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Long-term Incentive Compensation Plans (Tables) | 9 Months Ended
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Sep. 30, 2025
Share-Based Payment Arrangement [Abstract] |
Schedule of Unit Award Repurchase Activity | Repurchases of AB Holding Units for the three and nine months ended September 30, 2025 and 2024 consisted of the following:
|  | Three Months Ended September 30, |  | Nine Months Ended September 30,
|  | 2025 |  | 2024 |  | 2025 |  | 2024
|  | (in millions)
Total amount of AB Holding Units Purchased (1) |  | 0.1 |  |  | 1.1 |  |  | 1.3 |  |  | 2.1 |
Total Cash Paid for AB Holding Units Purchased (1) |  | $ | 4.1 |  |  | $ | 38.6 |  |  | $ | 47.8 |  |  | $ | 71.7 |
Open Market Purchases of AB Holding Units Purchased (1) |  | 0.1 |  |  | 1.1 |  |  | 1.1 |  |  | 1.8 |
Total Cash Paid for Open Market Purchases of AB Holding Units (1) |  | $ | 3.9 |  |  | $ | 38.6 |  |  | $ | 42.3 |  |  | $ | 60.1 |
(1) Purchased on a trade date basis. The difference between open-market purchases and total amount of units purchased 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.

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- Definition Tabular disclosure of employee stock purchase plan activity. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 718 -SubTopic 50 -Name Accounting Standards Codification -Publisher FASB -URI https://asc.fasb.org/718-50/tableOfContent Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (g) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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