(a) If there are 70 voters and 5 candidates, how many total points would there be in a Borda count?
(b) If there are 60 voters and 4 candidates, how many total points would there be in a Borda count?
(c) If there are 900 voters and 3 candidates, how many total points would there be in a Borda count?
Each voter of the Borda count gives 1 point to the least favoured candidate, 2 for the next, until N points for the most favoured candidate out of N.
(a) With five candidates, each voter gives 1+2+3+4+5=15 points for a total of 15*70=1050 points.
(b) and (c) can be solved similarly.
For more examples and explanations, see:
http://www.ctl.ua.edu/math103/voting/borda.htm
To determine the total points in a Borda count, you need to understand the methodology behind the count.
In a Borda count, each voter ranks the candidates in order of preference. The top-ranked candidate receives the highest number of points, and the points decrease sequentially for each lower-ranked candidate. The total number of points in a Borda count depends on the number of candidates and the number of voters.
(a) If there are 70 voters and 5 candidates:
In a Borda count, the top-ranked candidate receives (n-1) points, the second-ranked candidate receives (n-2) points, and so on, where "n" is the number of candidates.
Since there are 5 candidates, the top-ranked candidate would receive (5-1) = 4 points, the second-ranked candidate would receive (5-2) = 3 points, the third-ranked candidate would receive (5-3) = 2 points, and the fourth-ranked candidate would receive (5-4) = 1 point. The last-ranked candidate, in this case, would receive zero points.
To calculate the total points in this scenario:
Total points = (70 x 4) + (70 x 3) + (70 x 2) + (70 x 1) + (70 x 0)
= 280 + 210 + 140 + 70 + 0
= 700
Therefore, the total points in a Borda count with 70 voters and 5 candidates would be 700.
(b) If there are 60 voters and 4 candidates:
Using the same logic, the total points can be calculated as follows:
Total points = (60 x 3) + (60 x 2) + (60 x 1) + (60 x 0)
= 180 + 120 + 60 + 0
= 360
Therefore, the total points in a Borda count with 60 voters and 4 candidates would be 360.
(c) If there are 900 voters and 3 candidates:
Applying the above formula, the total points can be calculated as:
Total points = (900 x 2) + (900 x 1) + (900 x 0)
= 1800 + 900 + 0
= 2700
Therefore, the total points in a Borda count with 900 voters and 3 candidates would be 2700.