The word "vote" does not appear in the KJV. However, the words "choose" and "chosen" do appear in the KJV, in the context of choosing a king.
The first relevant passage is Deut. 17: 14-20: "When you come to the land which Yahweh your Elohim is giving you, and possess it and dwell in it, and say, 'I will set a king over me like all the nations that are around me,' you shall surely set a king over you whom Yahweh your Elohim chooses; one from among your brethren you shall set as king over you; you may not set a foreigner over you, who is not your brother. [...]" (Please read verses 16-20 for yourself.)
The first relevant passage is Deut. 17: 14-20: "When you come to the land which Yahweh your Elohim is giving you, and possess it and dwell in it, and say, 'I will set a king over me like all the nations that are around me,' you shall surely set a king over you whom Yahweh your Elohim chooses; one from among your brethren you shall set as king over you; you may not set a foreigner over you, who is not your brother. [...]" (Please read verses 16-20 for yourself.)