But why did Bamboot get 4 of Gort’s votes while Aggy-Waggy got only 1, even though the latter got over half the number of the former?

Because Bamboot isn’t getting Gort’s votes. Now that Gort is eliminated, all of the voters that voted Gort #1 now have their #2 vote counted as if it’s their #1 vote.

• 4 people that voted Gort #1 voted Bamboot #2.
• 1 person that voted Gort #1 voted Floundra #2.
• 1 person that voted Gort #1 voted Aggy-Waggy #2.

This keeps happening down the choices until someone has a majority. People that voted Floundra #1 don’t end up having their #2 vote counted because their candidate wasn’t eliminated in the end. This is why it’s not possible to throw your vote away have your vote taken away - if your favourite candidate is eliminated, your vote goes to your second favourite, then your third favourite, etc until someone has the majority.

Not sure what it looks like in the US, but Australian ballot slips have all the candidates and you number them 1, 2, 3, 4, etc.

Here’s a brief explanation of how preferential voting works in Australia: https://www.chickennation.com/voting/