According to J.K. Rowling, the Elder Wand knows no loyalty except to strength:
JKR: The Elder Wand is simply the most dispassionate and ruthless of wands in that it will only take into consideration strength. [..] the Elder Wand knows no loyalty except to strength. So it's completely unsentimental. It will only go where the power is. So if you win, then you've won the wand. So you don't need to kill with it. But, as is pointed out in the books, not least by Dumbledore because it is a wand of such immense power, almost inevitably, it attracts wizards who are prepared to kill and who will kill. And also it attracts wizards like Voldemort who confuse being prepared to murder with strength.
However, in the limbo between the two worlds, Dumbledore says:
“Maybe a man in a million could unite the Hallows, Harry. I was fit only to possess the meanest of them, the least extraordinary. I was fit to own the Elder Wand, and not to boast of it, and not to kill with it. I was permitted to tame and to use it, because I took it, not for gain, but to save others from it.”
— Harry Potter and the Deathly Hallows, Chapter 35: "King's Cross"
(In a previous question, we didn't discuss the word "permitted".)
What did Dumbledore mean? Does he believe in Death or other higher forces?