Eärendil and Elwing were given the choice of kindreds after their journey to Valinor. This choice was extended to their sons (specifically sons, not daughters or grandchildren).
Elrond chose the race of the Eldar and his brother Elros chose to be counted amongst the Edain. Thus far Manwë's proclamation has been fulfilled.
There are some inconsistencies here:
- Arwen was given the choice, but Elladan and Elrohir remained as Eldar in Imladris.
- Tar-Vardamir was not given the choice.
- The offspring of Imrazôr and Mithrellas in Dol Amroth don't seem to have been given a choice.
I can think of only one explanation: that the Mannish blood is dominant over the blood of the Eldar. Thus, as Vardamir was the offspring of two mortals, he did not fall under Manwë's proclamation despite being the son of a half-elven.
However this does not seem to explain the other inconsistencies. Is it possible that Elladan and Elrohir, and also the princes of Dol Amroth, weren't considered important enough by Manwë or Eru to be given the choice?
Also as a side note Tolkien states there were only three unions between Man and Elf, but this seems to ignore Túrin/Finduilas and Imrazôr/Mithrellas.
My question is, Why was Arwen given the choice and not the sons of Elros?