since Patton and I combine like Voltron to form a reasonable facsimile of approximately one person, I'm taking the 'answer' portion of the explanations
They're ordered the way they are in the box for a reason. You're also assuming that two of the three Jeffersons can unite their votes at this stage- that they aren't running as separate individuals who happen to be from the same family, as though the family name was somehow of greater interest than the good of the country, or, hell, that they were even closely related enough to care that much about each other.
But since it's clear that ordering the candidates by descending order of number of mandates is insufficient, I'll explain- in brief, on the death of the king/queen, the people who are qualified to hold mandates provide them to an elector, who then votes on their behalf at the convocation (since it would be difficult to fit several million people at the Greenbrier). Something happens that we can't see because of all the smoke filling all those rooms, and someone walks out king/queen.