Simple, reliable, fast and anonymous system for voting would help, but unfortunately, it is not possible to have all four. Many would argue that anonymity is the most important feature of the current voting system, to the point of showing bulletins being illegal in some places, but what if importance of anonymity is mostly an artefact of rarity and non-granularity of decisions we vote for?
Now we need extra protection against selling votes, or voters being intimidated, because vote gives very little benefit to the voter, and huge benefit to the elected, leading to most people not being able to correctly price the effects of their vote. If voters had opportunity to decide on every issue individually, the game dynamics would change, and people would be able to protect their votes by themselves.
The software needed for this shouldn't be much more complicated than normal forum/social media app/change.org. The startup would partner with local politicians/small parties/activists to collect and verify the users. Users do not have to pay attention to every vote. They can set their vote to match someone else's, can trade their support for a law with other users, but most importantly they have a real way to influence decisions they care about instead of screaming into void in forms of petitions or costly protests. To do this registered users must to vote on election day, and must provide selfie proofs of a vote where it is allowed, or have votes rescaled by the final count from districts where results are published.
Politicians if elected via app, have to always vote according to the changing preferences of users who have voted for them.
In short this would do to politicians same thing that Uber did to taxists.