Masters of Intransitive Group Preferences: The Jedi Council

A long time ago in a galaxy far, far away Condorcet's paradox reared its ugly head. In class Sabrina got to the heart of how this happens, which is when the options to choose from or vote on are viewed with varying factors and different aspects being important to each voter. As we approach the holiday season, my heart has begun to yearn for some movie marathons on TV, none more anticipated in my mind than the Star Wars Weekend on TNT. In the 3rd best movie of the entire franchise, comment to disagree I dare you, Episode III: Revenge of the Sith, there is a fascinating Public Choice problem where an unthinkable voting result occurs granting Anakin Skywalker a seat on the Jedi Council but not the rank of master. Let's look at a model that could explain this seemingly intransitive behavior by the group of "masters".

In the table below the voting preferences are shown for the model and to simplify it is assumed there are only 3 members of the council voting with only three options and a simple majority is needed to pass the decision. Decisions are as follows: MC means Anakin gets the rank of master and a seat on the council, M means he is only granted the rank of master, and C means he is only granted a seat on the council.

In a vote between MC and M, MC will win out; between M and C, M will win out; between MC and C, paradoxically C will win. This is Condorcet's paradox, where a group with transitive preferences exhibits non-transitive group preferences under simple majority. This arises because the different voters value different things in each outcome. For example, Yoda seeks to honor the old Jedi way and have a master and seat on the council be mutually inclusive, but Mace Win-du values limiting the influence and power of "the chosen one" because he believes Anakin has been corrupted. Off screen we can only assume the agenda setting power belongs to Mace Win-du because C is the result and Anakin is famously outraged leading perhaps to the crumbling of the Galactic Senate and the republic. Maybe in Episode IX coming out Christmas 2019 we will see a Borda Count and democracy will reign supreme.