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.

hi ed,

1) i agree there is a bit of sloppiness in how some of the proposed questions were formulated. i didn't make a big deal about it because i felt we all understood what was meant, although i did attempt a reformulation in one of my last posts to dej mar.

2) a liar is a standard character appearing in the genre "knights and liars". i wouldn't think of spending many electrons describing the liar any more than i would for a stock character in a chinese opera, comedy francaise, or even a strip show! having said that, the problem text does give a definition. a liar, .. well .. lies, and does so consistently. you encapsulated this well with "a liar understands the question, has a clear concept of his unstated opinion on the question, and then SAYS the opposite".

a more pertinent question might address the nature of the subversive. despite my best efforts, this fellow gave several problem solvers indigestion and, in the end, caused me some aggravation as well. the point i had been aiming for was a character that answers "normal" questions like a liar, but responds to certain meta-questions differently. i invite you to review the published solution to see this in action.  

3) i don't immediately see how the election can be manipulated, nor do i understand how such possibilities would be opened if the "citizenry knew the game".

despite the sometimes byzantine nature of a quality you can call their honesty, each Logistani is bound to respond to a question according to the precepts of the problem text. for KLS this depend only on their personal preferences and for CR on the expressions of recent voter(s). there is no possibility, e.g. for a contrarian who harboured a passionate wish to see candidate B elected, to act against his own nature and pose as a knight voting for B.