Professor of Decision Sciences
Approval voting is the voting method recently adopted by the Society for Social Choice and Welfare. Positional voting methods include the famous plurality, anti-plurality, and Borda methods.The authors extend their inference framework (2003) from majority rule to approval voting and all positional voting methods. They 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.They illustrate their 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, they find that, under certain statistical assumptions, approval voting tends to agree with positional voting methods, and with Borda, in particular.