Are there collective decision methods which (i) give everyone, including minorities, an equal share of effective power even if voters act strategically, (ii) promote consensus and equality, rather than polarization and inequality, and (iii) do not favour the status quo or rely too much on...

In this paper we show how theorems of Borsuk-Ulam and Tucker can be used to construct a consensus-halving: a division of an object into two portions so that each of n people believe the portions are equally split. Moreover, the division takes at most n cuts, which is best possible. This extends...