A recent Slate blog post contains the following correction:

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 probably be the term used by the [excessively knowledgeable and pedantic] 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—in particular Arwen's father Elrond and his brother Elros, eventually the first king of Númenor and a distant ancestor of Aragorn—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 would in some sense be most accurate to understand both Aragorn and Arwen as half-Elven who chose the fate of Men, though even then few citizens of Gondor would think of Aragorn as anything but a Man. (Indeed Aragorn, descended from Elros, who chose mortality, is not even given the choice of identifying as an Elf, in the sense that his bloodline does not give him access to Aman.) 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.

[thank you to @osutein, @dubdobdee and @NedRaggett for Middle-earth genealogy expertise. For more safe-for-work reading on Elf Sex, click here. This post has been updated to clarify certain concepts about descent per the work of @BlakeAued]