M, military ruler of Logistan, has deferred to international pressure and agreed to hold an election in which he will run against his arch-nemesis, B. Both M and B, being politicians, are liars. You have been engaged as an independent consultant and charged with devising a representative voting procedure, i.e., your mission is to tally the true preference of each citizen who has a consistent, determinable opinion, and no other.

The chief complication relates to the fact that the Logistani electorate is composed of five (to your eyes) indistinguishable ethnic groups, each of which have a distinctive relationship to the truth. When expressing their voting preference:

• Knights respond honestly.
• Liars negate their true view.
• Subversives consider how a a knight with the same views would respond, then say the opposite.
• Revisionists admire knights and liars, and despise subversives. A revisionist will copy the most recent knight or liar to have voted, unless a subversive has voted more recently. In this latter case, the revisionist will vote for the opposite of that subversive.
• Contrarians reverse the answer of the most recent voter.

A contrarian or revisionist would respond randomly if he were the first voter queried.

You are to hold the election at the national stadium, to which the entire Logistani electorate has been invited. After some thought, you decide you can conduct the vote by asking members of the assembled electorate a single yes/no question. This is an open ballot, so each voter will call out his/her answer to the question for all to hear.

Suggest a viable question and any procedural arrangements, explaining how they enable you to fulfill your mission.

Though it may be the intent of FrankM to allow the individual to cast more than one ballot (with, at most, only being counted once), the procedure also requires the question to be asked of an individual multiple times. This seems contrary to requirement that it be a "single" question.
Perhaps FrankM was meaning the statement is to be distinct in phrasing, only, and not limiting it to a unitary quantity of queries for each member, but that the words "question" and "answer" in the statement 'This is an open ballot, so each voter will call out his/her answer to the question for all to hear' are both in singular form, inferring the word "single" to mean the question is asked no more than once per voter.

Edited on March 26, 2008, 10:16 am

Posted by Dej Mar on 2008-03-26 09:35:49