Approval voting and positional voting methods: Inference, relationship, examples

Abstract

Approval voting is the voting method recently adopted by the Society for Social Choice and Welfare. Positional voting methods include the famous plurality, antiplurality, and Borda methods. We extend the inference framework of Tsetlin and Regenwetter (2003) from majority rule to approval voting and all positional voting methods. We also establish a link between approval voting and positional voting methods whenever Falmagne et al.'s (1996) size-independent model of approval voting holds: In all such cases, approval voting mimics some positional voting method. We illustrate our inference framework by analyzing approval voting and ranking data, with and without the assumption of the size-independent model. For many of the existing data, including the Society for Social Choice and Welfare election analyzed by Brams and Fishburn (2001) and Saari (2001), low turnout implies that inferences drawn from such elections carry low (statistical) confidence. Whenever solid inferences are possible, we find that, under certain statistical assumptions, approval voting tends to agree with positional voting methods, and with Borda, in particular.