Share-based Compensation (Share-Based Compensation Expense) (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2024	Mar. 31, 2023
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based compensation expense	$ 44.6	$ 43.8
Percent of annual incentive compensation receivable in shares	100.00%
Other operating expense
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based compensation expense	$ 5.3	2.2
SG&A expense
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based compensation expense	39.3	41.6
Liberty Global
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based compensation expense	43.4	36.0
Non-performance based incentive awards | Liberty Global
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based compensation expense	32.5	29.2
Performance-based incentive awards | Liberty Global
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based compensation expense	2.1	0.0
Other | Liberty Global
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based compensation expense	8.8	6.8
Other
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based compensation expense	$ 1.2	$ 7.8