beauty contest

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A contest in which a number of people, especially women or girls, are judged with regard to their physical beauty and often their talent or personality, usually with a single winner.
• noun A competition or comparison based primarily on external or superficial factors.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A competition in which participants compete for a determination that one is the most physically attractive.