The same way you check what you buy from an online store: by the number and content of the negative reviews or downvotes. But they don't exist here because inclusivity is wanted more than quality.

Like counts, be it likes alone or Reddit-style with downvotes, is the wrong mechanic for community-generated content, as it incentivises posting something "for a quick like". As explained in my other reply, Slashdot has a really healthy, decade-old community without having like counts. Posts are ranked by comment count and if there is something really bad, users can report it. It's that easy and it works.

Wouldn't comment counts incentivize controversy-inducing content instead?

That's how I feel about it, it's essentially the way stuff is incentivized on 4chan, and we all know that community isn't really know for its high quality, friendly discourse...

Why is it necessary to measure quality?

Slashdot is around for like decades, a real internet antiquity, and made it without any likes or view counts. Posts that generate a lot of comments are ranked higher, as one can assume it generates more discourse. What else is really needed for a community? Isn't it about sharing knowledge and discussing it?

A front page, as you mentioned it, can consist of either posts that generate a lot of discourse. Or make it simple and just display the latest posts of the people you follow on it.

Same way more sophisticated content algorithms work, such as measuring retention (e.g. % of scroll depth) and bounce rate as a source of relevancy.