A scaling procedure has been developed for ordering binary parallelogram preference data. The procedure uses minimum variance of the item ranks averaged across persons as the optimization criterion. Two seriation strategies are employed. One is pairwise interchange. The second joins together the vector end points and breaks this circle between each pair of points. The two strategies are alternated until the minimum variance across persons is found. The procedure has been used successfully on artificial data, attitudinal data collected by the authors, and previously published archeological data. The procedure is an improvement on alternate methods in that it uses all of the information in the data and provides easily interpretable results. Three attitudinal scales are included. (Author)