When judging objectively we act as sovereigns, but also as subjects: we command, but must also obey. Put less tersely: when we judge objectively we are making a claim against the judgment of all, yet if our judgment is not open to the trial of all it fails its claim to objectivity. Being a sovereign and also a subject is a paradoxical condition, and so it may seem we act in a contradictory manner when pursuing objective knowledge.
One thing that may be suggested about this paradox is to accept that we cannot judge objectively, and that each submits his subjective judgment to the community. We may then say it is the community that advances objectively. However, even in this case we find a problem: if an individual cannot judge what would at least be a candidate for objectivity then there is no way to legitimate a conversion of a collection of subjective judgments into objective ones.
The distinction between objective candidacy and objectivity can help us develop some insights. When we judge something objectively, and so demand universal agreement, we always produce at minimum a candidate for objectivity. This is to say we really demand universal agreement for the judgment of candidacy for objectivity. This tells us something interesting about objectivity itself: even though we judge particular characteristics of objects to be objective, the objectivity of the judgment does not depend on these characteristics, instead it depends upon some capacity in our own judging that recognizes these characteristics as universally affirmable. Because this universal affirmability thought in the objective judgment comes before the actual trial it is thought a priori and provides a reflection of how we think others (i.e. humans) relative to the conditions of our own judgments. Put briefly: judging something as objective submits a characteristic to be approved, but also contains an a priori judgment of candidacy for objectivity which is the same time a judgment of what it is to be a subject. (Those familiar with Kant will gain in understanding by reflecting on the categories of the understanding, or the apprehension of the beautiful.)
Typically the consideration of what it is to be a subject per se is not considered in objective investigations. This should be entirely expected, since it is a strict pre-condition of such investigations. However, when we find difficulties, and conflicts, in our attempt to advance in our objective judgments it would be a good exercise to return to the foundations and form of the judgments themselves and to investigate if we are having a conflict in the same kind of judgment, or really in two different kinds of judgments under the same name (objective).
Philosophy (critical philosophy) should seek an agreement about the characterization of judgments generally. In our case with judgments concerning the candidacy of objectivity, we are seeking agreement in how to talk about ourselves and our relationships to each other in judging, and to lay a stronger foundation for universal communicability and for the understanding (read: science, or morals). Wherever we find a priori rules at work we should seek to understand how those things condition our universal judgments, but also how they condition the understanding of ourselves. Agreement in terms on these matters would be no small gain for culture and the advance of humanity.