The problem with approval and score voting

Approval voting and score voting provide a lot of flexibility to the voter. In approval voting, you can vote for as many candidates as you want. You can vote for one, two, or even all of the candidates. In score voting, you give each candidate a score in a range, for example from 0 to 10.

Assume your organization is having an election for President by score voting. There are three candidates: A, B, and C. One particular member thinks A is by far the best candidate, B is mediocre, and C is awful. If this member voted honestly, he/she might give the following scores (assuming the range is 0 to 10):

However, your members are very competitive and are willing to vote strategically to help their first choice candidates. So that particular member might instead give the following scores:

If all members did this, then the score voting system becomes the same as plurality voting. Plurality voting is a very poor voting system. Approval voting exhibits the same behavior. Assume that the same election was conducted using approval voting. That same member might have honest preferences as follows:

However, if that member wants to give his/her first choice the highest chance of winning, that member might instead vote this way:

If all members did this, then the approval voting system becomes the same as plurality voting. Plurality voting is a very poor voting system.