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Why is the outcome of majority voting dominated by the preferences of the median voter?

Why is the outcome of majority voting dominated by the preferences of the median voter?

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According to the theorem of the median voter (also abbreviated as MVT) a majority rule voting system will choose the outcome dominated by the median voter. It is an abstraction of a specific preference form of aggregation which is based on each actor in a group that wants to maximize their own utility; thus each individual wants an outcome which will benefit them the most. Under specific constraints, such behavior results in the middle, or “median” voter in the group who holds the ability to cast the vote which is decisive in a contest. The theorem implies that voters hold an incentive to vote for their accurate preferences. Therefore the candidates vying for the votes of the group can be both better off if directly appealed to the median voter.

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