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.

"Do you consider it your duty as a knight to cast your vote for military ruler M?"  If one says "yes" count that as a vote for M; if one says "no" count that as undecided (i.e. disregard it); if any other reply, say "You must answer yes or no" and disregard the reply.  No votes for B will be tabulated ! (what do you think this is, a democracy??).  Your tableau is too confused (at least to me) to take it seriously.  Knights would respond honestly, but the others either would not or would reply based on something other than a preference (i.e. no "consistent" opinion). The intent is clearly to keep B from being "elected" by any system chosen. In a "stadium" full of the electorate, would you ask people to vote sequentially, or just with one voice acclaim M? When you say you are trying to tabulate those who have "an opinion" what does this mean? An opinion regarding M vs B? (At least this is MY initial opinion of the task.)

Out of curiosity, are you assuming that each member of the electorate knows to which "ethnic group" every other member belongs, and moreover even knows the political preferences of all others?

Edited on March 24, 2008, 4:52 pm

Edited on March 24, 2008, 4:56 pm

Posted by ed bottemiller on 2008-03-24 16:49:12