The certainty that uniqueness exists IS dependent upon the judgement of a group of humans. The greater the number of persons communicating the existence of a uniqueness - the greater the certainty that it exists. To answer that, we must distinguish exogenous from endogenous certainty. Most people find it sufficient to have a low level of exogenous certainty regarding their own uniqueness. This low level of exogenous certainty is, usually, accompanied by a high level of endogenous certainty.
Most people love themselves and,thus, feel that they are distinct and unique.
So, the main determinant in feeling unique is the level of endogenous certainty regarding one's uniqueness possessed by an individual. Communicating this uniqueness becomes a limited, secondary aspect, provided for by specific role-players in the life of the individual. Narcissists, by comparison, maintain a low level of endogenous certainty. They hate or even detest themselves, regard themselves as failures. They feel that they are worthy of nothing and lack uniqueness.