 The literature contains several variants of this theorem. One variant drops the agenda property of path-connectedness and strengthens independence to systematicity. A second variant drops the agenda property of pair-negatability and imposes a monotonicity condition on the aggregation rule (requiring that additional support never hurt an accepted proposition) (Nehring and Puppe 2010, reformulating a result from Nehring and Puppe 2002, Other Internet Resources). A final variant drops both path-connectedness and pair-negatability while imposing both systematicity and monotonicity (ibid.).