Chapter 1, Problem 54E

Use the Math Club election (Example 1.10) to illustrate why the Borda count method violates the IIA criterion.(Hint: Find the winner, then eliminate D and see what happens.)

Table 1-6 shows the preference schedule for the Math Club election with the Borda points for the candidates shown in parentheses to the right of their names. For example, the 14 voters in the first column ranked A first (giving A $14\times 4=56$ points), B second ( $14\times 3=42$ points), and so on.

Table 1-6

Borda points for the Math Club election
Number of Voters	14	10	8	4	1
1st (4 points)	$A\left(56\right)$	$C\left(40\right)$	$D\left(32\right)$	$B\left(16\right)$	$C\left(4\right)$
2nd (3 points)	$B\left(42\right)$	$B\left(30\right)$	$C\left(24\right)$	$D\left(12\right)$	$D\left(3\right)$
3rd (2 points)	$C\left(28\right)$	$D\left(20\right)$	$B\left(16\right)$	$C\left(8\right)$	$B\left(1\right)$
4th (1 points)	$D\left(14\right)$	$A\left(10\right)$	$A\left(8\right)$	$A\left(4\right)$	$A\left(1\right)$