Question

Please solve the questions below and show your work. Thank you.

The town of Utopia has three equal-size groups of people: (i) type A people consistently prefer larger
public parks to smaller; type B people prefer small public parks to large public parks, and they prefer
large size to medium size parks; type C people most prefer medium size to small size public parks, which
they in turn prefer by a modest amount to large levels.

a. Draw on a graph the preferences of the three groups of individuals. Which types of people have
single-peaked preferences? Which have multi-peaked preferences?

b. Will round-robin majority voting generate consistent outcomes in this case? Why or why not?

Answer 1

Part a) types a and c have single peaked preferences with peaks at high and medium respectively. Type b has multiple peaked preferences, with peaks at high and low and a dip at medium.

Part b) majority voting does not usually generate consistent outcomes whem some people preferences that fail to be single peaked. But they do happen to generate consistent outcomes in this case. If high and low are the two options on the ballot high will win since type a and b will vote for it. Similarly high wins when high and medium are the two options on the ballot. When low and medium are om the ballot, medium wins since type A and c will vite for it. Finally when all the three are on ballot , types a and b will vote for highwhich will therefore win. Notice that there are no cycles so the voting outcomes are in fact consistent. Tge decision coincide with those tgat would be made by society that prefer high to medium and medium to low.