R. Shalom Carmy has an article in the current issue of the Torah U-Mada Journal in which he analyzes R. Joseph B. Soloveitchik's approach to "Da'as Torah" (link - PDF). Here is a relevant excerpt (pp. 10, 12):
There is enough public oral evidence that the Rav did not favor direct rabbinic intervention in political affairs, especially where they lack the requisite expertise to speak with authority. His 1967 ruling that decisions about possible territorial compromise in the land of Israel for the sake of peace should be made by experts in the field, rather than by rabbis, is currently the most discussed example of his outlook. While I am reluctant to rely on private comments, I am sure that many who enjoyed the Rav’s company can confirm my recollections of sarcasm on the subject of rabbis whose adherents encourage them to pontificate on matters of which they were inadequately informed. If his outlook can be inferred from his practice, it is appropriate for gedolei Torah who comment on public matters to recognize the complexity of human affairs and the existence of different informed opinions on most contested questions, and to modulate their voices accordingly. As noted earlier, such leadership inculcates the right “frame of reference” for individual and communal decisions rather than imposing such decisions from above. This model of teaching authority is alive and well in certain segments of our community, though not as much as one might wish, where laity and middle–level rabbinic scholars respectfully solicit and listen to multiple perspectives among their teachers, who, in turn, treat their audience and opponents with respect...In other words, giants of Torah scholarship have insight based on their unique perspectives. But they have to know the intricacies of what they are talking about in order to have insight into it.
The Rav’s practical orientation towards the idea of da‘at Torah has been presented by some of his most faithful talmidim. R. Aharon Lichtenstein, for example, has written about the importance of such guidance. And R. Walter Wurzburger, in arguing that religious ethics requires personal examples, model individuals who embody Torah and are worthy of emulation, especially in areas where right conduct cannot be formulated in precise halakhic categories, has observed the relation between this insight and the special status of gedolim. Though we believe, following the Mishnah (Avot 3:1) that wisdom is the ability to learn from all human beings, how can we not grant pride of place to those who have seen Torah steadily and seen in whole (to adapt Matthew Arnold’s line)? The alternative is virtually unthinkable.
UPDATE: Additionally, and significantly, R. Soloveitchik was wont to discuss the relevant issues and allow his questioner to reach a decision rather than simply give a straight answer. My many discussions with his grandson, R. Mayer Twersky, found him to be similar.