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Segment Information Operating Results (Detail) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2020	Sep. 30, 2019
Segment Reporting Information [Line Items]
Revenues	$ 10,947.2	$ 9,530.5	$ 31,242.3	$ 28,281.2
Pretax Profit (Loss)	1,923.5	1,010.3	5,067.0	3,821.4
Amortization of intangible assets	14.2	15.8	42.8	51.7
Personal Lines | Agency | Underwriting operations
Segment Reporting Information [Line Items]
Revenues	4,001.6	3,703.4	11,749.3	10,851.5
Pretax Profit (Loss)	596.5	380.2	1,748.7	1,267.9
Personal Lines | Direct | Underwriting operations
Segment Reporting Information [Line Items]
Revenues	4,309.8	3,804.0	12,470.1	11,113.7
Pretax Profit (Loss)	517.6	291.7	1,637.8	940.2
Operating Segments | Underwriting operations
Segment Reporting Information [Line Items]
Revenues	9,973.5	9,012.2	29,052.8	26,296.7
Pretax Profit (Loss)	1,217.1	732.5	3,642.3	2,533.0
Operating Segments | Personal Lines | Underwriting operations
Segment Reporting Information [Line Items]
Revenues	8,311.4	7,507.4	24,219.4	21,965.2
Pretax Profit (Loss)	$ 1,114.1	$ 671.9	$ 3,386.5	$ 2,208.1
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	$ 1,214.8	$ 1,106.9	$ 3,532.8	$ 3,190.4
Pretax Profit (Loss)	155.9	69.7	448.2	360.7
Operating Segments | Property | Underwriting operations
Segment Reporting Information [Line Items]
Revenues	447.3	397.9	1,300.6	1,141.1
Pretax Profit (Loss)	(52.9)	(9.1)	(192.4)	(35.8)
Amortization of intangible assets	14.2	15.8	42.8	51.7
Segment Reconciling Items | Fees and other revenues
Segment Reporting Information [Line Items]
Revenues	151.8	138.4	434.8	403.4
Segment Reconciling Items | Service businesses
Segment Reporting Information [Line Items]
Revenues	58.8	51.5	169.4	144.1
Pretax Profit (Loss)	4.4	2.8	14.7	12.0
Segment Reconciling Items | Investment income
Segment Reporting Information [Line Items]
Revenues	763.1	328.4	1,585.3	1,437.0
Pretax Profit (Loss)	758.4	322.5	1,570.8	1,418.7
Segment Reconciling Items | Interest expense
Segment Reporting Information [Line Items]
Pretax Profit (Loss)	$ (56.4)	$ (47.5)	$ (160.8)	$ (142.3)

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