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Shareholders' Equity (Details) - USD ($)
$ / shares in Units, $ in Millions
 1 Months Ended 3 Months Ended 9 Months Ended 12 Months Ended
Oct. 01, 2021
Jun. 30, 2021
Mar. 31, 2021
Sep. 30, 2022
Jun. 30, 2022
Mar. 31, 2022
Sep. 30, 2021
Jun. 30, 2021
Sep. 30, 2022
Sep. 30, 2021
Dec. 31, 2021
Feb. 07, 2022
Aug. 31, 2021
Jun. 14, 2021
Jan. 31, 2021
Dec. 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                                
Ordinary shares, issued (in shares)       674,166,494         674,166,494   683,139,210          
Ordinary shares, par value (in dollars per share)       $ 0         $ 0   $ 0          
Treasury shares (in shares)       365,014         365,014   547,136          
Preferred stock, dividend rate, percentage                 5.25%            
Preferred Stock, Liquidation Preference Per Share                           $ 100.00    
Shares issued as dividends on our 5.25% Series A Mandatory Convertible Preferred Shares                 $ 0.0 $ 16.1            
Treasury stock sold, average cost per share (in dollars per share)       $ 9.60   $ 15.01                    
Treasury stock acquired, average cost per share (in dollars per share) $ 30.99               $ 16.33              
Stock repurchase program, authorized amount                       $ 1,000.0 $ 250.0      
Stock repurchased and retired (in shares)                 10,700,000              
Treasury Stock Retired, Average Cost Per Share                 $ 16.33              
Stock repurchased and retired             $ 0.0 $ 0.0 $ 175.0 $ 5,117.4            
Stock repurchase program, remaining authorized repurchase amount       $ 825.0         $ 825.0              
Repurchase of ordinary shares (in shares)                 10,700,000              
Treasury Stock, Common, Value       $ 11.3         $ 11.3   $ 16.9          
Ordinary shares, outstanding (in shares)       673,801,480         673,801,480   683,139,210          
Treasury stock sold at lower than repurchase price       $ (1.3) $ (0.3) $ (0.6)                    
Sale of treasury shares (in shares)       140,400   41,700                    
Common Stock, Voting Rights                 one              
Treasury Stock, Value, Acquired, Par Value Method         $ 108.6 $ 66.4     $ 175.0              
CPA Global                                
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                                
Newly issued ordinary shares (in shares)                   1,500,000            
Newly issued ordinary shares, value                             $ 43.9  
Decision Resources Group                                
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                                
Newly issued ordinary shares (in shares)     2,900,000         2,900,000                
Newly issued ordinary shares, value   $ 61.6           $ 61.6                
Treasury Stock                                
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                                
Treasury shares (in shares)   6,300,000 6,300,000 400,000 500,000 2,500,000 6,300,000 6,300,000 400,000 6,300,000 500,000         6,300,000
Stock repurchased and retired (in shares)         8,600,000 2,100,000                    
Stock repurchased and retired         $ (141.7) $ (33.3)                    
Repurchase of ordinary shares (in shares)         6,600,000 4,100,000                    
Treasury Stock, Value   $ 196.0 $ 196.0 $ 11.3 $ 15.6 $ 48.7 $ 196.0 $ 196.0 $ 11.3 $ 196.0 $ 16.9         $ 196.0
Treasury stock sold at lower than repurchase price       $ (4.3) $ 0.0 $ (1.3)                    
Sale of treasury shares (in shares)       (100,000) 0 0                    
Treasury Stock, Value, Acquired, Par Value Method         $ 108.6 $ 66.4                    
Accumulated Deficit                                
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                                
Stock repurchased and retired         9.2 (1.5)     $ 7.7              
Treasury stock sold at lower than repurchase price       $ 3.0 $ (0.3) $ 0.7                    
Ordinary Shares                                
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                                
Dividends to preferred shareholders (in shares)       0 0 0 700,000                  
Stock repurchased and retired (in shares)         0 0                    
Stock repurchased and retired         $ 132.5 $ 34.8                    
Repurchase of ordinary shares (in shares)         6,600,000 4,100,000                    
Ordinary shares, outstanding (in shares)   641,400,000 611,300,000 673,800,000 673,300,000 679,000,000.0 639,700,000 641,400,000 673,800,000 639,700,000 683,100,000         606,300,000
Sale of treasury shares (in shares)       100,000 0 0                    
Preferred Shares                                
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                                
Number of shares issued (in shares)   14,400,000                            
Preferred stock, dividend rate, percentage                 5.25%              
Dividends accrued on our 5.25% Series A Mandatory Convertible Preferred Shares       $ 6.2     $ 6.3   $ 6.2 $ 6.3            
Preferred Shares | Over-Allotment Option                                
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                                
Number of shares issued (in shares)   1,900,000