Why did Franz Joseph agree to the Ausgleich with Hungary in 1867?

Emperor Franz Joseph agreed to the Ausgleich (Compromise) of 1867 primarily as a strategic necessity following the Habsburg monarchy's defeat in the Seven Weeks’ War against Prussia in 1866.12

The defeat weakened the empire and made the constitutional reorganization of the monarchy—a topic of discussion since 1859—an urgent priority to ensure stability. By granting Hungary full internal autonomy and a responsible ministry, Franz Joseph secured a compromise that maintained the empire as a single great power for the purposes of war and foreign affairs, thereby preserving his dynastic prestige abroad.12

The process was facilitated by the appointment of Friedrich Ferdinand, Graf von Beust as chancellor, who encouraged the emperor to treat negotiations with Hungarian leaders like Ferenc Deák and Gyula, Gróf Andrássy as a purely dynastic affair. While the monarch accepted this arrangement to stabilize his rule, he remained reluctant to extend similar federalist concessions to other parts of his empire, preferring to maintain centralist policies elsewhere.1