But if you make the democracy in such a way that unalienatable rights can't be voted on then you can have both. Its all how you design the system. Its why I am pro direct democracy, but with the required systemic changes such as multiple choice instead of yes/no and things that would destroy liberty / democracy off the table.
Discussion
Direct democracy is very dangerous.
An Individual Freedom Democracy would work, where people can vote on something, and then those that want it can support and pay for it, and those that want nothing to do with it are not forced into supporting it.
For example, those that want public education pay for it themselves and those that want nothing to do with it don't pay anting into public education and get their education elsewhere if they so desire.