Quantum Vote Based on Quantum Logical Operators

We study quantum vote in which ballots are represented by not classical but quantum information. Our main aim is to design the quantum analogue of two well-known voting rules in reality: the majority vote and the board vote. We adopt a step-by-step approach. We first design two primitive quantum voting rules, called quantum logical veto (QLV) and quantum logical nomination (QLN). Not only can they be used independently in scenarios where classical veto-like vote and nomination-like vote are applied, but they can also be used as building blocks to construct quantum majority vote. We also use them to define a quantum voting game to show that quantum ballots can achieve something that can never be achieved by classical ballots. The conjunction and disjunction from quantum computational logic are used to define QLV and QLN, which makes them relatively easy to be implemented by the current or near-future technology. To design quantum board vote, we first introduce the quantum weighted average operation and then construct quantum board vote by the combination of quantum weighted average operation and QLN.