The Maharsha on Makkot 23b, D"H Taryag writes:
"...ואמר בזה דנמנו וגמרו ר"ל שבאו בזה למנין המצות שהלאוין הם יותר מהעשיים וע"כ הסכימו וגמרו לומר שלא נברא האדם בשביל עצמו ויותר היה טוב לו שלא נברא כי הוא קרוב להפסד מחמת הלאוין שהם רבים ורחוק לשכר מצד העשיין שהם מועטים ועכשיו שנברא לא נברא אלא לכבוד המקום..."
Translation: "...and it was stated by this that they counted and concluded, meaning that they counted the number of the commandments [and saw] that the negative commandments were greater [in number] than the positive commandments and therefore agreed and concluded that Man was not created for himself and it would have been better for him to not have been created because he is close to losing because of the great number of negative commandments and is far from receiving reward from the positive commandments for they are few, and now that he has been created, he has not been created but to honor Hashem..."
Therefore, the term "נמנו" (counted) does not necessarily mean that they voted but rather that they counted something else, i.e., they quantified a certain factor. In this case, after a drawn-out debate, they decided that the deciding factor would be the number of mitzvot and proceeded to count the mitzvot, and that's how they reached their conclusion.
And a few other examples of non-halachic issues settled by נמנו (whatever that might mean in context):
Shir Hashirim Rabbah 1:1:
"“He will stand before kings”—he will stand before kings of the Torah. “He will not stand before dark ones,” this is the group of the wicked. Rabbi Yehoshua ben Levi said: When [the Sages] voted, and concluded that three kings and four commoners do not have a portion in the World to Come, they sought to add Solomon to them. A Divine Voice emerged and said: “Do not touch My anointed ones” (Psalms 105:15)."
In light of the Maharsha, we might therefore change the translation to "they counted the number of kings and commoners". Otherwise, it would be strange that they voted and then suddenly remembered "Oh, hey, what about Shlomo?". The portion about Shlomo took place while they were counting out the number of wicked kings.
Shir Hashirim Rabbah 2:14:
"Rabbi Yosei HaGelili interpreted the verse regarding the kingdoms. “My dove, in the clefts of the rock,” as [Israel is] shadowed in the recesses of the kingdoms. “Show me your appearance,” this is [Torah] study. “Let me hear your voice,” this is a good deed. They already once voted in the house of Aliyat Arim in Lod and they said: ‘Which is greater, study or action?’ Rabbi Tarfon said: ‘Action is greater.’ Rabbi Akiva said: ‘Study is greater.’ They voted and concluded: Study is greater, as it engenders action. “For your voice is pleasant,” this is study. “And your appearance is lovely,” this is a good deed."
Again, how would voting be a deciding factor in what is greater, study or action? They must have quantified some factor (I'm not sure what that was exactly) and decided per that.
Beresheet Rabbah 98:8 (my translation):
"They counted and said: Hillel [is a descendant] of Shlomi(t)."1
In this case, per the corrected nusach (see footnote), they counted backwards Hillel's genealogy and concluded he was a descendant of Shlomit, Zerubavel's daughter (see also Yerushalmi Ketubot 12:3).
1 Nusach corrected per Rabbi Reuven Margolies's essay (in Hebrew) "The Genealogy of Rabbi Yehudah Ha'Nasi" - "לתולדות רבי יהודה הנשיא", Sinai 39, pp. 104-105.