P lacks international recognition not only in Asia but also in other parts of the world. It's admission is the least diverse among HYP. Eating club is a turn off for lots of applicants. Quality of admits is a hair lower than HY. But I still prefer P over MIT though since it's a better place for college education. MIT is super hot for Chinese since smartest Chinese study science and engineering. Also, science and engineering are still different things. My perosnal opinion is HYP represents best liberal arts education and either is great. Even S and M pale in prestige.