People regularly get information about the political world in visual form, such as graphs of past economic growth, nonverbal cues from politicians, or projections of future climate change. Visual characteristics affect people’s preferences, but it is difficult to measure the extent of this effect precisely and concisely in surveys. We present a new adaptive design that measures the impact of visual characteristics on people’s preferences: The plot staircase. We apply it to graphs of time series data, identifying the effect of the slope of a sequence on evaluations of the sequence. The plot staircase replicates the existing finding that people have a strong preference for increasing trends. Using fewer survey questions than past approaches, it measures at the individual level how much overall welfare a survey respondent is willing to sacrifice for an increasing trend. We demonstrate the flexibility of the plot staircase across domains (economic growth, jobs creation, and the COVID-19 vaccine rollout) and across sequence characteristics. Survey measurement is more difficult for concepts that cannot be represented textually or numerically; our method enables researchers to measure preferences for graphical properties not reducible to the individual pieces of information.