Multiwinner approval rules as apportionment methods

During the first round of the 2012 French presidential election, participants in an in situ experiment were invited to vote according to "evaluative voting", which involves rating the candidates using a numerical scale. Various scales were used: (0,1), (-1,0,1), (0,1,2), and (0,1,…,20). The paper studies scale calibration effects, i.e., how individual voters adapt to the scale, leading to possibly different election outcomes. The data show that scales are not linearly equivalent, even if individual ordinal preferences are not inconsistent. Scale matters, notably because of the symbolic power of negative grades, which does not affect all candidates uniformly.