The changing shape of Hemoglobin allows it to bind each successive Oxygen pair more efficiently than the last. As each Heme group binds to an Oxygen it puts a strain on the Oxygen-less Heme groups in the other subunits of Hemoglobin and will eventually cause a conformational change in the other subunits that makes Oxygen bind more efficiently. This switch from a Tense state to a relaxed state and back again is the reason Oxygen binds to Hemoglobin with a sigmoid pattern instead of a hyperbolic curve.
As Epsi said....this is a theory that is widely supported by experimental data and the scientific community as a whole.
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