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.

Dej Mar,

I maintain that the problem text to be without fault in this regard.

You seem to be suggesting that the problem text should have read: "each voter will call out his answers ..". But this is clearly wrong: For at each turn a voter will be responding to just one question.

Only at a later time (i.e., after other voters have been queried and responded in their turn) will a voter be asked to respond again.

___________________

I am writing this portion of my comment after having reflected further on the remarks above. It occurs to me that, perhaps, you were not objecting to the appearance of the word: answer in the singular. Instead, your complaint may relate to the word single in the following problem text:

you can conduct the vote by asking members of the assembled electorate a single yes/no question

If so, I would agree that there is a case to be made.  

If I ask you the same question (and no other) several times, having I asked you a single question? My understanding is that the English language is ambiguous on this point.

Therefore, while disagreeing with your claim that the problem text is flawed, I still wish I had chosen a clearer formulation, leaving no chance for misinterpretation.

Edited on March 26, 2008, 6:01 pm

Posted by FrankM on 2008-03-26 12:22:31