An acquaintance is the claimant in a case which is going to arbitration before the American Arbitration Association. The first step in the process is to select an arbitrator.

The way the process works is that the Association gives each side (claimant and respondent) a list of 10 possible arbitrators. Each side gets to strike 2 arbitrators and then rank the remaining 8 in order of preference. The Association takes the list, removes all arbitrators which have been stricken by either side, and then adds the rankings for each arbitrator. The arbitrator with the lowest total is selected. (Ties are resolved by choosing the arbitrator who is least busy.)

Obviously the claimant wants to end up with the most liberal arbitrator possible; the respondent wants to end up with the most conservative arbitrator possible. Both sides have a rough idea of which arbitrators are more liberal and which are more conservative but those ideas won’t be exactly the same.

Let’s assume that the respondent will strike the two most liberal arbitrators and then rank the remaining arbitrators from most conservative to most liberal.

The question is whether the claimant’s best strategy is to strike the two most conservative arbitrators and then rank the remaining arbitrators in true preference order? Intuitively, it seems a waste for the claimant to give a number one rank to the most liberal arbitrator, since that arbitrator is very likely to be stricken by the other side. Might not the claimant do better by choosing the 3rd or 4th most liberal arbitrator as his or her number one choice?