Board Thread:General Discussion/@comment-28398720-20160525013106/@comment-28398720-20160525021748

It doesn't mater who voted him in, I am not trying to flash out the specifics of the Arks government system, only note in Jaha's Early history that he was voted in.

Also your quote isn't ambiguous if you consider, S02E07:
 * Byrne: "Unfortunately, sir, Dr. Griffin is still in command. Until a vote can be taken, or you willingly transfer your authority."

Abby and the people voted in Jaha. However since they crash landed on to ground the authority was passed to Kane, then Abby and considering that their constituents has been much changed they govern with little legitimacy and need a new election.