Investment Securities - Other Long-Term Investments (Details) - USD ($) $ in Millions	Sep. 30, 2023	Dec. 31, 2022
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	$ 1,895.8	$ 1,488.0
PassportCard/DavidShield
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	150.0	135.0
Elementum Holdings, L.P.
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	35.0	30.0
Mandatorily redeemable preferred securities
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	58.5
Other unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	41.8	37.2
Private equity funds and hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	299.3	197.8
Bank loan fund
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	189.3	174.8
ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	159.5	49.3
Lloyd’s trust deposits
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	150.3	137.4
Private debt instruments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	14.8	9.6
Other
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	22.0	21.0
Kudu’s Participation Contracts
Debt and Equity Securities, FV-NI [Line Items]
Equity method investments	775.3	695.9
Kudu’s Participation Contracts | Asset Management (Kudu)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	775.3	695.9
Investments, Excluding MediaAlpha | Total unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	1,060.6	898.1
Operating Segments | P&C Insurance and Reinsurance (Ark/WM Outrigger)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	416.6	373.6
Operating Segments | P&C Insurance and Reinsurance (Ark/WM Outrigger) | PassportCard/DavidShield
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | P&C Insurance and Reinsurance (Ark/WM Outrigger) | Elementum Holdings, L.P.
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | P&C Insurance and Reinsurance (Ark/WM Outrigger) | Mandatorily redeemable preferred securities
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0
Operating Segments | P&C Insurance and Reinsurance (Ark/WM Outrigger) | Other unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | P&C Insurance and Reinsurance (Ark/WM Outrigger) | Private equity funds and hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	55.4	40.4
Operating Segments | P&C Insurance and Reinsurance (Ark/WM Outrigger) | Bank loan fund
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	189.3	174.8
Operating Segments | P&C Insurance and Reinsurance (Ark/WM Outrigger) | ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | P&C Insurance and Reinsurance (Ark/WM Outrigger) | Lloyd’s trust deposits
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	150.3	137.4
Operating Segments | P&C Insurance and Reinsurance (Ark/WM Outrigger) | Private debt instruments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | P&C Insurance and Reinsurance (Ark/WM Outrigger) | Other
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	21.6	21.0
Operating Segments | P&C Insurance and Reinsurance (Ark/WM Outrigger) | Kudu’s Participation Contracts | Asset Management (Kudu)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | P&C Insurance and Reinsurance (Ark/WM Outrigger) | Investments, Excluding MediaAlpha | Total unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | Kudu
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	780.7	695.9
Operating Segments | Kudu | PassportCard/DavidShield
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | Kudu | Elementum Holdings, L.P.
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | Kudu | Mandatorily redeemable preferred securities
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0
Operating Segments | Kudu | Other unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | Kudu | Private equity funds and hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | Kudu | Bank loan fund
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | Kudu | ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | Kudu | Lloyd’s trust deposits
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | Kudu | Private debt instruments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	5.4	0.0
Operating Segments | Kudu | Other
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Operating Segments | Kudu | Kudu’s Participation Contracts | Asset Management (Kudu)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	775.3	695.9
Operating Segments | Kudu | Investments, Excluding MediaAlpha | Total unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	775.3	695.9
Other Operations
Debt and Equity Securities, FV-NI [Line Items]
Equity method investments	188.8	168.6
Other long-term investments	698.5	418.5
Other Operations | PassportCard/DavidShield
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	150.0	135.0
Other Operations | Elementum Holdings, L.P.
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	35.0	30.0
Other Operations | Mandatorily redeemable preferred securities
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	58.5
Other Operations | Other unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	41.8	37.2
Other Operations | Private equity funds and hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	243.9	157.4
Other Operations | Bank loan fund
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Other Operations | ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	159.5	49.3
Other Operations | Lloyd’s trust deposits
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Other Operations | Private debt instruments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	9.4	9.6
Other Operations | Other
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.4	0.0
Other Operations | Kudu’s Participation Contracts | Asset Management (Kudu)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Other Operations | Investments, Excluding MediaAlpha | Total unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	$ 285.3	$ 202.2