b'@online{Afshinmehr2410.02274,'b'\nTITLE = {{MMS} Approximations Under Additive Leveled Valuations},\nAUTHOR = {Afshinmehr, Mahyar and Kazemi, Mehrafarin and Mehlhorn, Kurt},\nLANGUAGE = {eng},\nURL = {https://arxiv.org/abs/2410.02274},\nEPRINT = {2410.02274},\nEPRINTTYPE = {arXiv},\nYEAR = {2024},\nMARGINALMARK = {$\\bullet$},\nABSTRACT = {We study the problem of fairly allocating indivisible goods to a set of<br>agents with additive leveled valuations. A valuation function is called leveled<br>if and only if bundles of larger size have larger value than bundles of smaller<br>size. The economics literature has well studied such valuations.<br> We use the maximin-share (MMS) and EFX as standard notions of fairness. We<br>show that an algorithm introduced by Christodoulou et al. ([11]) constructs an<br>allocation that is EFX and $\\frac{\\lfloor \\frac{m}{n} \\rfloor}{\\lfloor<br>\\frac{m}{n} \\rfloor + 1}\\text{-MMS}$. In the paper, it was claimed that the<br>allocation is EFX and $\\frac{2}{3}\\text{-MMS}$. However, the proof of the<br>MMS-bound is incorrect. We give a counter-example to their proof and then prove<br>a stronger approximation of MMS.<br>},\n}\n'