for example if you change the voter distribution from 42–26–15–17 to 52–22–12–14 so that Memphis is the majority winner, they may still end up picking Nashville!
There may not be any problem with that. It just depends what their honest utilities are.
It’s critical to note that probably the most critical elementary fact of voting theory is that it’s logically proven a majority preferred candidate may not be the candidate most preferred by the group. This is essentially what was so interesting about Arrow’s Theorem. It proved that the only possibly correct social welfare function had to be cardinal not ordinal.