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.

With the exchanges in the past days I've had a chance to reflect on how I wish I had formulated the problem. My hope is to come up with a version that enforces utilisation of revisionists as transducers, as well as requiring differentiation between liars and subversives (to key themes that were missed in the proposed solution).

I also wanted to include a fuller and clearer definition of the subversives (which gave many people difficulties) as well as eliminate any ambiguity that could lead a reader to suppose a prohibition against repeated interogation of a voter. My hope was to greatly reduce the risk of misinterpretation, although experience shows that there will always be some risk misinterpretation will always remain for complex problems like this one.

With there goals in mind I have come up with a new version, included below (significant changes are marked in boldface).

I'd be happy to receive comments from readers who have been following the discussion:

________________________________________

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 races, each of which have a distinctive relationship to the truth. (The physical features which distinguish members of each race are imperciptible to you, although they are clearly visible to all Logistanis.)

When answering a question about their voting preference:

• a Knight responds honestly.
• a Liar negates her true view.
• a Contrarian reverses the answer of the most recent voter.
• a Subversive considers how he would have responded if he had been a knight, then says 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.

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

With it's history of racial persecution, civil war and lingering prejudice; race is a very sensitive issue in Logistani society, so that the Logistani constitution forbids the mention of race in any way in a voting question.

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 yes/no question (the same question to each voter). 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 procedural arrangements, explaining how they enable you to fulfill your mission.