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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: ( You must be logged in to post comments.)
  Subject Author Date
Hints/TipsAnswer to EdFrankM2008-04-04 07:20:51
re: Reformulated version - remarks and encouragement to Dej Mared bottemiller2008-04-03 09:43:44
Some ThoughtsReformulated version - remarks and encouragement to Dej MarFrankM2008-03-27 14:24:30
re: Reformulated versionDej Mar2008-03-26 23:47:29
QuestionReformulated versionFrankM2008-03-26 18:28:55
Hints/Tipsclarifications for edFrankM2008-03-26 17:37:09
No Subjected bottemiller2008-03-26 16:43:35
Reformulating the problem to make the transducer step indispensibleFrankM2008-03-26 12:57:52
That seems to work Dej Mar (with minor adjustment)FrankM2008-03-26 12:40:41
Hints/TipsOn repeatingly questioning a voter and the correctness of the problem text - (for Dej Mar)FrankM2008-03-26 12:22:31
re: To Elements - Kudos, you've brought us three quarters of the way thereDej Mar2008-03-26 12:15:21
re: Response to Dej Mar - on repeatingly questioning a voterDej Mar2008-03-26 12:04:33
Some ThoughtsTo Elements - Kudos, you've brought us three quarters of the way thereFrankM2008-03-26 11:38:26
Hints/TipsResponse to Dej Mar - on repeatingly questioning a voterFrankM2008-03-26 11:20:08
re(7): Much more than just a Simplistic solutionDej Mar2008-03-26 09:35:49
re(6): Much more than just a Simplistic solutionelementofsurprize2008-03-26 09:25:07
re(5): Much more than just a Simplistic solutionbrianjn2008-03-26 09:19:56
re(4): Much more than just a Simplistic solutionelementofsurprize2008-03-26 08:53:48
re(3): Much more than just a Simplistic solutionbrianjn2008-03-26 08:41:23
Solutionre(2): Much more than just a Simplistic solutionelementofsurprize2008-03-25 20:22:23
Hints/Tipsre: Much more than just a Simplistic solutionFrankM2008-03-25 12:35:12
Hints/Tipsfor Dej Mar (Subversive reprise, etc.)FrankM2008-03-25 12:29:18
Simplistic solutionelementofsurprize2008-03-25 09:17:30
QuestionQuestionsDej Mar2008-03-25 08:22:31
Hints/TipsFurther clarification: SubversivesFrankM2008-03-24 20:35:15
Hints/TipsReply to Ed B's No Subject + General CommentFrankM2008-03-24 20:17:40
re: another thoughted bottemiller2008-03-24 19:12:40
Some Thoughtsanother thoughtPaul2008-03-24 17:38:34
No Subjected bottemiller2008-03-24 16:49:12
Hints/TipsComments on: A thoughtFrankM2008-03-24 14:32:33
Some ThoughtsA thoughtCorey2008-03-24 14:03:53
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