# Aggregation Rules for Choosing Among the Social Alternatives

Question

Consider a polity of 77 citizens who are choosing among the social alternatives in the set A = {w, x, y, z}. Consider the following aggregation rules:

(i)The constant rule- for any profile of preferences the social preference is always w ›- x ›- y ›-z.

(ii) The minority rule- Alternative v is ranked above alternative u if and only if there is at most half of the citizens that prefer v to u.

(iii) The sequential rule- Look first at only the top ranked alternatives of the citizens. Choose the alternative that most people put on top. If there are several alternatives like that, choose the one which is lowest in alphabetical order. This alternative is ranked first in the social preference. Now take this alternative out of the citizens' rankings and repeat the procedure on the rest of the alternatives to determine the second ranked alternative. Repeat recursively to determine the whole social ranking.

(a) Which of Arrow's criteria is violated by the Constant rule?

(b) Show by example that the Minority rule might lead to an intransitive social preference?

(c) Does the Minority rule violate any other of Arrow's criteria? Prove your answer.

(d) Suppose that the preferences of the citizens are:

1 2 3 4

w x y z

x y z y

y z w z

z w x w

What would be the social ranking under the Sequential rule?

(e) Which of Arrow's criteria is violated by the Sequential rule? Prove your answer.

Summary: This question belongs to political economy and discusses about aggregation rules for choosing among the social alternatives.

Total word count: 494

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