## 2 The Setting
### The Quantum Setting  
In this subsection we describe the quantum parliament we envision and state clearly the assumptions underlying its operation. Let us point out beforehand that many important issues will not be addressed in this work. Undoubtedly, the most critical issue left out is the possibility of quantum general elections. We shall take for granted that elections, either of a classical type, or of an unspecified quantum type have resulted in the formation of a given quantum parliament. For ease of exposition, we assume that the quantum parliament consists of two parties and we further consider the case where, apart from the two parties, there are also independent representatives. Below we list the assumptions, the terminology and the notation used throughout this paper. **A1:**: There are two political parties/coalitions, [PERSON]'s party and [PERSON]'s party, designated by \(A\) and \(B\), respectively. **A2:**: \(n_{A}\) denotes the number of representatives from [PERSON]'s party, \(n_{B}\) the number of representatives from [PERSON]'s party, and \(n_{I}\) the number of independent representatives. Obviously  
\[n_{A}+n_{B}+n_{I}=N. \tag{1}\]  
If there are no independent representatives, the above Equation (1) simplifies to  
\[n_{A}+n_{B}=N. \tag{2}\]
**A3:**: For every bill, both parties decide whether to vote in favor of or against, that is, _yes_ or _no_. The decision made by the leadership of each party is \"classical\" in the sense that it is an absolute yes or no. The fact that this is a quantum parliament means that every legislator casts a _quantum_ vote. Each vote is considered a 2-dimensional quantum system in the 2-dimensional Hilbert space \(\mathcal{H}_{2}\) and, as such, is represented by a _qubit_. The intuition behind this abstraction is straightforward: the two basis kets \(|yes\rangle\) and \(|no\rangle\) of \(\mathcal{H}_{2}\) correspond to the classical decisions _yes_ and _no_, respectively. The whole voting process involves all \(N\) legislators and is viewed as a composite \(2^{N}\)-dimensional quantum system in the Hilbert space \(\mathcal{H}_{2}^{\otimes N}\). Some aspects of the voting process are only indirectly incorporated in the present model. For instance, if some legislators from [PERSON]'s party abstain from voting we assume that the number \(n_{A}\) of representatives from her party is appropriately adjusted, and the same holds in case some legislatorsfrom [PERSON]'s party abstain. This simplification does not alter the final outcome of the voting because passing the bill requires the majority of those present to vote in favor. **A4:**: As seems fitting in a quantum parliament, this party decision is viewed as a _suggestion_ or _recommendation_ from the leadership of the party to its representatives. Specifically, both parties \(A\) and \(B\) adopt and tolerate _free will_ radii \(r_{A}\) and \(r_{B}\), respectively, such that \(0\leq r_{A},r_{B}<1\). This is viewed as a result of the democratic tradition and sociopolitical culture of each party. Therefore, the vote \(\left|\psi\right\rangle\) of a legislator need not coincide with the decision of the party's leadership; it suffices to be within a _distance_ less than or equal to the free will radius of the party. The notion of _distance_ will be made rigorous in the next Section 4. **A5:**: The above assumptions describe the typical operation of the quantum parliament. However, we allow for exceptional circumstances, in which one or both parties view the bill in question to be of great importance, and to succeed in passing or stopping the bill, they decide to temporarily abolish their corresponding free will radius. This forces their representatives to obey the party decision but, at the same time, this behavior, being deeply autocratic and undemocratic, incurs a heavy political and social cost. Such situations will be examined in Section 5. **A6:**: In case there are independent legislators, these are unaffected by the decisions of the parties.