It's just a simple yes or no, whether you think at least one or more of the candidates on your ballot list shares a lot of your concerns, beliefs, et values to at least vote for them
If you don't approve any of them, just don't mark them, and write down "I don't like any of these candidates" as a reason
I don't like "first past the post" for this reason... it just perpetuates the idea of "spoiled" votes...
Only voting for your favorite gives the other candidates less approval, which swings the vote towards the candidate who has voters who are the most "selective". Plus even if that isn't the case, who's to say the person who wins is the best and not just the most status quo or calculated politician?
They already have something better than single-member voting districts in "western democracy": direct proportional representation. It clearly doesn't make much difference.
Barack Obama has a 63% approval rating. I guess you saud local politicians but I bet you can find similar examples.
I think you underestimate the level to which propaganda and ruling class maneuvering determines who has power, and overestimate the amount that elections matter, which are in fact glorified polls.
We all saw how it took them just a couple days to completely crush Bernie Sanders' last election campaign.
I'm not against elections, but they have to serve a specific pupose and not just exist for the ceremony. Maybe elections they have in Cuba or China work better if it's just a neighborhood voting for a leader, but idk.
Yes liberal electoralism is a smokescreen. You're right that no voting method will ever be perfect. Even if we find the perfect system with no spoiled votes, no gamified voting whatsoever, you still haven't solved the IMO most glaring problem with electoral systems, which is (If you will entertain a hypothetical) you might like candidate A because they promised you a free subway footlong with chips, and I might like candidate B because they're the only candidate who doesn't want to kill me. Our relative "wants" aren't equal.
All that said, I think you're being a little black and white in your thinking about this. You can still say definitively that one voting method is better than another at doing a particular thing. I think the point OP was making was that approval voting is better than FPTP while requiring almost no changes to the current system, demonstrating that the current system doesn't care about being more democratic because if they did we would already be approval voting. There's literally no valid argument against it. You could use the same ballots and count them the same way, just instead of marking one vote you mark (potentially) multiple. Gamified voting is much less effective, "spoiler" voting from outside the established center doesn't exist, and the two party system would be severely weakened. Three marked improvements.
As for Obama's approval rating, if you had only ever tasted smarties and root beer barrels your perception of what candy you like would be pretty heavily skewed. I'm willing to bet that 4 years of a decent administration (an act of god) would change everyone's approval range by a lot.