Arrow Impossibility Theorem

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“The Arrow impossibility theorem and its implications for voting and elections”

Arrow’s impossibility theorem represents a fascinating problem in the philosophy of economics, widely discussed for insinuating doubt on commonly accepted beliefs towards collective decision making procedures.
This essay will introduce its fundamental assumptions, explain its meaning, explore some of the solutions available to escape its predictions and finally discuss its implications for political voting and elections. I will begin by giving some definitions and presenting the fundamental issue of social choice theory, consisting of the identification of an “ideal” device for preference aggregation, capable of converting individual
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The existence of such trade-off poses serious obstacles for the identification of an optimal voting system in real society elections and has strong consequences in welfare economics and justice theory.

There are possible solutions to escape the paradox by accepting to relax one or more of the theorem fundamental assumptions. For example, by restricting the voting choice between just two alternatives, a coherent group decisions can always be obtained through majority voting.
In politics this is commonly achieved using different methods among which are the assignment of agenda power to an individual, the elimination of defeated alternatives from the vote and the limitation of voting rounds. Individuals having the power of making such choices can actively influence the results of the elections and have their most preferred outcome implemented.
Another popular approach consists of restricting the application of the voting system to a specific type of individual preferences denoted as “single-peaked”, characterized by the presence of a most preferred alternative for each individual. Furthermore, in the context of a uni-dimensional policy space we can also apply “Black’s median voter theorem” to identify the Condorcet winner in the societal ranking, consisting of the most preferred alternative of the median voter.
Despite the existence of a number of cases where it’s possible to circumnavigate the paradox, many political problems present complex and

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