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Long-term Incentive Compensation Plans (Tables)
 9 Months Ended
Sep. 30, 2024
Share-Based Payment Arrangement [Abstract]  
Schedule of Share-based Compensation, Employee Stock Purchase Plan, Activity
Repurchases of AB Holding Units for the three and nine months ended September 30, 2024 and 2023 consisted of the following:
Three Months Ended September 30,Nine Months Ended September 30,
2024202320242023
(in millions)
Total amount of AB Holding Units Purchased (1)
1.1 1.8 2.1 2.3 
Total Cash Paid for AB Holding Units Purchased (1)
$38.6 $56.9 $71.7 $75.7 
Open Market Purchases of AB Holding Units Purchased (1)
1.1 1.8 1.8 1.8 
Total Cash Paid for Open Market Purchases of AB Holding Units (1)
$38.6 $56.9 $60.1 $56.9 
(1) Purchased on a trade date basis. The difference between open-market purchases and units retained reflects the retention of AB Holding Units from employees to fulfill statutory tax withholding requirements at the time of delivery of long-term incentive compensation awards.