No, the many do not gain a right to rule over the few

Democracy is seen as the ultimate form of governance, taking the moral high ground over all other forms of governance. But in fact it is nothing but the majority dictating its terms for the minorities. It is ruling by force just as most other types of governance, it is not better motivated nor more moral. A dictator may make better or worse decisions than a democracy. Plato already knew this and considered democracy as a bad form of government. Later on democracy was seen as problematic but accepted by the lack of better alternatives. Today people think democracy is great and there is little honest resistance to democracy without people thinking you are entirely nuts.

People claim democracy is the civilised way of finding compromises. Sometimes it is, but that does not mean it is the nature of democracy. It's the same fallacy as calming weapons equal protection. Sometimes they provide safety, but sometimes they dont.
Democracy is finding a compromise only to the point of 51% (assuming zero corruption!) and then forcing that on everybody else. Why do we need to apply force? What provides the moral authority to do so? Clearly a majority cannot do that and people actually agree (see for example nazi germany, publicly condemned even though there was a majority in the beginning). In the end there is no percentage at which forcing your will on others becomes acceptable. The only civilised compromise is one where 100% agree. Otherwise it is not really a compromise in the first place.

I will decide for my own life. It does not matter if there are ten people that want me to do something else, one million, or the entire rest of humanity. Unless acting in self-defence nobody can claim to be acting morally when forcing their will on anyone else.