Segment Information Operating Results (Detail) - USD ($) $ in Millions	3 Months Ended	6 Months Ended
Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Segment Reporting Information [Line Items]
Revenues	$ 11,905.5	$ 10,971.7	$ 23,350.7	$ 20,295.1
Pretax Profit (Loss)	999.2	2,268.8	2,867.1	3,143.5
Amortization of intangible assets	14.3	14.1	28.5	28.6
Personal Lines \| Agency \| Underwriting operations
Segment Reporting Information [Line Items]
Revenues	4,220.3	3,919.0	8,318.5	7,747.7
Pretax Profit (Loss)	207.5	550.6	755.0	1,152.2
Personal Lines \| Direct \| Underwriting operations
Segment Reporting Information [Line Items]
Revenues	4,633.9	4,167.9	9,065.6	8,160.3
Pretax Profit (Loss)	128.4	647.2	543.0	1,120.2
Operating Segments \| Underwriting operations
Segment Reporting Information [Line Items]
Revenues	10,982.3	9,648.6	21,402.5	19,079.3
Pretax Profit (Loss)	382.8	1,188.9	1,502.7	2,425.2
Operating Segments \| Personal Lines \| Underwriting operations
Segment Reporting Information [Line Items]
Revenues	8,854.2	8,086.9	17,384.1	15,908.0
Pretax Profit (Loss)	$ 335.9	$ 1,197.8	$ 1,298.0	$ 2,272.4
Personal auto insurance percentage of the total personal lines segment net premiums earned	94.00%	94.00%	94.00%	94.00%
Operating Segments \| Commercial Lines \| Underwriting operations
Segment Reporting Information [Line Items]
Revenues	$ 1,621.8	$ 1,129.0	$ 3,039.6	$ 2,318.0
Pretax Profit (Loss)	130.1	179.8	358.6	292.3
Operating Segments \| Property \| Underwriting operations
Segment Reporting Information [Line Items]
Revenues	502.3	432.7	974.8	853.3
Pretax Profit (Loss)	(83.3)	(188.7)	(154.0)	(139.5)
Amortization of intangible assets	14.1		28.3	28.6
Operating Segments \| Other Indemnity \| Underwriting operations
Segment Reporting Information [Line Items]
Revenues	4.0	0.0	4.0	0.0
Pretax Profit (Loss)	0.1	0.0	0.1	0.0
Segment Reconciling Items \| Fees and other revenues
Segment Reporting Information [Line Items]
Revenues	176.2	129.5	341.9	283.0
Segment Reconciling Items \| Service businesses
Segment Reporting Information [Line Items]
Revenues	74.5	59.0	128.3	110.6
Pretax Profit (Loss)	6.6	6.2	11.1	10.3
Segment Reconciling Items \| Investment income
Segment Reporting Information [Line Items]
Revenues	672.5	1,134.6	1,478.0	822.2
Pretax Profit (Loss)	666.2	1,130.1	1,466.1	812.4
Segment Reconciling Items \| Interest expense
Segment Reporting Information [Line Items]
Pretax Profit (Loss)	$ (56.4)	$ (56.4)	$ (112.8)	$ (104.4)

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