Fair Value Measurements - Summary of the assets and liabilities that are measured at fair value on a recurring basis (Details) - USD ($) $ in Millions	3 Months Ended	6 Months Ended
Mar. 31, 2020	Jun. 30, 2020	Dec. 31, 2019
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds		$ 253.5	$ 303.8
Total fair value assets		253.5	303.8
Liabilities of consolidated Funds
Total fair value liabilities		$ (1.2)	(0.9)
Various Investments
Asset of BSIF and consolidated Funds
Uncategorized			48.2
Real estate investment funds \| Minimum
Liabilities of consolidated Funds
Term over which the underlying assets are expected to be liquidated by the investees		1 year
Real estate investment funds \| Maximum
Liabilities of consolidated Funds
Term over which the underlying assets are expected to be liquidated by the investees		11 years
Consolidated Funds
Asset of BSIF and consolidated Funds
Common and preferred stock		$ 7.9	9.8
Short-term investment funds		1.6	0.1
Bank loans		99.7	109.0
Derivatives		0.8	0.6
Investments in unconsolidated Funds		110.0	119.5
Total fair value assets		110.0	119.5
Liabilities of consolidated Funds
Common stock			(0.5)
Derivatives		(1.2)	(0.4)
Total fair value liabilities		(1.2)	(0.9)
Consolidated Funds \| Other Investments
Asset of BSIF and consolidated Funds
Uncategorized		0.0	0.0
Investments in unconsolidated Funds
Asset of BSIF and consolidated Funds
Investments in separate accounts		31.5	44.3
Investments related to long-term incentive compensation plans		88.9	88.8
Uncategorized		20.1
Total fair value assets		143.5	184.3
Investments in unconsolidated Funds \| Various Investments
Asset of BSIF and consolidated Funds
Uncategorized		20.1	48.2
Investments in unconsolidated Funds		23.1	51.2
Investments in unconsolidated Funds \| Investment Funds Subject To Longer Redemption Restrictions
Asset of BSIF and consolidated Funds
Uncategorized		6.3	6.4
Quoted prices in active markets (Level I)
Asset of BSIF and consolidated Funds
Total fair value assets		120.0	132.4
Liabilities of consolidated Funds
Total fair value liabilities		(1.1)	(0.6)
Quoted prices in active markets (Level I) \| Consolidated Funds
Asset of BSIF and consolidated Funds
Common and preferred stock		7.9	9.8
Short-term investment funds		1.6	0.1
Bank loans		0.0	0.0
Derivatives		0.5	0.5
Total fair value assets		10.0	10.4
Liabilities of consolidated Funds
Common stock			(0.5)
Derivatives		(1.1)	(0.1)
Total fair value liabilities		(1.1)	(0.6)
Quoted prices in active markets (Level I) \| Investments in unconsolidated Funds
Asset of BSIF and consolidated Funds
Investments in separate accounts		21.1	33.2
Investments related to long-term incentive compensation plans		88.9	88.8
Total fair value assets		$ 110.0	122.0
Liabilities of consolidated Funds
Investment in cash	3.00%	2.00%
Investment in equity securities	97.00%	98.00%
Quoted prices in active markets (Level I) \| Investments in unconsolidated Funds \| Various Investments
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds		$ 0.0	0.0
Significant other observable inputs (Level II)
Asset of BSIF and consolidated Funds
Total fair value assets		110.4	120.2
Liabilities of consolidated Funds
Total fair value liabilities		(0.1)	(0.3)
Significant other observable inputs (Level II) \| Consolidated Funds
Asset of BSIF and consolidated Funds
Common and preferred stock		0.0	0.0
Short-term investment funds		0.0	0.0
Bank loans		99.7	109.0
Derivatives		0.3	0.1
Total fair value assets		100.0	109.1
Liabilities of consolidated Funds
Common stock			0.0
Derivatives		(0.1)	(0.3)
Total fair value liabilities		(0.1)	(0.3)
Significant other observable inputs (Level II) \| Investments in unconsolidated Funds
Asset of BSIF and consolidated Funds
Investments in separate accounts		10.4	11.1
Investments related to long-term incentive compensation plans		0.0	0.0
Total fair value assets		10.4	11.1
Significant other observable inputs (Level II) \| Investments in unconsolidated Funds \| Various Investments
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds		0.0	0.0
Significant unobservable inputs (Level III)
Asset of BSIF and consolidated Funds
Total fair value assets		3.0	3.0
Liabilities of consolidated Funds
Total fair value liabilities		0.0	0.0
Significant unobservable inputs (Level III) \| Consolidated Funds
Asset of BSIF and consolidated Funds
Common and preferred stock		0.0	0.0
Short-term investment funds		0.0	0.0
Bank loans		0.0	0.0
Derivatives		0.0	0.0
Total fair value assets		0.0	0.0
Liabilities of consolidated Funds
Common stock			0.0
Derivatives		0.0	0.0
Total fair value liabilities		0.0	0.0
Significant unobservable inputs (Level III) \| Investments in unconsolidated Funds
Asset of BSIF and consolidated Funds
Investments in separate accounts		0.0	0.0
Investments related to long-term incentive compensation plans		0.0	0.0
Total fair value assets		3.0	3.0
Significant unobservable inputs (Level III) \| Investments in unconsolidated Funds \| Various Investments
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds		$ 3.0	$ 3.0

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