Theoretical guarantee for crowdsourcing learning with unsure option

•The upper bound of minimally sufficient number of crowd labels required for learning a probably approximately correct (PAC) classification model with and without the unsure option, are given respectively.•A condition under which providing (or not to provide) unsure option for crowdsourcing learning is derived.•The first two theoretical results are extended to guide non-identical label options to different workers, i.e., provide different label options (with or without unsure option) to different workers.•Several useful applications of theoretical results are presented.