Choice architecture during data collection influences consumers’ expressed privacy valuations. We explore how this influence affects the quality of data collected, including both volume and representativeness. To this end, we run a large-scale choice experiment to elicit consumers’ valuation for their Facebook data while randomizing two common choice frames: default and price anchor. An opt-out default decreases valuations by 14-22% compared to opt-in, while a $0–50 price anchor decreases valuation by 37-53% compared to a $50–100 anchor. Moreover, in some consumer segments, the susceptibility to frame influence negatively correlates with consumers’ average valuation. This negative correlation creates a potential trade-off between data volume and representativeness. Thus, conventional frame optimization practices that maximize the volume of data supply can have opposite effects on its representativeness. A bias exacerbating effect can emerge when consumers’ privacy valuations and frame effects are negatively correlated. We demonstrate the magnitude of the volume-bias trade-off in our data and argue that it should be a decision making factor in choice architecture design.