At this moment how I do it: The initial score is 0, based on year of construction (newer is better ofc) I add 0-36 points, amount of square meters I multiply by 0.5 and add it as extra points, based on how prestigious is the district I add extra 0-4 points and there are many other things.

So why it's not possible like that to give score to each apartment? I mean if I find right weight for each parameter? How f.e. google rates websites, I guess it gives some kind of score to each of them? Or not?

An obvious problem is that the linear score doesn't represent the value I feel I get from the attribute.

For instance, I live in a 2000 sq ft. space, I will have to store things if I move into a 1500 sq ft. space, and have to sell them or throw them out if I move to a 500 sq ft. space.

A 3000 sq ft space would feel spacious to me but I would not get 10x the utility if I had a 30,000 sq ft space because I don't have enough stuff to fill it.

See https://en.wikipedia.org/wiki/Utility

That's why I'm wondering how to score it. If I give too much weight to the surface it won't make sense definitely. So at the beginning surface and price were the most important so then I had a lot of really big and cheap apartments from suburbs as first results, which didn't make sense, then I introduced rating based on district and few other parameters and it improved rating a lot but still, it's not good enough. I will check this Utility, thanks.