Voting Methods.edited

docx

School

South America University *

*We aren’t endorsed by this school

Course

Subject

Statistics

Date

Nov 24, 2024

Type

docx

Pages

Uploaded by CasperNyoveri

Voting Methods Student Name Date Course Name/ Course Number Instructor Name

VOTING METHODS 2 Introduction Scholars and practitioners alike in the field of mathematics have for eons now argued that voting systems are based on mathematical principles which help define and estimate voter patterns. Every election procedure is marked by a voter casting ballots for their specific candidate. The ballots are then counted after which the candidates are ranked based on the number of votes. There are numerous voting methods applied in modern-day society although the topmost include majority, pairwise comparisons, and plurality with elimination methods. The subsequent essay presents an expository analysis of the aforementioned methods under the auspice of the thesis that they improve the validity and reliability of ballot counts. Individual Method Analysis (a) Majority Voting Method The majority voting method emphasizes that the candidate of choice has to receive more than 50% of the vote in order to be declared the winner. The method is fairly simple with the Borda Count (Point System) being applied in most instances. The system requires every place on the preference ballot to have an assigned point. For instance, the 4 th choice in table 1 below gets 1 point, while the 3 rd choice gets 2 points, the 2 nd choice gets 3 points and the 1 st choice gets 4 points. The value for each place is multiplied by the number of voters at the top of the column to identify the points that every candidate or preference won. The points for every candidate are then totaled up.

VOTING METHODS 3 Table 1: Preferences Now, using the Borda Count method, the below calculations can be derived: Column 1 Twitter (T): (number of votes) 3*4 (number of points)= 12 points Instagram (M): 3*3= 9 points Snapchat (S): 3*2= 6 points Tiktok (K): 3*1= 3 points Column 2 Twitter (T): (number of votes) 11*3(number of points)= 33 Instagram (M): 11*1= 11 Snapchat (S): 11*4= 44 Tiktok (K): 11*2= 22 Column 3 Twitter (T): (number of votes) 8*3 (number of points)= 24 Instagram (M): 8*4= 32 Snapchat (S): 8*2= 16 Tiktok (K): 8*1= 8 Column 4

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

VOTING METHODS 4 Twitter (T): (number of votes) 5*3 (number of points)= 15 Instagram (M): 5*2= 10 Snapchat (S): 5*1= 5 Tiktok (K): 5*4= 20 Thereafter the total points are calculated for every candidate with Twitter winning with at least 84 points Twitter= 12+33+24+15= 84 points Instagram= 9+11+32+10=62 points Snapchat: 6+44+16+5= 71 points Tiktok=3+22+8+20=53 points (b) Pairwise Comparisons The Pairwise Comparisons method involves comparing every candidate to each other using close matchups. The winner in every comparison is accorded a point with the one with the most points winning the final tally. Using the preference schedule in table one, the below calculations were conducted: First match-up Twitter= 3 Instagram= 8+5= 13 points Instagram- 1point

VOTING METHODS 5 Second Match-Up Instagram=8+5= 13 points Snapchat= 11+8+5 =24 points Snapchat= 1 point Third Match-Up Snapchat= 24 points Tiktok= 3+11+8+5 =27 points Tiktok= 1 point Based on the calculations, Tiktok has more points compared to the other platforms. (C) Plurality with Elimination Methods The plurality with elimination method involves eliminating the candidate with fewer 1 st place votes and redistributing them among the other candidates. Using the table 1, one can note that: Twitter: 3 votes Instagram: 8 Snapchat:11 Tiktok:5

VOTING METHODS 6 Therefore Twitter is eliminated from the schedule with the votes being distributed to the other candidates which lead to the creation of a new preference table as shown below: Number of voters 3 11 8 5 1 st choice M S M K 2 nd choice S K S M 3 rd choice K M K S Table 2: Updated Table In the above table, Instagram has a vote count of 12 while Snapchat and TikTok report a count of 11 and 5 respectively. This means that Tiktok is removed from the preference table: Number of voters 3 11 8 5 1 st choice M K M M 2 nd choice S M S S Table 2: Updated table The calculations show that Instagram has the highest amount of votes at 16 (3+8+5) while Tiktok has only 11 votes. This means that Instagram is the winner. Comparison of Voting Method In my opinion, I think that the best method is plurality with elimination since it allows for the redistribution of votes. It also creates room for a candidate to be declared a winner if they have the majority of first-place votes without undergoing rigorous analyses. I think the pairwise comparisons are worse since it is complex and requires constant analyses. The majority criterion violated the Borda count fairness as it requires the candidate to be declared the winner as long as they receive the majority of the 1 st place votes. I think that if one choice wins one method and loses using another then it's because of the Condorcet paradox which means that preferences change ergo winning is not absolute. Conclusion

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

VOTING METHODS 7 The preceding essay shows that voting methods are seminal in understanding voter patterns and preferences. The Condorcet paradox is prevalent in all three methods as different winners are shown in each. There is a need for scholars to develop an iron-clad universal method that ensures that a candidate wins every election or vote count without any fairness violations. Evaluation Summary I learned that math is at the core of voting processes. Using voting methods, practitioners can be able to declare a winner and also validate their conclusions effectively without any hassles whatsoever.

Voting Methods.edited

Related Documents