Then it is not a democracy in any meaningful form, but a tyranny. It is insufficient with pure majority rule to form a democracy - democracy requires participation and at least basic levels of protection of all participants as well.

There are many ways of doing this, with various suitability depending on context, but e.g. one alternative is simply to guarantee the right of withdrawal - if you can always remove yourself from the group if a decision is unacceptable to you, a majority will need to seek compromise if it wishes to avoid shedding members. Other alternatives include requiring super-majorities for particularly important decisions, guaranteeing rule of law and basic human rights.