This paper characterizes the set of income allocations attainable through a sequence of equalizing decentralized pair-wise transfers that each preserve the original ranking of the donor and the recipient. This kind of transfer has been considered in the literature on income distribution following Daltons famous 1920 article, and the concept is often attributed to him. We provide a description of the set of allocations attainable through a sequence of such transfers. This paper argues that, although those transfers are often mentioned in the literature on income inequality, they do not really play any role there. It also argues that such a transfer concept is, on the other hand, of great interest in modeling altruism and its consequences.