Disclaimer: I wrote this all for myself not to change your mind or argue. Helps if I write down my thoughts and I don’t see a problem sharing. Feel free to discuss if you like.

35 voters: Alice > Carol > Bob 35 voters: Bob > Carol > Alice 30 voters: Carol > Alice > Bob

Vs.

41 voters: Alice > Carol > Bob 29 voters: Bob > Carol > Alice 30 voters: Carol > Alice > Bob

Alice wins

Vs.

Carol wins

Say you have:

41 voters: Republican > Third-party > Democratic 29 voters: Third-party > Democratic > Republican 30 voters: Democratic > Third-party > Republican

If those 29 voters couldn’t vote Third-party they would vote Democratic. So when the Third-party candidate is knocked out, their votes should favor their second pick. Democratic wins 59-41.

If it was:

41 voters: Republican > Third-party > Democratic 29 voters: Third-party > Republican > Democratic 30 voters: Democratic > Third-party > Republican

Which makes more since on why the 6 votes moved to Republican because Republican was their second choice.

Then Republicans win 70-30.

In America you’d have 4 basic senarios

25 voters: Republican > Third-party > Democratic 25 voters: Third-party > Democratic > Republican 25 voters: Third-party > Republican > Democratic 25 voters: Democratic > Third-party > Republican

In RCV, Third-party wins.

Let’s say this

30 voters: Republican > Third-party > Democratic 25 voters: Third-party > Democratic > Republican 20 voters: Third-party > Republican > Democratic 25 voters: Democratic > Third-party > Republican

Third-party still wins

40 voters: Republican > Third-party > Democratic 10 voters: Third-party > Democratic > Republican 10 voters: Third-party > Republican > Democratic 40 voters: Democratic > Third-party > Republican

It would be a tie

45 voters: Republican > Third-party > Democratic 10 voters: Third-party > Democratic > Republican 5 voters: Third-party > Republican > Democratic 40 voters: Democratic > Third-party > Republican

It would still be a tie

45 voters: Republican > Third-party > Democratic 5 voters: Third-party > Democratic > Republican 10 voters: Third-party > Republican > Democratic 40 voters: Democratic > Third-party > Republican

Republicans win

Let’s change it to this:

35 voters: Alice > Carol > Bob 35 voters: Bob > Alice > Carol 30 voters: Carol > Alice > Bob

Vs.

41 voters: Alice > Carol > Bob 29 voters: Bob > Alice > Carol 30 voters: Carol > Alice > Bob

Alice wins

Vs.

Alice wins

They couldn’t make their whole point if you just switched Alice and Carol. And it makes much more sense that someone with Alice second would change it to Alice first.

But when 29 votes still hold Alice as last, it does have some weight.

Something just seems off about it and it’s because they cherry picked a senario that would work for their point.

Alice > Carol > Bob Alice > Bob > Carol Bob > Alice > Carol Bob > Carol > Alice Carol > Alice > Bob Carol > Bob > Alice

There are 6 ways to vote and they leave out half of them. Then they make Carol supporters favor Alice as their second choice.

20 voters: Alice > Carol > Bob 15 voters: Alice > Bob > Carol 15 voters: Bob > Alice > Carol 20 voters: Bob > Carol > Alice 20 voters: Carol > Alice > Bob 10 voters: Carol > Bob > Alice

Carol eliminated, +10 Bob +20 Alice. Alice would win.

If 5 voters from Bob > Alice > Carol were moved to Alice > Bob > Carol

20 voters: Alice > Carol > Bob 20 voters: Alice > Bob > Carol 10 voters: Bob > Alice > Carol 20 voters: Bob > Carol > Alice 20 voters: Carol > Alice > Bob 10 voters: Carol > Bob > Alice

Alice would win

What if everyone from Bob > Alice > Carol moved to vote for Alice > Bob > Carol

20 voters: Alice > Carol > Bob 30 voters: Alice > Bob > Carol 0 voters: Bob > Alice > Carol 20 voters: Bob > Carol > Alice 20 voters: Carol > Alice > Bob 10 voters: Carol > Bob > Alice

It would be a tie.

In bold are the three they selected:

20 voters: Alice > Carol > Bob 15 voters: Alice > Bob > Carol 15 voters: Bob > Alice > Carol 20 voters: Bob > Carol > Alice 10 voters: Carol > Alice > Bob 20 voters: Carol > Bob > Alice

5 voters from Bob > Carol > Alice moved to Alice > Carol > Bob. Just like their example.

26 voters: Alice > Carol > Bob 15 voters: Alice > Bob > Carol 15 voters: Bob > Alice > Carol 14 voters: Bob > Carol > Alice 10 voters: Carol > Alice > Bob 20 voters: Carol > Bob > Alice

Alice 41 Bob 28 Carol 30

Bob is eliminated.

15 votes goes to Alice. 14 goes to Carol.

Alice still wins.

But they set it up like:

20 voters: Alice > Carol > Bob 15 voters: Alice > Bob > Carol 0 voters: Bob > Alice > Carol 35 voters: Bob > Carol > Alice 10 voters: Carol > Alice > Bob 20 voters: Carol > Bob > Alice

5 voters from Bob > Carol > Alice moved to Alice > Carol > Bob. Just like their example.

26 voters: Alice > Carol > Bob 15 voters: Alice > Bob > Carol 0 voters: Bob > Alice > Carol 29 voters: Bob > Carol > Alice 10 voters: Carol > Alice > Bob 20 voters: Carol > Bob > Alice

Then when Bob is eliminated all 29 votes go to Carol.

Then they say “It’s unfair that Carol wins”. When in reality those 29 people would prefer Carol over Alice.

RCV might have some flaws but that article has some flaws.

I haven’t looked at the others. I might later.