Consider the given preference schedule with the number of voters ranking the candidates in a local community plebiscite.Rank13155121stWXYY2ndXWZX3rdZZXW4thYYWZ22. Compute candidate W's Borda score.Group of answer choices9614512683
Question
Consider the given preference schedule with the number of voters ranking the candidates in a local community plebiscite.Rank13155121stWXYY2ndXWZX3rdZZXW4thYYWZ22. Compute candidate W's Borda score.Group of answer choices9614512683
Solution
To compute candidate W's Borda score, we need to assign points to each rank and then sum up the points for each candidate. In a Borda count, if there are 4 candidates, the candidate ranked first gets 3 points, the candidate ranked second gets 2 points, the candidate ranked third gets 1 point, and the candidate ranked fourth gets 0 points.
From the given preference schedule:
- 13 voters rank W as their 1st choice, so W gets 13*3 = 39 points.
- 15 voters rank W as their 2nd choice, so W gets 15*2 = 30 points.
- 5 voters rank W as their 3rd choice, so W gets 5*1 = 5 points.
- 12 voters rank W as their 4th choice, so W gets 12*0 = 0 points.
Adding these up, candidate W's Borda score is 39 + 30 + 5 + 0 = 74.
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