Comparison of Systems Prescribed by Llull
-
I see that three writings on how to elect by Llull seeem to have survived. He wrote the oldest one before 1283.
I judge that the system Llull first describes tries to make a good decision in case of what today we would call a Condorcet cycle, asking the voters to vote again, and falling back to randomness if the cycle persists. But in his later two writings, he just recommends a round-robin comparison. If there is no Condorcet cycle, this should find the winner. But if there would be a cycle, the procedure doesn't detect it and just elects some candidate in the cycle, determined by the order in which the candidates are brought into comparison.
In the first writing, he gives a diagram illustrating the exhaustive list of pairs of candidates. This is used to collect the comparison of every candidate to every other. It's a bit puzzling to me that the later writings still refer back to the diagram. They don't recommend using it in any particular way, and I don't see that it would really be any use, given that round-robin matching is used. The number of comparisons is on the order of the number of candidates rather than the square of the number.