Aside from the issue of age of course, if they're intelligent enough to understand the relationship and what it means, then they can make the list.

Very. Not saying that I need them to be extremely intelligent, but should be at/around the same level as me, and have similar interests as me. Otherwise conversations would be more difficult?

I think intelligence/personality are about even for me. I think I would not have rejected my wife if she were average intelligence, but the fact that she has a science background, and the quick way she thinks are part of the package that I fell for. So I will say very important, but not the most important.

Smart enough for her strengths to make up for my weaknesses.

Simplified at the cost of accuracy:

On a scale from 1-10 on attractiveness you get ±1 for being below/above one standard deviation on intelligence.

Other standard deviations: Sad/happy ±2 Mean/kind ±1. Different/same life goals ±5.

For me, capacity and curiosity is more important because it usually means the other person can change based on information rather than thinking they already know. Usually, that means they are somewhat intelligent as a result.

So so so important. But I'd rather someone be a bit dumb and really nice to me than the hellscape I am living now.

If I were the type to choose a partner, I'd say it's very important for them to be not dumb, but less important to be actually smart. It would still be a positive, but someone who's not a genius but still had many other good qualities can still be fun to hang out with. It's also a mindset thing-- someone with little knowledge but a will to learn is better than someone who knows more, but refuses to learn anything new. (Not that knowledge == intelligence, anyways.)

This is going to sound so bad, but I can't look for someone smarter without limiting my options too much, just as I am tall for a lady in my area so can't make taller than me a requirement.

So: smart enough to be funny, to understand the things I talk about? To understand how money works , live in the world easily, not stupid? Competent in some area, different from what I am good at? Required. Smart enough that I think "wow you are smart!" Not a consideration. I do think I assign extra 'points' to intelligence, it makes someone more attractive, but it's not something I need as much as I need kindness and open mindedness, and in myself I value those qualities more too.

Pretty important. As well as good emotional regulation.

I just want somebody I can play strategic (in the looser sense) board games with at a level compatible with me tbh.

Important, but not as important as loyalty.

I think I would need some kind of example of what we're counting as 'intelligence.'

Not much. As long as she's a person with common sense and a bit of intelligence, I'm fine.

So this is an interesting question to me and got me thinking... I think the qualities that are important to me in a partner (compassion, empathy, openness, open mindedness, passion, etc.) aren't strictly tied to intelligence? Maybe there's a correlation, I guess? Depends on how you define intelligence.

I probably wouldn't go out of my way to look for particularly intelligent people. In fact I'd probably avoid anyone who puts their IQ in their bio (because... Eww). But based on my interests and personally, I can see myself naturally sharing more in common with "intelligent" people (wow that sounds pretentious).

I do wonder if I'd feel frustrated with a partner who couldn't understand me when explaining complex things though...

As long as they're able to go about their life without doing dumb shit that's good enough for me. More important is being ethical and having good emotional intelligence (I suppose this could be lumped in with intelligence but it's not the same as being book smart).

yes.

There is a Chinese expression: "The ugly wife is a treasure at home"

It is possible ugly can be substituted for dull (mentally).

That depends on what you mean by intelligence.