Rosh Hashanah, Chapter 1, Mishnah 5. This Mishnah addresses the question of under what circumstances someone who saw the new moon may desecrate Shabbos in order to reach Jerusalem and testify about the sighting of the new month.
"Bein shenireh ba'alil, bein shelo nireh ba'alil - mechallelin alav es haShabbos. Rabbi Yosi omer: im nireh ba'alil, ein mechallelin alav es haShabbos":
The two situations in the Mishnah:
"Nireh ba'alil" - the new moon was seen clearly, and therefore we know that many people saw it.
"Lo nireh ba'alil" - the moon was not seen clearly, and we do not know for certain whether others saw it.
The view of the Tanna Kamma: In both situations alike, the witness desecrates Shabbos and sets out on his way to Jerusalem. This does not apply only to someone who thinks that he alone saw the moon while others did not see it; even when it is clear that hundreds and thousands of people saw the new moon, the witness may still desecrate Shabbos on its account.
The view of Rabbi Yosi: When the moon was seen clearly, and it is known that many people saw it, one does not desecrate Shabbos on its account. The reason: someone who is already in Jerusalem does not need to travel at all, and he is the one who will testify about the sighting of the new moon, and on his word the month will be sanctified.
In summary: The Tannaim disagree about desecrating Shabbos for the sake of testimony about the new month. According to the Tanna Kamma, whether the moon was seen clearly or was not seen clearly, one desecrates Shabbos on its account, even if many people saw it. According to Rabbi Yosi, when it was seen clearly one does not desecrate Shabbos, since the testimony will be given by someone who is already in Jerusalem and does not need to travel.