There is a known law that if one has a ruling from a rabbi, you should not go to a second rabbi for a ruling except under specific circumstances such as where you have real doubts as to the correctness of the first ruling. This makes sense, as you do not want people to go fishing for the best rulings.
But what if someone decided ahead of time to ask 3 different rabbis for a ruling and go by the majority? Would this be permitted (possibly he'd notify each of the rabbis about his plans before getting the rulings from each)?
One reason to think this might be permitted is because of the way R' Yosef Karo ruled in the Beit Yosef/Shulchan Aruch.
(From R' Karo's intro to the Beit Yosef):
ולכן הסכמתי בדעתי כי להיות שלושת עמודי ההוראה אשר הבית, בית ישראל, נשען עליהם בהוראותיהם, הלא המה הרי"ף והרמב"ם והרא"ש ז"ל אמרתי אל ליבי ...שבמקום ששנים מהם מסכימים לדעה אחת - נפסוק הלכה כמותם
Translation (my own):
And so I decided that since the rulings of House of Israel lean on the rulings of these three Pillars [of halacha] -- the Rif, the Rambam and the Rosh, I decided that in a place where two of them agree, we should rule as they did.
Note that the idea of "majority rules" is not unique to the Beit Yosef, and is in fact used to decide in other places as well. On the other hand, perhaps this only pertains to how a rabbi can decide on a ruling, but for an individual, one must ask a single rabbi.