It is regretted that the originally published paper (doi:10.1017/S0266267111000010, published online 22 June 2011) was not the author's final amended version. We apologise for this oversight and reproduce the entire corrected paper here in print and online, with revised notation. In order to account for non-traditional preference relations the present paper develops a new, richer framework for preference relations. This new framework provides characterizations of non-traditional preference relations, such as incommensurateness and instability, that may hold when neither preference nor indifference do. The new framework models relations with swaps, which are conceived of as transfers from one alternative state to another. The traditional framework analyses dyadic preference relations in terms of a hypothetical choice between the two compared alternatives. The swap framework extends this approach by analysing dyadic preference relations in terms of two hypothetical choices: the choice between keeping the first of the compared alternatives or swapping it for the second; and the choice between keeping the second alternative or swapping it for the first.