Does having more potential mates make us focus on deep qualities or shallow ones?

Shallow ones.

Via APA:

A study published in Psychological Science found that volunteers who have the choice of many potential mates pay less attention to important characteristics that take more time to elicit and pay more attention to trivial characteristics that are quickly and easily assessed.

And:

…Results found that in small speed-dating sessions, people made choices based primarily on important characteristics that take more time to evaluate while those in large speed-dating sessions made choices based on quick and easy-to-assess characteristics.

Why? It’s taxing to sort through so many so we go with what’s easy to see:

Cognitive resources are constrained by bountiful choice so if you want to find a compatible partner who holds the qualities you value, go somewhere with a smaller selection.