Since io9 readers aren't necessarily Gawker readers, I'll copy the writeup here instead of forcing you to read it on Gawker. Any Tolkienite Odeckers want to expand on this subject matter?
"Correction, Jan. 2, 2014: The caption for this story originally stated that Arwen and Aragorn are half-elf and half-human. Aragorn is three-fourths human and one-fourth elf. Arwen is 3/16 human, 25/32 elf, and 1/32 Maia. Thanks to reader Auros Harman for the genealogical analysis."
Hm. It's true that "half-elf and half-human" is not the best way to describe Arwen and Aragorn, given that the descriptor implies (to our ears at least) that each has one elf parent and one human parent. ("Half-Elven" or peredhel would be the term used by the denizens of Middle-earth and Arda more broadly, but: See below.)
But the formulation proposed by reader Auros Harman is worse. Most importantly, Aragorn is not "one-quarter elf." It's entirely unclear where this description comes from; Aragorn's closest full-Elvish forebear, Idril Celebrindal, is some sixty-odd generations away.
But even if it were correct it's problematic. Peredhil are required by the Valar to choose sides, so to speak: either join the Valar in the Undying Lands as Elves, or receive the Gift of Men as, yes, Men. There is little room for those of mixed descent in Middle-earth, where relationships between the various races are incredibly rare and regarded with apprehension.
Given this it makes the most sense, and would be most accurate, to understand both Aragorn and Arwen as half-Elvish who chose the fate of Men, though even then few citizens of Gondor would think of Aragorn as anything but a Man. What none would do is think of Arwen as "3/16 human." Attempting to force this kind of "scientific" racialism, obsessed with fractional bloodline, on to Middle-earth and Arda is a sort of cultural imperialism: It's just not how Elves or Men (or Valar) understand race.