Tibni was an unsuccessful candidate for king of Israel. Although many people don't recognize it, democratic election of leaders has always existed. The only difference between ancient times and the present (or vice versa) is what form the "votes" take. Regardless of the system, all that "counts" is who has the most support to get, and remain, in power. No king has ever come to power, and remained in power, without the support (in whatever form that takes, whether paper ballots, or swordsmen) of the majority of the people. In the case of Tibni, after a 4 year "campaign," Omri had more support from the people of Israel than Tibni did.
"Then were the people of Israel divided into two parts: half of the people followed Tibni the son of Ginath, to make him king; and half followed Omri"
Tibni was just one player in what was an endless struggle for political control of the kingdoms of Israel and Judah (see the Fact Finder question below).
"In the twenty and seventh year of Asa king of Judah did Zimri reign seven days in Tirzah. And the people were encamped against Gibbethon, which belonged to the Philistines. And the people that were encamped heard say, Zimri hath conspired, and hath also slain the king: wherefore all Israel made Omri, the captain of the host, king over Israel that day in the camp. And Omri went up from Gibbethon, and all Israel with him, and they besieged Tirzah. And it came to pass, when Zimri saw that the city was taken, that he went into the palace of the king's house, and burnt the king's house over him with fire, and died, For his sins which he sinned in doing evil in the sight of The Lord, in walking in the way of Jeroboam, and in his sin which he did, to make Israel to sin."
"Now the rest of the acts of Zimri, and his treason that he wrought, are they not written in the book of the chronicles of the kings of Israel?"
"Then were the people of Israel divided into two parts: half of the people followed Tibni the son of Ginath, to make him king; and half followed Omri. But the people that followed Omri prevailed against the people that followed Tibni the son of Ginath: so Tibni died, and Omri reigned."
"In the thirty and first year of Asa king of Judah began Omri to reign over Israel, twelve years: six years reigned he in Tirzah. And he bought the hill Samaria of Shemer for two talents of silver, and built on the hill, and called the name of the city which he built, after the name of Shemer, owner of the hill, Samaria."
"But Omri wrought evil in the eyes of The Lord, and did worse than all that were before him. For he walked in all the way of Jeroboam the son of Nebat, and in his sin wherewith he made Israel to sin, to provoke The Lord God of Israel to anger with their vanities."
"Now the rest of the acts of Omri which he did, and his might that he showed, are they not written in the book of the chronicles of the kings of Israel? So Omri slept with his fathers, and was buried in Samaria: and Ahab his son reigned in his stead." (1 Kings 16:15-28 KJV)
Fact Finder: Who were the successful candidates for king of Israel and Judah? How many royal dynasties (i.e. a son ruling after a father - a situation that is sometimes just as evident in other forms of democracy) were there in Israel and Judah?
See Kings of Israel and Judah and Israelite Dynasties