Segment Information - Adjusted EBITDA (Details) - USD ($)	3 Months Ended								12 Months Ended			24 Months Ended
	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2018	Dec. 31, 2016
Segment Reporting Revenue Reconciling Item [Line Items]
Adjusted EBITDA									$ 946,360,000	$ 1,124,390,000	$ 1,078,571,000
Less adjustments:
Impairment and related charges									0	0	81,112,000
Depreciation and amortization of property and equipment									310,573,000	303,612,000	264,880,000
Amortization of capitalized implementation costs									39,444,000	41,724,000	40,131,000
Acquisition-related amortization									64,604,000	68,008,000	95,860,000
Amortization of upfront incentive consideration									82,935,000	77,622,000	67,411,000
Interest expense, net									156,391,000	157,017,000	153,925,000
Loss on extinguishment of debt									0	633,000	1,012,000
Other, net									9,432,000	8,509,000	(36,530,000)
Restructuring and other costs									0	0	23,975,000
Acquisition-related costs									41,037,000	3,266,000	0
Litigation costs, net									(24,579,000)	8,323,000	(35,507,000)
Stock-based compensation									66,885,000	57,263,000	44,689,000
Provision for income taxes									35,326,000	57,492,000	128,037,000
Income from continuing operations	$ 11,824,000	$ 65,180,000	$ 28,094,000	$ 59,214,000	$ 87,028,000	$ 70,879,000	$ 92,565,000	$ 90,449,000	$ 164,312,000	340,921,000	249,576,000
TRA liability benefit (expense)										5,000,000	58,000,000	$ (55,000,000)
Minimum
Less adjustments:
Average expected life of the service contract to cost of revenue									3 years
Maximum
Less adjustments:
Average expected life of the service contract to cost of revenue									10 years
Workforce Reduction
Less adjustments:
Restructuring and other costs											25,000,000
US Airways Litigation
Less adjustments:
Litigation costs, net											(43,000,000)
Accrued loss		$ 32,000,000							$ 32,000,000
Litigation accrual	$ 0								$ 0				$ 32,000,000
Unasserted Claim
Less adjustments:
Litigation accrual					$ 5,000,000					5,000,000		$ 5,000,000
Other, Net
Less adjustments:
TRA liability benefit (expense)										(5,000,000)	60,000,000
Gain on sale of investments										8,000,000
Loss on debt modification											15,000,000
Income Tax Provision
Less adjustments:
Remeasurement of deferred tax assets										$ 27,000,000	$ 47,000,000