We propose a new method for conducting Single transferable vote (STV) elections and provide a unified method for describing classic STV procedures (the Gregory Method, the inclusive Gregory method and the Weighted inclusive Gregory method) as an iterative procedure.We also propose a modification for quota definition that improves the theoretical properties of the procedures. The method is justified by utilising a newset of axioms.We showthat this method extends theWeighted inclusive Gregorymethod with themodified definition of quota and random equiprobable selection of a winning coalition in each iteration. The results are extended to the methods, allowing fractional numbers of votes.