With the emergence of the Software 3.0 era, there is a growing trend of compressing and integrating large models into software systems, with significant societal implications. Regrettably, in numerous instances, model compression techniques impact the fairness performance of these models and thus the ethical behavior of DNN-powered software. One of the most notable example is the Lottery Ticket Hypothesis (LTH), a prevailing model pruning approach. This paper demonstrates that fairness issue of LTHbased pruning arises from both its subnetwork selection and training procedures, highlighting the inadequacy of existing remedies. To address this, we propose a novel pruning framework, Ballot, which employs a novel conflict-detection-based subnetwork selection to find accurate and fair subnetworks, coupled with a refined training process to attain a high-performance model, thereby improving the fairness of DNN-powered software. By means of this procedure, Ballot improves the fairness of pruning by 38.00%, 33.91%, 17.96%, and 35.82% compared to state-of-the-art baselines, namely Magnitude Pruning, Standard LTH, SafeCompress, and FairScratch respectively, based on our evaluation of five popular datasets and three widely used models. Our code is available at https://anonymous.4open.science/r/Ballot-506E.