Are there any startups that work on improving or reinventing democracy?

If "startup" is defined as a for-profit company, then I'm not aware of any. There are non-profit organizations that work on alternative voting (Approval voting [0] and STAR voting [1] and Instant Run-off/Rank Choice), non-partisan primaries, non-partisan districting, proportional representation (no districts), electoral college reform.

[0] https://electionscience.org/

[1] https://www.starvoting.us/

Valley mentality.

Everything is solved with an app

Nonprofits are startup-like. You are just not going to get that six figure salary you are accustomed to. At least not til you reach the c-suite.

Not everything can be solved by a startup.

Probably some nontraditional nonprofits but they're likely to be classified as "Terrorist organizations" by those who disagree with their goals... Defnitely a higher risk investment.

Yes, probably too many. Check AngelList.

The main improvement to democracy was liberalism (the belief that individual rights trump majority rule). Is there an app for that?