Question 12.45
17. Prove that if a distribution is discrete and there is no single median position, there is always an extended median.
17.
Because there is no median position, there must be an even number of voters. List the ideal positions of the voters in left-to-right/numerical order. Assume that there are voters. Because there is no single median, the th and st ideal positions are not the same. Any position in between these two ideal points has an equal number of voters’ ideal points to both the left and the right. These two ideal points are the endpoints of the extended median.