies in the fact that Malebranch requires that an additional extrinsic condition be met, and so not every mental state that is intrinsically like a judgment winds up also being a judgment. Hume on the other hand gives an account of judgment on which only these intrinsic features matter (well, on my reading of Hume, at least).
Anyone who knows more about Malebranche's theory of judgment, or who has recommendations of good papers about it, should definitely let me know.
*Malebranche's occaisionalism may gum up the works somewhat in an attempt to spell this out more precisely, but the gist is that judgment is a sort of privation, while suspension of judgment is something positive. At the same time, I think Sean Greenberg argues that this view of judgment as a voluntary omission is crucial for combining the occaisionalism with the view "that rash judgments are sinful, and that all sin is voluntary" while still attributing all real changes that occur to God.
