We analyze 10 three-candidate elections (and mock elections) conducted under approval voting (AV) using a method developed by Falmagne and Regenwetter (1996) that allows us to construct a distribution of rank orders from subset choice data. The elections were held by the Institute of Management Science, the Mathematical Association of America, several professional organizations in Britain, and the Institute of Electrical and Electronics Engineers. Seven of the 10 elections satisfy the conditions under which the Falmagne-Regenwetter method is suitable. For these elections we recreate possible underlying preferences of the electorate. On the basis of these distributions of preferences we find strong evidence that AV would have selected Condorcet winners when they exist and would have always selected the Borda winner. Thus, we find that AV is not just simple to use, but also gives rise to outcomes that well reflect voter preferences. Our results also have an important implication for the general study of social choice processes. They suggest that transitive majority orderings may be expected in real-world settings more often then the formal social choice literature suggests. In six out of seven data sets we find social welfare orders; only one data set generates cycles anywhere in the solution space.