Long-term Incentive Compensation Plans - Unit Purchase Activity (Details) - USD ($) shares in Millions, $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Share-Based Payment Arrangement [Abstract]
Total amount of AB Holding Units Purchased/Retained (in shares)	0.0	1.0	2.6	2.9
Total Cash Paid for AB Holding Units Purchased/Retained	$ 1.0	$ 50.0	$ 107.7	$ 125.7
Open Market Purchases of AB Holding Units Purchased (in shares)	0.0	0.9	2.3	2.3
Total Cash Paid for Open Market Purchases of AB Holding Units	$ 0.0	$ 44.9	$ 92.7	$ 103.7