Voting with rubber bands, weights, and strings

We introduce some new voting rules based on a spatial version of the median known as the mediancentre, or Fermat-Weber point. Voting rules based on the mean include many that are familiar: the Borda Count, Kemeny rule, approval voting, etc. (see Zwicker (2008a,b)). These mean rules can be implemented by “voting machines” (interactive simulations of physical mechanisms) that use ideal rubber bands to achieve an equilibrium among the competing preferences of the voters. One consequence is that in any such rule, a voter who is further from consensus exerts a stronger tug on the election outcome, because her rubber band is more stretched.