How would global peace cause the lack of intellectual humility in individuals?

I'm not sure what you mean by "intellectual humility." Does that mean that you are humble about your individual intellectual abilities? If so, why would global peace make that change?

In my opinion, humility would be likely to increase, because global peace would probably increase job competition, with more "farming out" of jobs between nations. This is assuming that global peace would lead to improvement in educational opportunities in undeveloped countries.

I don't know if it helps, but I hope so. Thanks for asking.