You've practically answered this question by asking it. Thoreau believed - and lived up to his beliefs - that just because MOST people were able to agree on a rule, that didn't necessarily make it a good rule.
This was during a time when the notions of majority rule and "Law and Order" had reached almost religious veneration. Today we give a little lip service to the notion of "minority rights," but in many ways we continue to act in accordance with Roman dictum, "Vox populi, vox Dei" (The voice of the People is the voice of God) which often leads to the "tyranny of the majority."
Some disturbing experiments in the 1950's showed the people were willing to do all sorts of horrible things as long as they were sanctioned in these by an authority figure; as long as they weren't, in the words of so many authority figures, "taking the law into their own hands." Thoreau's point was that the individual conscience was still in charge of each person's behavior, no matter what the "law" said.
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Henry David Thoreau was a great supporter of the system of democracy, which implies decision making by majority votes. On the other hand he was known to refuse to pay taxes of which he did not approve and fiercely attacked laws (like the Fugitive Slave Law) that he did not approve of, even though these taxes and laws had once been approved by majority votes.
But in that sense he was not much different from political activists before and after him. Although he firmly believed in Government that should meddle as little as possible in people's affairs, the general conclusion should be that he believed in a system where State decisions were made democratically, by majority vote and rule.
Thoreau believes that an individual's conscience should be prioritized over majority rule. He argues that individuals should not blindly follow laws or conform to societal norms if they go against their own moral principles. Thoreau advocates for civil disobedience as a way to confront unjust laws and promote individual integrity.
Thoreau believed that it was preferable for the conscience to determine right from wrong.
He says that majority rule is flawed in that the majority rules not because they are most likely to be right, but because they are physically the strongest.