Condorcet's method is the correct method. The non-transitive "weakness" is not really there:
1. Even if it was possible for millions of votes and candidates to perfectly 'match up' It's good to know that instead of incorrectly using another system that, with the same votes, places one 90% over the other. Elections are not done in small numbers where you're just comparing 3 almost equal people with a small integer number of votes. If you asked "Do you prefer Hilary over candidate A?", who knows if 85% of the population would select candidate A?
2. You're going to get topological inconsistencies between every voter. It doesn't matter if voter 1 likes A -> B -> C then voter 2 likes C -> B -> A. You just add them up and get a total satisfaction score as stated. This is trivial.
The voting system in the States is not mathematically accurate because it isn't a pairwise vote. If I asked for a vote between only 3 options, chocolate, cheesecake, and strawberry:
Let's say
15% choc -> cheese -> straw
40% cheese -> choc -> straw
45% straw -> choc -> cheese
So it seems like only 15% wanted chocolate and the largest group voted for strawberry. However, compare them pairwise using all information:
55% prefer cheesecake over strawberry, so strawberry already shouldn't win
But wait,
60% prefer choc over straw and
55% prefer choc over straw So actually, chocolate should win.
It makes perfect sense that Trump and Hilary would be the remaining candidates because they represent the largest groups of people that give them their first vote, but that doesn't take into account the remaining population's preference. Someone could be preferred first pairwise and not even get a single first vote. This is basic graph theory and the everyday person doesn't catch on to it.
The only positive thing that could be imagined from going with everyone's first votes only would be a system where you need that. For instance, "guys, one of us is going to take a team to accomplish a mission, but the team needs to fully believe in the leader" Then, even though the winner does not take the pairwise win, he has a large group of people who would choose him first, but even that situation is completely imaginary. In real life, I can't think of an actual situation where you'd do that in place of a pairwise (AKA Condorcet's) vote.
Condorcet's method is the correct method. The non-transitive "weakness" is not really there:
1. Even if it was possible for millions of votes and candidates to perfectly 'match up' It's good to know that instead of incorrectly using another system that, with the same votes, places one 90% over the other. Elections are not done in small numbers where you're just comparing 3 almost equal people with a small integer number of votes. If you asked "Do you prefer Hilary over candidate A?", who knows if 85% of the population would select candidate A?
2. You're going to get topological inconsistencies between every voter. It doesn't matter if voter 1 likes A -> B -> C then voter 2 likes C -> B -> A. You just add them up and get a total satisfaction score as stated. This is trivial.
The voting system in the States is not mathematically accurate because it isn't a pairwise vote. If I asked for a vote between only 3 options, chocolate, cheesecake, and strawberry:
Let's say
15% choc -> cheese -> straw
40% cheese -> choc -> straw
45% straw -> choc -> cheese
So it seems like only 15% wanted chocolate and the largest group voted for strawberry. However, compare them pairwise using all information:
55% prefer cheesecake over strawberry, so strawberry already shouldn't win
But wait,
60% prefer choc over straw and
55% prefer choc over straw So actually, chocolate should win.
It makes perfect sense that Trump and Hilary would be the remaining candidates because they represent the largest groups of people that give them their first vote, but that doesn't take into account the remaining population's preference. Someone could be preferred first pairwise and not even get a single first vote. This is basic graph theory and the everyday person doesn't catch on to it.
The only positive thing that could be imagined from going with everyone's first votes only would be a system where you need that. For instance, "guys, one of us is going to take a team to accomplish a mission, but the team needs to fully believe in the leader" Then, even though the winner does not take the pairwise win, he has a large group of people who would choose him first, but even that situation is completely imaginary. In real life, I can't think of an actual situation where you'd do that in place of a pairwise (AKA Condorcet's) vote.