Segment Information Operating Results (Detail) - USD ($) $ in Millions	3 Months Ended
Mar. 31, 2021	Mar. 31, 2020
Segment Reporting Information [Line Items]
Revenues	$ 11,445.2	$ 9,323.4
Pretax Profit (Loss)	1,867.9	874.7
Amortization of intangible assets	14.2	14.5
Personal Lines \| Agency \| Underwriting operations
Segment Reporting Information [Line Items]
Revenues	4,098.2	3,828.7
Pretax Profit (Loss)	547.5	601.6
Personal Lines \| Direct \| Underwriting operations
Segment Reporting Information [Line Items]
Revenues	4,431.7	3,992.4
Pretax Profit (Loss)	414.6	473.0
Operating Segments \| Underwriting operations
Segment Reporting Information [Line Items]
Revenues	10,420.2	9,430.7
Pretax Profit (Loss)	1,119.9	1,236.3
Operating Segments \| Personal Lines \| Underwriting operations
Segment Reporting Information [Line Items]
Revenues	8,529.9	7,821.1
Pretax Profit (Loss)	$ 962.1	$ 1,074.6
Personal auto insurance percentage of the total personal lines segment net premiums earned	94.00%	94.00%
Operating Segments \| Commercial Lines \| Underwriting operations
Segment Reporting Information [Line Items]
Revenues	$ 1,417.8	$ 1,189.0
Pretax Profit (Loss)	228.5	112.5
Operating Segments \| Property \| Underwriting operations
Segment Reporting Information [Line Items]
Revenues	472.5	420.6
Pretax Profit (Loss)	(70.7)	49.2
Amortization of intangible assets	14.2	14.5
Segment Reconciling Items \| Fees and other revenues
Segment Reporting Information [Line Items]
Revenues	165.7	153.5
Segment Reconciling Items \| Service businesses
Segment Reporting Information [Line Items]
Revenues	53.8	51.6
Pretax Profit (Loss)	4.5	4.1
Segment Reconciling Items \| Investment income
Segment Reporting Information [Line Items]
Revenues	805.5	(312.4)
Pretax Profit (Loss)	799.9	(317.7)
Segment Reconciling Items \| Interest expense
Segment Reporting Information [Line Items]
Pretax Profit (Loss)	$ (56.4)	$ (48.0)

Percentage of segment revenue attributable to personal auto insurance.

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Amount of revenue recognized from goods sold, services rendered, insurance premiums, or other activities that constitute an earning process. Includes, but is not limited to, investment and interest income before deduction of interest expense when recognized as a component of revenue, and sales and trading gain (loss).

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