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Election in Logistan (Posted on 2008-03-24) Difficulty: 4 of 5

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.

See The Solution Submitted by FrankM    
Rating: 2.5000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips Answer to Ed Comment 31 of 31 |
(In reply to re: Reformulated version - remarks and encouragement to Dej Mar by ed bottemiller)

Ed,

we seem have arrived at a ending of sorts.

dej mar submitted a solution meeting the requirements. it was not the solution i had been looking for though, and his contribution pointed out a weakness in the problem formulation. ive now published a reformulated version of the problem. the official solution has been published as well.

elementsofsurpise came very close to the official solution, only missing the right question to ask. if you enjoyed the problem you could try reading the revised version together with elements comments, then try to come up with the missing piece. you could also check against the published solution.

 


  Posted by FrankM on 2008-04-04 07:20:51
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