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Significant Transactions - MediaAlpha (Details) - USD ($) $ / shares in Units, $ in Millions |  |  | 6 Months Ended |  |
--- | --- | --- | --- | --- | ---
Mar. 23, 2021 | Oct. 30, 2020 | Jun. 30, 2021 | Jul. 30, 2021 | Dec. 31, 2020
White Mountains |  |  |  |  |
Other Significant Noncash Transactions [Line Items] |  |  |  |  |
Increase in value per share of investment |  |  | $ 5.50 |  |
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) |  |  | $ 42.10 |  | $ 39.07
Investment owned, balance |  |  | $ 713.2 |  | $ 802.2
Increase in value per share of investment |  |  | $ 1.00 |  |
Marketing Technology (MediaAlpha) | Subsequent Event |  |  |  |  |
Other Significant Noncash Transactions [Line Items] |  |  |  |  |
Share price (in usd per share) |  |  |  | $ 33.40 |
Investment owned, balance |  |  |  | $ 565.8 |
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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