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Investments - Cost, Gross Unrealized Gains and Losses, and Estimated Fair Value of Available for Sale Investments in Fixed Income Maturities and Short-Term Investments (Details) - USD ($) $ in Millions	Sep. 30, 2024	Dec. 31, 2023	Dec. 31, 2022
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost	$ 4,657.4	$ 4,330.0	$ 4,131.3
Gross unrealized gains	43.9	17.3	3.6
Gross unrealized losses	(143.5)	(221.8)	(338.6)
Allowance for credit losses	(2.0)	(2.9)	(7.7)
Fair market value	4,555.8	4,122.6	3,788.6
Total short-term investments — Available for sale
Schedule of Trading Securities and Other Trading Items [Line Items]
Gross unrealized gains	0.0	0.0	0.0
Gross unrealized losses	0.0	0.0	(0.4)
Allowance for credit losses	0.0	0.0	0.0
Total fixed income securities — Available for sale
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost	4,749.0	4,438.3	4,183.7
Gross unrealized gains	44.1	17.5	3.6
Gross unrealized losses	(143.5)	(221.8)	(339.0)
Allowance for credit losses	(2.0)	(2.9)	(7.7)
Fair market value	4,647.6	4,231.1	3,840.6
U.S. government
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost	1,329.2	1,224.9	1,003.7
Gross unrealized gains	11.0	4.4	0.0
Gross unrealized losses	(13.8)	(26.7)	(50.7)
Allowance for credit losses	0.0	0.0	0.0
Fair market value	1,326.4	1,202.6	953.0
U.S. agency
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost	7.5	7.5	9.2
Gross unrealized gains	0.0	0.0	0.0
Gross unrealized losses	(0.1)	(0.3)	(0.4)
Allowance for credit losses	0.0	0.0	0.0
Fair market value	7.4	7.2	8.8
Municipal
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost	81.2	133.6	159.9
Gross unrealized gains	0.1	0.0	0.0
Gross unrealized losses	(1.6)	(5.0)	(9.4)
Allowance for credit losses	(0.3)	(0.5)	(1.0)
Fair market value	79.4	128.1	149.5
Corporate
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost	1,999.9	2,051.1	2,016.9
Gross unrealized gains	24.5	12.1	3.5
Gross unrealized losses	(58.5)	(101.5)	(169.1)
Allowance for credit losses	(1.7)	(2.4)	(6.3)
Fair market value	1,964.2	1,959.3	1,845.0
Non-U.S. government-backed corporate
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost	146.1	106.5	119.4
Gross unrealized gains	1.2	0.1	0.0
Gross unrealized losses	(3.1)	(5.9)	(8.8)
Allowance for credit losses	0.0	0.0	(0.2)
Fair market value	144.2	100.7	110.4
Non-U.S government
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost	273.0	279.9	225.2
Gross unrealized gains	2.1	0.6	0.1
Gross unrealized losses	(2.2)	(6.7)	(11.5)
Allowance for credit losses	0.0	0.0	(0.2)
Fair market value	272.9	273.8	213.6
Asset-backed
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost	198.9
Gross unrealized gains	1.4
Gross unrealized losses	(0.2)
Allowance for credit losses	0.0
Fair market value	200.1
Agency mortgage-backed
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost		519.9	590.4
Gross unrealized gains			0.0
Gross unrealized losses			(87.7)
Allowance for credit losses			0.0
Fair market value		445.1	502.7
Total short-term investments — Available for sale
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost		93.6	52.4
Fair market value		93.6	52.0
Agency commercial mortgage-backed securities
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost	5.0	6.6	6.6
Gross unrealized gains	0.0	0.0	0.0
Gross unrealized losses	(0.5)	(0.8)	(1.0)
Allowance for credit losses	0.0	0.0	0.0
Fair market value	4.5	5.8	$ 5.6
Residential Mortgage-Backed Securities
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost	616.6	519.9
Gross unrealized gains	3.6	0.1
Gross unrealized losses	(63.5)	(74.9)
Allowance for credit losses	0.0	0.0
Fair market value	556.7	445.1
Privately-held investments, available for sale
Schedule of Trading Securities and Other Trading Items [Line Items]
Fixed income securities, available for sale, amortized cost		14.7
Gross unrealized gains	0.2	0.2
Gross unrealized losses	0.0	0.0
Allowance for credit losses	0.0	0.0
Fair market value	$ 25.3	$ 14.9

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