Revenue - Disaggregation of revenue (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2020	Sep. 30, 2019
Disaggregation of Revenue [Line Items]
Revenue	$ 1,931.6	$ 2,118.8	$ 5,570.6	$ 6,143.5
Americas
Disaggregation of Revenue [Line Items]
Revenue	1,416.1	1,512.8	4,059.4	4,353.3
EMEA
Disaggregation of Revenue [Line Items]
Revenue	223.2	235.5	638.3	667.0
APAC
Disaggregation of Revenue [Line Items]
Revenue	292.3	370.5	872.9	1,123.2
Property, facilities and project management | Over time
Disaggregation of Revenue [Line Items]
Revenue	1,347.1	1,286.1	3,910.9	3,799.8
Property, facilities and project management | Americas | Over time
Disaggregation of Revenue [Line Items]
Revenue	1,007.7	906.1	2,919.8	2,667.9
Property, facilities and project management | EMEA | Over time
Disaggregation of Revenue [Line Items]
Revenue	117.1	96.6	326.2	280.3
Property, facilities and project management | APAC | Over time
Disaggregation of Revenue [Line Items]
Revenue	222.3	283.4	664.9	851.6
Leasing | At a point in time
Disaggregation of Revenue [Line Items]
Revenue	323.5	474.2	896.4	1,341.7
Leasing | Americas | At a point in time
Disaggregation of Revenue [Line Items]
Revenue	245.6	375.6	681.1	1,064.7
Leasing | EMEA | At a point in time
Disaggregation of Revenue [Line Items]
Revenue	44.0	56.0	126.3	161.9
Leasing | APAC | At a point in time
Disaggregation of Revenue [Line Items]
Revenue	33.9	42.6	89.0	115.1
Capital markets | At a point in time
Disaggregation of Revenue [Line Items]
Revenue	155.9	239.3	452.0	667.9
Capital markets | Americas | At a point in time
Disaggregation of Revenue [Line Items]
Revenue	124.2	182.8	347.4	494.8
Capital markets | EMEA | At a point in time
Disaggregation of Revenue [Line Items]
Revenue	24.0	41.7	69.6	101.3
Capital markets | APAC | At a point in time
Disaggregation of Revenue [Line Items]
Revenue	7.7	14.8	35.0	71.8
Valuation and other | At a point in time or over time
Disaggregation of Revenue [Line Items]
Revenue	105.1	119.2	311.3	334.1
Valuation and other | Americas | At a point in time or over time
Disaggregation of Revenue [Line Items]
Revenue	38.6	48.3	111.1	125.9
Valuation and other | EMEA | At a point in time or over time
Disaggregation of Revenue [Line Items]
Revenue	38.1	41.2	116.2	123.5
Valuation and other | APAC | At a point in time or over time
Disaggregation of Revenue [Line Items]
Revenue	$ 28.4	$ 29.7	$ 84.0	$ 84.7