I took a course in decisional models this semester. It is delightful because it allows to understand why are the weaknesses of every decision making process.
Yet, the teacher gave us an old exam subject with the following preferences profile:
\begin{array}{ccc} 17: & a \succ b \succ c \succ d\\ 11: & b \succ c \succ d \succ a\\ 8: & d \succ c \succ a \succ b\\ 5: &a \succ c \succ d \succ b\\ 2: & d \succ a \succ b \succ d \end{array}
I was asked to find the Condorcet winner
There is a typo on the last line, I tried to do this example in both cases: remplacing $d$ by $c$ on the left and then on the right but I didn't found any Condorcet winner.
"Condorcet" looks at all possible pairings of contestants and selects the one that wins the most pairings.
Looking at a vs b, a wins in 17, 8, 5, and 2 so wins that pairing. Looking at a vs. c, c wins in 11, 8, 2 so c wins that pairing. Looking at a vs d, d wins in 11, 8, and 2 so d wins that pairing. a wins only one pairing.
Looking at b vs c, c wins in 8, 5, and 2 so c wins that pairing. Looking at b vs d, b wins in 17, 11, and 2 so b wins that pairing. Since, above, a won the a vs b pairing, b wins only one pairing. d Looking at c vs d, c wins 17, 11, and 5 so c wins that that pairing. Since, above, c also won the pairings against a and b, c wins three pairings.
Finally, we see that d won only the pairing against a so d wins only one pairing.
By "Condorcet", c wins easily.