The preferences of voters show below Illustrate an actual scenario in Congress i

Question

The preferences of voters show below Illustrate an actual scenario in Congress in 1953 on legislation for public school funding. Before passage of the original bill, an amendment to the bill was Introduced that would require integration in schools before federal funding was provided. It was a possibility that Congress would decide to pass no bill for funding schools. Thus the "candidates" In this "election" are "No bill". "Amendment" and "Original bill" with the election being decided by voters In Congress. The voting preferences of the 435 members of the House of Representatives in Congress In 1953 are listed below. (a) Suppose that voting on the legislation is done by the sequential pair wise method with the agenda: Original. Amendment. No bill. Which candidate is the winner? Show how you arrive at your conclusion. (b) In the first stage of voting, whet) The original bill and the amendment arc up for a vote, which "candidate" wins? Which groups of voters in Congress have formed a coalition? (c) In the next stage of voting, when the amended legislation faces an up or down vote, what is the result? That is, comparing the "Amendment" versus "No bill", which is the winner? Which groups of voters in Congress have formed a coalition? (d) If the "Original bill" were compared with "No bill", which option would win with these voters? Which groups of voters have formed a coalition in this case? (e) The outcome of the Education Act of 1953 is an example of what paradox in voting? (f) Why is this a paradox?

Explanation / Answer

(a) we have to follow the sequential pairwise method with an agenda original bill, amendment and no bill

In the first round, election would happen between original and amendment.

203 republicans prefer amendment over original bill

116 northern democrats prefer amendment over original bill

116 southern democrats prefer original bill over amendment.

In total, amendment wins over original bill.

Now the second round of election would happen between amendment and no bill.

203 republicans prefer no bill over amendment

116 southern democrats prefer no bill over amendment

116 northern democrats prefer amendment over no bill

Therefore, in total no bill wins over amendment.

No bill is the final winner

(B) in the first stage of voting, amendment is the winner.

Republicans and northern democrats have formed a coalition.

(C) in the next stage of voting, no bill is the winner.

Republicans and southern democrats have formed a coalition.

(D) if the original bill was compared with no bill,

Then 203 republicans prefer no bill over original bill

But 116 southern and 116 northern democrats prefer original bill over no bill.

Hence, original bill would have been the winner.

In this case, northern and southern democrats would have formed a coalition.

(E) Condorcet paradox

(F) the reason why this is a paradox is if we change the agenda, the winner would be different.

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