Analysis of uncertainty and information acquisition in approval voting with abstention votes

Abstaining from voting is widespread in a voting process. Those candidates not be approved of are generally presumed to be disapproved in approval voting with abstention votes, which may ignore some genuine and meaningful information hidden in abstention votes. This paper constructs an analyzing model for abstention votes based on incomplete information system (IIS) and vague sets, and gives a new method for information acquisition from abstention votes. Corresponding propositions are given and proofed. A votes-counted model for winners in approval voting with abstention votes is constructed subsequently. The results show that comparing with some common methods in which abstention votes is ignored directly or replaced with specified data, quantitative information acquisition from abstention votes may reveal the group preference more truthfully to some extent, which presents a novel reference for information acquisition from uncertain data.