In online advertising, a set of potential advertisements can be ranked by a certain auction system where usually the top-1 advertisement would be selected and displayed at an advertising space. In this paper, we show a selection bias issue that is present in an auction system. We analyze that the selection bias destroy truthfulness of the auction, which implies that the buyers (advertisers) on the auction can not maximize their profits. Although selection bias is well known in the field of statistics and there are lot of studies for it, our main contribution is to combine the theoretical analysis of the bias with the auction mechanism. In our experiment using online A/B testing, we evaluate the selection bias on an auction system whose ranking score is the function of predicted CTR (click through rate) of advertisement. The experiment showed that the selection bias is drastically reduced by using a multi-task learning which learns the data for all advertisements.