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...

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...

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...

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...

We introduce the following basic voting method: voters submit both a “consensus” and a “fall-back” ballot. If all “consensus” ballots name the same option, it wins; otherwise, a randomly drawn “fall-back” ballot decides. If there is one potential consensus option that everyone...

Are there group decision methods which (i) give everyone, including minorities, an equal share of effective decision power even when 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...