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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.)
re: another thought | Comment 5 of 31 |
(In reply to another thought by Paul)

Are we to assume that a respondent, when in a group which refers to what other individuals/groups have said (or would say?), knows to which group each belongs (i.e. just the hapless consultant who does not know)? For example, in instance 3 for subversives, what does "same view" mean in the phrase "how a knight with the same views would respond" -- supporting the same candidate? subscribing to the same "theory of truth"? or what?

 

Also, I think in your second and fourth paragraphs the suggested queries need to clarify whether you intend inclusive or exclusive disjunction (i.e. is "a or b" true if BOTH a and b are true -- or not)(OR or XOR in some symbolisms, for inclusive and exclusive respectively). 

 

There is also a confusion (to me) regarding a Subversive (in addition to the ambiguity of "same views"); this would seem to make his reply dependent on how A knight (which knight??) has or would respond (to what?) -- which does not seem to me like a "consistent opinion" (even if perhaps it might be determinable if one knew which knight and which view involved).  I am really meandering, trying to get a sense of the task. (I gather there is an entire genre or category here of these "knights and liars" conundrums, so possibly the text assumes some things not stated in this particular one.)


  Posted by ed bottemiller on 2008-03-24 19:12:40
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