Rankings of candidates or other stimuli may often be easier to obtain than candidate ratings or other forms of survey responses. Unfortunately, rankings are interpersonally incomparable ordinal scales that present difficult statistical problems. This paper presents a new statistical method for estimating linear factor and ideal point models for ranking data. The method is explicated with artificial data and through the analysis of 1,200 rankings of eight presidential candidates by Democrats who attended the 1984 Iowa caucuses. The preferences of the Iowa Democrats can be represented adequately by two dimensions that can be described as liberalism-conservatism and personal suitability. These results for candidate rankings seem much more sensible than those obtained by arbitrarily assigning "ranking numbers" to the data and using standard factor analysis methods.