I had a very similar idea a while back. I wanted to rank news by "impact" which might be more concrete than "significance."
For an LLM prompt, it would be something like:
"estimate the number of people who's lives that will be materially changed by this news." and "estimate the average degree of change for those impacted."
Then impact is roughly the product of those two.
Additionally, I want a version that is tailored to me specifically "estimate the degree of change this will have on my life." + context of my life.
Tangentially, I've found that getting ratings out LLMs works better when I can give all options and request relative ratings. If I ask for rankings individually I get different and less good results. Not enough context length to rate all news from all time in one go though. Any thoughts on that? Maybe providing some benchmark ratings with each request could help? Something I'm exploring.