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Significant Transactions - MediaAlpha (Details) - USD ($) $ / shares in Units, $ in Millions			9 Months Ended
	Mar. 23, 2021	Oct. 30, 2020	Sep. 30, 2021	Oct. 31, 2021	Dec. 31, 2020
White Mountains
Other Significant Noncash Transactions [Line Items]
Increase in value per share of investment (in dollars per share)			$ 5.60
Secondary Offering | Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Sale of stock, number of shares issued in transaction (in shares)	8,050,000.00
Sale of stock, price per share (in usd per share)	$ 46.00	$ 19.00
Sale of stock, price per share, net of underwriting fees (in USD per share)	$ 44.62	$ 17.67
Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Proceeds from dividends received		$ 55.0
Investment owned (in shares)			16,900,000		20,500,000
Ownership interest (as a percent)			28.40%		35.00%
Fully diluted ownership interest (as a percent)			26.30%		32.30%
Share price (in usd per share)			$ 18.68		$ 39.07
Investment owned, balance			$ 316.4		$ 802.2
Increase in value per share of investment (in dollars per share)			$ 1.00
Marketing Technology (MediaAlpha) | Subsequent Event
Other Significant Noncash Transactions [Line Items]
Share price (in usd per share)				$ 17.53
Investment owned, balance				$ 297.0
Marketing Technology (MediaAlpha) | IPO
Other Significant Noncash Transactions [Line Items]
Sale of stock, number of shares issued in transaction (in shares)		3,600,000
Sale of stock, consideration received in transaction		$ 63.8
Marketing Technology (MediaAlpha) | Secondary Offering
Other Significant Noncash Transactions [Line Items]
Sale of stock, number of shares issued in transaction (in shares)	3,600,000
Sale of stock, consideration received in transaction	$ 160.3

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