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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)

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No Subject | Comment 25 of 31 |

It seems that the text clearly states that each Logistani is to answer either "Yes" or "No'" AND nothing else.  Several have proposed compound questions, including "OR" but no one yet seems to have addressed the matter of interpretation of such as inclusive vs exclusive disjunctions.

 

Also I do not see a consistent interpretation of what it means to be a "liar." If replies are limited to Yes and No, one interpretation is that a liar understands the question, has a clear concept of his unstated opinion on the question, and then SAYS the opposite (knowing full well that the effect will be reversed, IF he is identified as a "liar").   Another view would consider the INTENTION of the liar: although a liar, he does have a personal preference for one of the candidates. In this case presumably he wants his vote counted for the candidate he supports. How do "liars" as used here differ from being the "village idiots" who presumably hold no intelligible opinions and should not be counted at all? Dysphasic?

 

One can make a lot of assumptions about the meaning of terms in this problem,  with insufficient guidance (I think) in construing the mise-en-scène.  If the citizenry knew the game, couldn't they manipulate it to the advantage of their candidates? Do they think they are talking to a "consultant" or do they think they are actually voting?


  Posted by ed bottemiller on 2008-03-26 16:43:35
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