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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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Some Thoughts another thought | Comment 4 of 31 |

Contrarians and revisionists have no opinion as defined by the problem, but the other three do. The easiest way to see this is to note that if a member of one of these groups is the first to vote, the response is random. The other three groups' members are quite able to be the first respondant, and all three use their own views to determine their answer (knights honestly, liars dishonestly and subversives the opposite of knights.)

 

Subversives and liars need not answer the same, even though they're both in some sense the opposite of knights. For example, if the question were, "are you either a liar or a supporter of B", then knights will always answer no since they aren't liars, liars will also always answer no because they are liars and have to lie, but subversives will answer yes because knights will answer no. In this case, subversives and liars do not answer the same.

The strategy, whatever it is, must therefore ignore contrarian and revisionist remarks but capture and tally remarks from the other three groups.

If there were only liars and knights, then "are you a knight who supports B or a liar who supports M?" would be an easy question with which to poll the electorate. All supporters of B answer yes and all supporters of M answer no. Perhaps some variant of this idea can accommodate the additional ethnic groups. I like the idea of asking the same question multiple times to various individuals, but I'm not sure it's permitted by the terms of the problem.


  Posted by Paul on 2008-03-24 17:38:34
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