The Outcomes of Different Types of Voter Theory

I was recently exposed to approval voting, a type of ballot that allows you to check boxes for all the candidates, no candidates, or just a few. The candidate with the most ticks wins. The biggest upside to this approach, I think, is that it allows voters to express the intensity of their beliefs. If you really like someone, you can just vote for them and no one else. If you’re moderate, you can vote for several. The biggest downside to this approach is that you can end up with a candidate that few dislike, and few like. In other words, you’re left with a candidate who won’t piss anyone off, but also won’t have very many passionate supporters.

When does it make sense to use "traditional" voting where you can vote for only one candidate? For example, approval voting is great for voting on food, for example, since you don’t want anyone to not be able to eat anything, but is it best to approval-vote for a CEO? Would you want a CEO to have a passionately positive constituency and a constituency that does not like him/her? Or everyone in the organization more neutral?

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