Present an example of the two alternative voting systems. The preference schedul

Question

Present an example of the two alternative voting systems. The preference schedule of Table 1-31 in the book will serve as such an example. Reproduce the table and do the calculations for the method, with a discussion of what you are doing.

Net Plurality — Each voter casts a vote for their first choice and a negative vote for their bottom choice. The winner is the candidate whose net score of first place votes minus last place votes is the largest.

Plurality with Negative Elimination — Each voter submits a preference list with all candi- dates. Counting proceeds as in plurality-with-elimination, except that the candidate with the largest number of last-place votes is eliminated rather than the candidate with the smallest number of first-place votes.

Discuss whether each method satisfies each of the majority, monotonicity, and independence of irrelevant alternatives criteria. [Note that plurality with negative elimination is very much like plurality with elimination, so perhaps it satisfies the same criteria. Similarly, net plurality is very much like one of the other systems we have studied.]

Discuss the value of these systems. Taken together, what flaws in the presidential primary system would these correct, and what implications might this have on primary campaigns? Which of the two alternative systems do you prefer? What do you see as that system’s most significant drawback? Are its advantages sufficient for you to recommend its adoption, or would you instead stay with the plurality system or adopt one of the systems we learned in class? Explain your position. Note that we are only considering winner-take-all primaries.

vative plattorm), andMa percent of the delegates prefer L to M and M to C. Thirty two percent of the delegates like C the most and L the least. The rest of the delegates like M the most and C the least. Write out the preference schedule for this election. 1o. The Epicurean Society is holding its annual election for president. The three candidates are A, B, and C. Twenty percent of the voters like A the most and B the least. Forty percent of the voters like B the most and A the least. Of the remaining voters 225 prefer C to B and B to A, and 675 prefer C to A and A to B. Write out the preference schedule for this election. tics tes ein er- 1.2 Plurality Method 11. Table 1-31 shows the preference schedule for an election with four candidates (A, B, C, and D). Use the plurality method to (a) find the winner of the election. (b) find the complete ranking of the candidates. Number of voters |27 15 119 1st 2nd 3rd 4th C A B D B B D B D A A A A C CCD C TABLE 1-31 the nreference schedule for an electic

Explanation / Answer

Discussing with respect to above question we have Qu 11

Applying Net Plurality we have :

A-> first place votes = 15 , last place =27 ; net score = 15-27 =-12

B-> first place votes = 11+8+1 = 20, last place votes =0; net score = +20

C-> first place votes = 27 , last place votes = 15+11+9+1 = 36, net score = 27-36 = -9

D-> first place = 9 votes , last place = 8votes ; net score = 9-8 =1 votes.

So by net plurality method B is winner.

Net plurality is monotonic as adding to B's first prefernce would only increase margin of B

Net Plurality does not necessarily ensure majority

Applying Plurality with negative elimination we have :

First elimination C with 15+11+9+1 = 36 last place votes

Also since 27 is not the majority mark.

Second Elimination A with 38 (27+11) last place votes

Third Elimination B with 36 (27+9) last place votes which is greater than 35 last place vote of D

So here in this method D is the winner.

the method  Plurality with negative elimination is non monotonic as adding to winnner popular vote may not necesssarily add to chances of victory since a candidate to be eliminated gets changed and that candidate who is saved from elimination may give competition in last phases

Majority in this are guaranteed at last when we are left with 2 candidates.

Remedies

1. Monotonicity can be guaranteed in a single phase counting system. Calculating the net vote of each candidate.

2. Net plurality with elimination does not necessarily satisfies independence of relevant criterion as removing a non-winning candidate who is different from the one to be eliminated may change the result in final phase.

Alternative system

1. Single person single vote with single preference to ensure plurality and remove some of the biasness of

  multiple preference system since in net plursality only first and last prefeence are given weightage and not intermediate preferences.

   or

2. Single person single vote with multiple preference with each preference having certain weightage.

weightage

No of voters 27 15 11 9 8 1 1st D A B D B B 2nd B B D A A A 3rd A D A B D D

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