Suppose there are five people -1, 2, 3, 4, and 5-who rank projects A, B, C, and D as follows.
1 2 3 4 5
A A D C B
D C B B C
C B C D D
B D A A A
Will any project be chosen by a majority vote rule? If so, which one? lf not, explain why.
The way to find if an option is selected by majority voting rule it is useful to compare each option against every other one. Start with A.
Comparing A with B, you can see that A is preferred over B by 1 and 2, and B is preferred over A by 3, 4 and 5. Thus, A loses to B by a vote of 2-3.
Comparing A with C, again A is preferred over C by 1 and 2, and C is preferred over A by 3, 4 and 5. Thus, A loses to C by a vote of 2-3.
Comparing A to D, the results above follow, and A ...
The way to find if an option is selected by majority voting rule is demonstrated here.