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The executive branch (the government) is usually not directly elected by thepeople, but is created by another elected body or person such as the parliamentor the president. As a result, its members are not directly accountable to thepeople, individually or as a group.  We propose a scenario where government members are directly elected by thepeople, and seek to achieve proportional representation in the process.  We will present a formal model for the allocation of K offices, eachassociated with a disjoint set of candidates contesting for that seat.  A group of voters provides ballots for each of the offices. Since usingsimple majority voting for each office independently may result in minoritypreferences being completely ignored, here we adapt the greedy version ofproportional approval voting (GreedyPAV) to our framework.  In the article Electing the Executive Branch you can find an in-depthexplanation of the model and a demonstration - through computer-basedsimulations - of how voting for all offices together using this rule overcomesthis weakness and upholds the axiom of proportionality.  In this article, we will present the implementation of the algorithm(GreedyPAV) proposed by Rutvik Page, Ehud Shapiro, and Nimrod Talmon in thearticle mentioned above. In addition, we tested our implementation through asurvey, the results of which will be presented and analyzed later in thearticle.

Election of government ministers