Segment Information - Revenue (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Segment reporting information
Total revenues from contracts with customers									$ 307.9	$ 294.3	$ 401.2
Other revenues									872.8	599.1	(32.1)
Total revenues	$ 520.8	$ 459.5	$ 259.6	$ (59.2)	$ 175.3	$ 155.5	$ 129.0	$ 433.6	1,180.7	893.4	369.1
HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0.0	0.0	0.0
Other revenues									68.5	66.6	24.3
Total revenues									68.5	66.6	24.3
NSM
Segment reporting information
Total revenues from contracts with customers									285.1	233.1	101.6
Other revenues									0.0	0.0	0.0
Total revenues									285.1	233.1	101.6
Kudu
Segment reporting information
Total revenues from contracts with customers									0.0	0.0
Other revenues									45.7	21.2
Total revenues									45.7	21.2
MediaAlpha
Segment reporting information
Total revenues from contracts with customers										48.8	295.5
Other revenues										0.0	1.6
Total revenues									0.0	48.8	297.1
Other Operations
Segment reporting information
Total revenues from contracts with customers									22.8	12.4	4.1
Other revenues									758.6	511.3	(58.0)
Total revenues									781.4	523.7	(53.9)
Specialty Transportation
Segment reporting information
Total revenues from contracts with customers									85.5	77.6	28.3
Specialty Transportation | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0.0	0.0	0.0
Specialty Transportation | NSM
Segment reporting information
Total revenues from contracts with customers									85.5	77.6	28.3
Specialty Transportation | Kudu
Segment reporting information
Total revenues from contracts with customers									0.0	0.0
Specialty Transportation | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0.0	0.0
Specialty Transportation | Other Operations
Segment reporting information
Total revenues from contracts with customers									0.0	0.0	0.0
Real Estate
Segment reporting information
Total revenues from contracts with customers									44.9	34.7	17.8
Real Estate | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0.0	0.0	0.0
Real Estate | NSM
Segment reporting information
Total revenues from contracts with customers									44.9	34.7	17.8
Real Estate | Kudu
Segment reporting information
Total revenues from contracts with customers									0.0	0.0
Real Estate | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0.0	0.0
Real Estate | Other Operations
Segment reporting information
Total revenues from contracts with customers									0.0	0.0	0.0
Social Services
Segment reporting information
Total revenues from contracts with customers									28.9	25.9	14.7
Social Services | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0.0	0.0	0.0
Social Services | NSM
Segment reporting information
Total revenues from contracts with customers									28.9	25.9	14.7
Social Services | Kudu
Segment reporting information
Total revenues from contracts with customers									0.0	0.0
Social Services | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0.0	0.0
Social Services | Other Operations
Segment reporting information
Total revenues from contracts with customers									0.0	0.0	0.0
Pet
Segment reporting information
Total revenues from contracts with customers									55.0	30.0
Pet | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0.0	0.0
Pet | NSM
Segment reporting information
Total revenues from contracts with customers									55.0	30.0
Pet | Kudu
Segment reporting information
Total revenues from contracts with customers									0.0	0.0
Pet | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0.0
Pet | Other Operations
Segment reporting information
Total revenues from contracts with customers									0.0	0.0
Other
Segment reporting information
Total revenues from contracts with customers									29.7	25.9	16.9
Other | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0.0	0.0	0.0
Other | NSM
Segment reporting information
Total revenues from contracts with customers									21.4	19.0	12.8
Other | Kudu
Segment reporting information
Total revenues from contracts with customers									0.0	0.0
Other | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0.0	0.0
Other | Other Operations
Segment reporting information
Total revenues from contracts with customers									8.3	6.9	4.1
Total Commission and Other Revenue
Segment reporting information
Total revenues from contracts with customers									293.4	240.0	105.7
Total Commission and Other Revenue | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0.0	0.0	0.0
Total Commission and Other Revenue | NSM
Segment reporting information
Total revenues from contracts with customers									285.1	233.1	101.6
Total Commission and Other Revenue | Kudu
Segment reporting information
Total revenues from contracts with customers									0.0	0.0
Total Commission and Other Revenue | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0.0	0.0
Total Commission and Other Revenue | Other Operations
Segment reporting information
Total revenues from contracts with customers									8.3	6.9	4.1
Advertising revenues
Segment reporting information
Total revenues from contracts with customers										48.8	295.5
Advertising revenues | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers										0.0	0.0
Advertising revenues | NSM
Segment reporting information
Total revenues from contracts with customers										0.0	0.0
Advertising revenues | Kudu
Segment reporting information
Total revenues from contracts with customers										0.0
Advertising revenues | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										48.8	295.5
Advertising revenues | Other Operations
Segment reporting information
Total revenues from contracts with customers										0.0	0.0
Products
Segment reporting information
Total revenues from contracts with customers									14.5	5.5
Products | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0.0	0.0
Products | NSM
Segment reporting information
Total revenues from contracts with customers									0.0	0.0
Products | Kudu
Segment reporting information
Total revenues from contracts with customers									0.0	0.0
Products | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0.0
Products | Other Operations
Segment reporting information
Total revenues from contracts with customers									14.5	5.5
United Kingdom
Segment reporting information
Total revenues from contracts with customers									49.4	45.9	28.0
United Kingdom | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0.0	0.0	0.0
United Kingdom | NSM
Segment reporting information
Total revenues from contracts with customers									49.4	45.9	28.0
United Kingdom | Kudu
Segment reporting information
Total revenues from contracts with customers									0.0	0.0
United Kingdom | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0.0	0.0
United Kingdom | Other Operations
Segment reporting information
Total revenues from contracts with customers									$ 0.0	$ 0.0	$ 0.0