Sophisticated Voting on an Agenda

Five voters choose among four proposals: Alpha, Beta, Gamma, Delta. Their strict rankings, best to worst, are - Voter 1: Gamma, Beta, Alpha, Delta - Voter 2: Beta, Gamma, Delta, Alpha - Voter 3: Alpha, Beta, Delta, Gamma - Voter 4: Alpha, Beta, Delta, Gamma - Voter 5: Gamma, Alpha, Beta, Delta The agenda is: first, Alpha against Beta; second, the winner against Gamma; third, that winner against Delta. Each vote is decided by simple majority and the final survivor is adopted. Voters know all preferences and the agenda, and each votes strategically: at every vote he supports the option that leads to the final outcome he prefers, found by backward induction. Which proposal is adopted? Answer with its name.

• backward induction
• combinations
• induction

Source: Sequential agenda voting with sophisticated voters, after Farquharson (1969) and McKelvey and Niemi (1978). Statement written for AxiomIQ.