In a November 14 2009 message Jobst Heitzig gave us "Reverse Llull" a Condorcet method with nice properties, but subject to crowding. He challenged us to find a clone free version. Here is one:

1. Well before the election publish a binary tree whose leaves are the alternatives. Generate this tree with standard cluster analysis software applied to a questionnaire about the alternatives. Number the nodes of the tree

2. If there are n nodes, then a ballot is simply a list of the numbers 1 through n. Voters circle the numbers identifying the nodes for which they prefer the left branch in the published tree diagram.

3. If the number for the root node is circled on more ballots than not, discard the right branch, else discard the left branch.

4. Apply the method recursively to the remaining branch (if it has more than one leaf).

That's it basically. Optimal strategy is to circle the node identification numbers for which you prefer the likely winner of the left branch over the likely winner of the right. In other words, sincere strategy is optimal.

In the case of fully informed, intelligent voters following this optimal strategy, the sincere Condorcet Winner will be elected if there is one.

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