On two voting systems that combine approval and preferences: fallback voting and preference approval voting

Preference approval voting (PAV) and fallback voting (FV) are two voting rules that combine approval and preferences, first introduced by Brams and Sanver (in: Brams, Gehrlein and Roberts (eds) The mathematics of preference, choice and order, Springer, Berlin, 2009). Under PAV, voters rank the candidates and indicate which ones they approve of; with FV, they rank only those candidates they approve of. In this paper, we further develop the work of Brams and Sanver (2009) by exploring some other normative properties of FV and PAV. We show among other things that FV and PAV satisfy and fail the same criteria; they possess two properties that AV does not: Pareto optimality and the fact of always electing the absolute Condorcet winner when he exists. To provide a practical comparison, we evaluate the probabilities of satisfying the Condorcet majority criteria for three-candidate elections and a considerably large electorate, examining FV and PAV alongside other voting rules. Our findings indicate that PAV outperforms the Borda rule in this regard. Furthermore, we observe that in terms of agreement, FV and PAV align more closely with scoring rules than with approval voting. Our analysis is performed under the impartial anonymous culture assumption.