Fair Value Measurements - Summary of the assets and liabilities that are measured at fair value on a recurring basis (Details) - USD ($) $ in Millions	9 Months Ended	12 Months Ended
Sep. 30, 2020	Dec. 31, 2019
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds	$ 114.7	$ 303.8
Total fair value assets	254.6	303.8
Liabilities of consolidated Funds
Total fair value liabilities		(0.9)
Various Investments
Asset of BSIF and consolidated Funds
Uncategorized		48.2
Various Investments and Affiliate Held-for-Sale
Asset of BSIF and consolidated Funds
Uncategorized	$ 16.4
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 Entity Excluding Consolidated Funds
Asset of BSIF and consolidated Funds
Investments in separate accounts	$ 29.5	44.3
Investments related to long-term incentive compensation plans	66.1	88.8
Uncategorized	16.4
Investments in unconsolidated Funds	114.7	184.3
Fair value assets held-for-sale	27.0
Total fair value assets	114.7	184.3
Consolidated Entity Excluding Consolidated Funds \| Long-term Incentive Compensation Plans
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	27.0
Consolidated Entity Excluding Consolidated Funds \| Various Investments
Asset of BSIF and consolidated Funds
Uncategorized	16.4	48.2
Investments in unconsolidated Funds	19.1	51.2
Consolidated Entity Excluding Consolidated Funds \| Other Investments
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	0.0
Consolidated Entity Excluding Consolidated Funds \| Investment Funds Subject to Longer Redemption Restrictions
Asset of BSIF and consolidated Funds
Uncategorized	5.9	6.4
Consolidated Funds
Asset of BSIF and consolidated Funds
Common and preferred stock		9.8
Short-term investment funds		0.1
Bank loans		109.0
Derivatives		0.6
Investments in unconsolidated Funds	0.0	119.5
Fair value assets held-for-sale	112.9
Total fair value assets		119.5
Liabilities of consolidated Funds
Common stock		(0.5)
Derivatives		(0.4)
Total fair value liabilities		(0.9)
Consolidated Funds \| Common and preferred stock
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	5.9
Consolidated Funds \| Short-term investment funds
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	0.5
Consolidated Funds \| Bank loans
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	106.5
Consolidated Funds \| Other Investments
Asset of BSIF and consolidated Funds
Uncategorized		0.0
Fair value assets held-for-sale	0.0
Quoted prices in active markets (Level I)
Asset of BSIF and consolidated Funds
Total fair value assets	116.0	132.4
Liabilities of consolidated Funds
Total fair value liabilities		(0.6)
Quoted prices in active markets (Level I) \| Consolidated Entity Excluding Consolidated Funds
Asset of BSIF and consolidated Funds
Investments in separate accounts	16.5	33.2
Investments related to long-term incentive compensation plans	66.1	88.8
Fair value assets held-for-sale	27.0
Total fair value assets	$ 82.6	$ 122.0
Liabilities of consolidated Funds
Investment in cash	2.00%	3.00%
Investment in equity securities	98.00%	97.00%
Quoted prices in active markets (Level I) \| Consolidated Entity Excluding Consolidated Funds \| Long-term Incentive Compensation Plans
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	$ 27.0
Quoted prices in active markets (Level I) \| Consolidated Entity Excluding Consolidated Funds \| Various Investments
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds	0.0	$ 0.0
Quoted prices in active markets (Level I) \| Consolidated Funds
Asset of BSIF and consolidated Funds
Common and preferred stock		9.8
Short-term investment funds		0.1
Bank loans		0.0
Derivatives		0.5
Fair value assets held-for-sale	6.4
Total fair value assets		10.4
Liabilities of consolidated Funds
Common stock		(0.5)
Derivatives		(0.1)
Total fair value liabilities		(0.6)
Quoted prices in active markets (Level I) \| Consolidated Funds \| Common and preferred stock
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	5.9
Quoted prices in active markets (Level I) \| Consolidated Funds \| Short-term investment funds
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	0.5
Quoted prices in active markets (Level I) \| Consolidated Funds \| Bank loans
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	0.0
Significant other observable inputs (Level II)
Asset of BSIF and consolidated Funds
Total fair value assets	119.5	120.2
Liabilities of consolidated Funds
Total fair value liabilities		(0.3)
Significant other observable inputs (Level II) \| Consolidated Entity Excluding Consolidated Funds
Asset of BSIF and consolidated Funds
Investments in separate accounts	13.0	11.1
Investments related to long-term incentive compensation plans	0.0	0.0
Fair value assets held-for-sale	0.0
Total fair value assets	13.0	11.1
Significant other observable inputs (Level II) \| Consolidated Entity Excluding Consolidated Funds \| Long-term Incentive Compensation Plans
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	0.0
Significant other observable inputs (Level II) \| Consolidated Entity Excluding Consolidated Funds \| Various Investments
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds	0.0	0.0
Significant other observable inputs (Level II) \| Consolidated Funds
Asset of BSIF and consolidated Funds
Common and preferred stock		0.0
Short-term investment funds		0.0
Bank loans		109.0
Derivatives		0.1
Fair value assets held-for-sale	106.5
Total fair value assets		109.1
Liabilities of consolidated Funds
Common stock		0.0
Derivatives		(0.3)
Total fair value liabilities		(0.3)
Significant other observable inputs (Level II) \| Consolidated Funds \| Common and preferred stock
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	0.0
Significant other observable inputs (Level II) \| Consolidated Funds \| Short-term investment funds
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	0.0
Significant other observable inputs (Level II) \| Consolidated Funds \| Bank loans
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	106.5
Significant unobservable inputs (Level III)
Asset of BSIF and consolidated Funds
Total fair value assets	2.7	3.0
Liabilities of consolidated Funds
Total fair value liabilities		0.0
Significant unobservable inputs (Level III) \| Consolidated Entity Excluding Consolidated 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
Fair value assets held-for-sale	0.0
Total fair value assets	2.7	3.0
Significant unobservable inputs (Level III) \| Consolidated Entity Excluding Consolidated Funds \| Long-term Incentive Compensation Plans
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	0.0
Significant unobservable inputs (Level III) \| Consolidated Entity Excluding Consolidated Funds \| Various Investments
Asset of BSIF and consolidated Funds
Investments in unconsolidated Funds	2.7	3.0
Significant unobservable inputs (Level III) \| Consolidated Funds
Asset of BSIF and consolidated Funds
Common and preferred stock		0.0
Short-term investment funds		0.0
Bank loans		0.0
Derivatives		0.0
Fair value assets held-for-sale	0.0
Total fair value assets		0.0
Liabilities of consolidated Funds
Common stock		0.0
Derivatives		0.0
Total fair value liabilities		$ 0.0
Significant unobservable inputs (Level III) \| Consolidated Funds \| Common and preferred stock
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	0.0
Significant unobservable inputs (Level III) \| Consolidated Funds \| Short-term investment funds
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	0.0
Significant unobservable inputs (Level III) \| Consolidated Funds \| Bank loans
Asset of BSIF and consolidated Funds
Fair value assets held-for-sale	$ 0.0

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