[EM] Ramon Llull method = ?

[Jobst Heitzig]

Dear James!

Llull designed election methods under the assumption that there is a
best candidate which only has to be found. Obviously he implicitly
assumed that the voters vote not in their personal interest but in the
general interest to find the best candidate.

As Pukelsheim writes in the text quoted by Markus:
,-----
| As a devoted Christian in his time, Llull's concern was not the
| aggregation of many individual truths, but the discovery of the one
| and only truth existing, the truth of God. We understand Llull's
| electoral systems as manifestations of his Ars generalis, and as such
| they are means to set mankind on a trail leading to the unique, divine
| truth: «By this method,» said Natana, «is found the truth; by this
| truth we will be able to find the sister who is most suitable and best
| to be our abbess.» (B24, f. 32v, l. 17 - f. 33r, l. 3).
`-----

Llull argues that when there is a best candidate, say X, and everyone
votes in the general interest to find this candidate, then for each
other candidate, call her Y, at least half of the electorate will
correctly realize that X is better than Y and will thus vote for X in a
pairwise contest between X and Y. So, in our terminology, he assumes
that there is a sincere CW and that that CW is also the CW as expressed
by the votes.

Assuming this, his different election methods must all give the same
result, namely this CW. One of the methods is to process the candidates
in any order and always compare the next candidate pairwise with the
winner of the last pairwise comparison; this is what I called ROWS
(Random Order Winner Stays) last year. In another of his methods, all
pairs of candidates are compared and the candidate with the most wins
(nowadays called the "Copeland scores") is elected.

So, it seems that Llull had clear notions of what we now call "Condorcet
Winner" and "Copeland Score", but did not see a neccessity to resolve
cycles. By the way, didn't Condorcet also argue that there will always
be a Condorcet Winner in serious elections?

Yours, Jobst