# [EM] Random Ballot Condorcet

Ross Hyman rahyman at sbcglobal.net
Tue May 20 15:55:03 PDT 2014

```A better random ballot Condorcet method is: Chose a random ballot (and if it is not complete, draw others to break ties until there is a complete ranking).  Eliminate the pair-wise loser of the two lowest ranked candidates.  Repeat until one candidate remains.  Elect that candidate.

I believe it has the following desired properties: monotonic, clone independent, only Smith candidates get a non-zero probability of being elected, independence of zero probability alternatives, and it requires the fewest number of pair comparisons and chooses the candidate that tends to be higher ranked than the previous version. In the three candidate case, if there is a cycle, it will always choose the top ranked candidate from the random ballot.

One can form a complete social ranking by starting from the lowest ranked candidate and moving candidates down if they lose to the one below it.  The social ranking from the previous method is equivalent to starting from the highest ranked candidate and moving candidates up if they beat the one above it.

On Wednesday, May 7, 2014 6:51 PM, Ross Hyman <rahyman at sbcglobal.net> wrote:

Random Ballot Condorcet:  Choose a random ballot.  Elect the lowest ranked candidate that pairwise beats all higher ranked candidates.

Has this method been discussed before?  I believe that the following are true:  It will always elect a Condorcet candidate if there is one.  Otherwise it will elect a member of the Smith set with some nonzero probability for each member of the Smith set.  Non-Smith set candidates will have zero probability of being elected.  It is monotonic in that raising a candidate on some ballots cannot decrease its probability of being elected.  It is clone proof in that the probability of electing from the clone set is independent of the number of clones in the set. It is independent of irrelevant alternatives in that deleting a candidate with zero probability of winning cannot effect the probabilities for electing other candidates.
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