Segment Information - Revenue (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Segment reporting information
Revenues from contracts with customers	$ 427.5	$ 307.9	$ 294.3
Other revenues	517.3	872.8	599.1
Total revenues	944.8	1,180.7	893.4
HG Global-BAM
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Other revenues	23.0	68.5	66.6
Total revenues	23.0	68.5	66.6
Ark
Segment reporting information
Revenues from contracts with customers	0.0
Other revenues	668.5
Total revenues	668.5	0.0	0.0
NSM
Segment reporting information
Revenues from contracts with customers	330.4	285.1	233.1
Other revenues	0.0	0.0	0.0
Total revenues	330.4	285.1	233.1
Kudu
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Other revenues	134.0	45.7	21.2
Total revenues	134.0	45.7	21.2
MediaAlpha
Segment reporting information
Revenues from contracts with customers			48.8
Other revenues			0.0
Total revenues	0.0	0.0	48.8
Other Operations
Segment reporting information
Revenues from contracts with customers	97.1	22.8	12.4
Other revenues	(308.2)	758.6	511.3
Total revenues	(211.1)	781.4	523.7
Specialty Transportation
Segment reporting information
Revenues from contracts with customers	97.2	85.5	77.6
Specialty Transportation | HG Global-BAM
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Specialty Transportation | Ark
Segment reporting information
Revenues from contracts with customers	0.0
Specialty Transportation | NSM
Segment reporting information
Revenues from contracts with customers	97.2	85.5	77.6
Specialty Transportation | Kudu
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Specialty Transportation | MediaAlpha
Segment reporting information
Revenues from contracts with customers			0.0
Specialty Transportation | Other Operations
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Pet
Segment reporting information
Revenues from contracts with customers	76.3		45.9
Pet | HG Global-BAM
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Pet | Ark
Segment reporting information
Revenues from contracts with customers	0.0	55.0	45.9
Pet | NSM
Segment reporting information
Revenues from contracts with customers	76.3	0.0	0.0
Pet | Kudu
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Pet | Other Operations
Segment reporting information
Revenues from contracts with customers	0.0	55.0	0.0
Real Estate
Segment reporting information
Revenues from contracts with customers	34.4	44.9	34.7
Real Estate | HG Global-BAM
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Real Estate | Ark
Segment reporting information
Revenues from contracts with customers	0.0
Real Estate | NSM
Segment reporting information
Revenues from contracts with customers	34.4	44.9	34.7
Real Estate | Kudu
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Real Estate | MediaAlpha
Segment reporting information
Revenues from contracts with customers			0.0
Real Estate | Other Operations
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Social Services
Segment reporting information
Revenues from contracts with customers	33.9	28.9	25.9
Social Services | HG Global-BAM
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Social Services | Ark
Segment reporting information
Revenues from contracts with customers	0.0
Social Services | NSM
Segment reporting information
Revenues from contracts with customers	33.9	28.9	25.9
Social Services | Kudu
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Social Services | MediaAlpha
Segment reporting information
Revenues from contracts with customers			0.0
Social Services | Other Operations
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Other
Segment reporting information
Revenues from contracts with customers	45.1	29.7	25.9
Other | HG Global-BAM
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Other | Ark
Segment reporting information
Revenues from contracts with customers	0.0
Other | NSM
Segment reporting information
Revenues from contracts with customers	35.5	21.4	19.0
Other | Kudu
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Other | MediaAlpha
Segment reporting information
Revenues from contracts with customers			0.0
Other | Other Operations
Segment reporting information
Revenues from contracts with customers	9.6	8.3	6.9
Total commission and other revenue
Segment reporting information
Revenues from contracts with customers	340.0	293.4	240.0
Total commission and other revenue | HG Global-BAM
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Total commission and other revenue | Ark
Segment reporting information
Revenues from contracts with customers	0.0
Total commission and other revenue | NSM
Segment reporting information
Revenues from contracts with customers	330.4	285.1	233.1
Total commission and other revenue | Kudu
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Total commission and other revenue | MediaAlpha
Segment reporting information
Revenues from contracts with customers			0.0
Total commission and other revenue | Other Operations
Segment reporting information
Revenues from contracts with customers	9.6	8.3	6.9
Advertising revenues
Segment reporting information
Revenues from contracts with customers			48.8
Advertising revenues | HG Global-BAM
Segment reporting information
Revenues from contracts with customers			0.0
Advertising revenues | NSM
Segment reporting information
Revenues from contracts with customers			0.0
Advertising revenues | Kudu
Segment reporting information
Revenues from contracts with customers			0.0
Advertising revenues | MediaAlpha
Segment reporting information
Revenues from contracts with customers			48.8
Advertising revenues | Other Operations
Segment reporting information
Revenues from contracts with customers			0.0
Products and service revenues
Segment reporting information
Revenues from contracts with customers	87.5	14.5	5.5
Products and service revenues | HG Global-BAM
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Products and service revenues | Ark
Segment reporting information
Revenues from contracts with customers	0.0
Products and service revenues | NSM
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
Products and service revenues | Kudu
Segment reporting information
Revenues from contracts with customers	0.0	0.0
Products and service revenues | MediaAlpha
Segment reporting information
Revenues from contracts with customers			0.0
Products and service revenues | Other Operations
Segment reporting information
Revenues from contracts with customers	87.5	14.5	5.5
United Kingdom
Segment reporting information
Revenues from contracts with customers	53.1		30.0
United Kingdom | HG Global-BAM
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
United Kingdom | Ark
Segment reporting information
Revenues from contracts with customers	0.0	49.4	30.0
United Kingdom | NSM
Segment reporting information
Revenues from contracts with customers	53.1	0.0	0.0
United Kingdom | Kudu
Segment reporting information
Revenues from contracts with customers	0.0	0.0	0.0
United Kingdom | Other Operations
Segment reporting information
Revenues from contracts with customers	$ 0.0	$ 49.4	$ 0.0