Suppose that a society consists of three individuals, 1, 2 and 3, who must choos

Question

Suppose that a society consists of three individuals, 1, 2 and 3, who must choose one among three proposed budgts,z, y, and a Their preferences over these three posible budgets are as follows Write down the majority preference relation for this profile of preferences (e.g., indicate which alternatives would beat which in two-way contests). Does Black's Median-Voter Theorem support a predic-tion about which policy will be chosen if the group uses simple majority rule? Why or why not? Suppose that the group is going to use a voting agenda v-(y,x,z) to select the budget, where this notation means that the group first votes over y and x, and then votes over the winner of this contest and z, where the winner of this second vote is chosen as the budget. If each individual votes sincerely at each stage of the agenda, what would the outcome be? What would the outcome be if v'-(z,z, y) or u"-(z, y,z)?

Explanation / Answer

ANSWER:-

Given as per the question

Three possible budges as shown below

1.xP1yP1zP1

2.YP2zP2xP2

3.zP3Xp3Yp3

Ranks of 3 budges:-

Here the majority prefers from x to y( budget 1 and budget 3)

A majority prefers from y to z (budget 1 and budget 2) and

A majority prefers from z to x( budget 2 and budget 3).

There fore preferences not transitive and no best and set alternative( x>y , y>z => x>z but here z>x).

As per the question

Result:-

x vs y 1: x ; 2:y ; 3:x x

Between x and y THE BUDGET will get x ,

budget 2 will choose y , and

budget 3 will choose x

as the above result the option x is median

y vs z 1:y ; 2:y ;3:z y

z vs x 1:x ; 2:z ; 3:z z

preferences are not transitive.

Therefore no policy can be chosen collectively among the three budgets x, y, z

Hence the majority prefers from budget 1 x to y ,

the budget 2 contest from between x and z ,

hence z will be the result.

hence majority prefers budget between z to x ,

the second budget will be between z and y ,

hence the y is taken as majority prefers from y to z( budget 1 and budget 2)

hence the majority prefers between y to z ,

the second budget will be between y and x ,

hence xis taken as majority prefers from x to y.

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