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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.)
Some Thoughts To Elements - Kudos, you've brought us three quarters of the way there | Comment 19 of 31 |
(In reply to re(2): Much more than just a Simplistic solution by elementofsurprize)

Bravo! Bravo!

I was worried that this would be too hard and I'd have to release hint after hint. But every time I was about to give a clue, you beat me to it.

Let's see what you've done: 

1) You realised that the true views of contrarians and revisionists were inaccessible; ergo that you'd need some means to recognise Cs and Rs so as to discard their votes.

2) You were ready to violate an unexpressed default assumption to raise a query multiple times with the same voter.

3) You had the idea of using the revisionist as a transducer to extract the true views of knights, liars and subversives.

Thereby you've managed to solve 3 parts of this 4 part puzzle. The still missing element is to determine a fully effective question. The question you have now:

Are you a knight who wants to vote B or a lier who votes M?

Serves well to identify Cs and Rs, while also extracting true responses from Ks and Ls. But this question has a serious drawback: it lacks finesse in dealing with subversives. Indeed, each subversive would answer this question affirmatively regardless of his political orientation. (Subversive thinking: "I am neither a liar nor a knight; therefore I fail to fit either criteria, so I will answer yes.")

Since the question fails to elicit a differentiated expression of the subversive's views, there is no way that the revisionist can restore the missing information.

In order to finish solving the problem we still need a better question. Good luck!

Edited on March 26, 2008, 11:45 am
  Posted by FrankM on 2008-03-26 11:38:26

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