The paper mentioned above has been published:

Stephan Kreutzer, Sang-il Oum, Paul Seymour, Dominic van der Zypen, David R. Wood. 
"Majority Colourings of Digraphs"
Electronic Journal of Combinatorics, 24(2):#P2.25, 2017. 
http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i2p25

Other papers have appeared on this topic: 

Marcin Anholcer, Bartłomiej Bosek, Jarosław Grytczuk. 
"Every digraph is majority 4-choosable"
http://arxiv.org/abs/1608.06912

Fiachra Knox, Robert Šámal. 
"Linear Bound for Majority Colourings of Digraphs"
https://arxiv.org/abs/1701.05715

A. Girao, T. Kittipassorn, and K. Popielarz. 
"Generalised majority colourings of digraphs"
https://arxiv.org/abs/1701.03780