In this paper we characterise the Orlovsky solution and what we refer to as the family of threshold solutions. Our family of threshold solutions are somewhat larger than the family of solutions which select only those alternatives that secure a certain prespecified proportion of the votes against all other alternatives. Our family of threshold solutions also include ones which select only those alternatives that exceed a certain prespecified proportion of the votes against all other alternatives. This is the price we pay for ommitting continuity from our axiomatic characterizations.