For sufficiently large n, agents with XOS valuations receive an α-APS allocation (hence α-MMS) with α > 1/4.
Sincew α+w 1 = 1, we can express β≤αwα+ (1−wα) =⇒wα≤1−β 1−α
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On MMS, APS and XOS
For sufficiently large n, agents with XOS valuations receive an α-APS allocation (hence α-MMS) with α > 1/4.