full transcript

From the Ted Talk by Alex Gendler: Can you solve the pirate riddle?

Unscramble the Blue Letters

It's a good day to be a pirate. Amaro and his four mateys, Bart, Charlotte, dieanl, and Eliza have struck gold: a cseht with 100 coins. But now, they must divvy up the booty according to the pirate code. As captain, Amaro gets to propose how to distribute the coins. Then, each pirate, including Amaro himself, gets to vote either yarr or nay. If the vote passes, or if there's a tie, the conis are divided according to plan. But if the majority votes nay, Amaro must walk the plank and Bart becomes captain. Then, Bart gets to propose a new distribution and all remaining pirates vote again. If his plan is rcjeeted, he walks the plank, too, and Charlotte takes his place. This process repeats, with the captain's hat moving to Daniel and then Eliza until either a paosprol is accepted or there's only one pirate left. Naturally, each ptriae wants to stay alive while getting as much gold as possible. But being pirates, none of them trust each other, so they can't caaroltbloe in advance. And being blood-thirsty pirates, if anyone thinks they'll end up with the same amount of gold either way, they'll vote to make the captain walk the plank just for fun. Finally, each pirate is excellent at logical dotudicen and knows that the others are, too. What distribution should Amaro poorspe to make sure he lives? puase here if you want to figure it out for yourself! Answer in: 3 Answer in: 2 Answer in: 1 If we follow our intuition, it seems like aarmo should try to bribe the other pirates with most of the gold to increase the chances of his plan being accepted. But it turns out he can do much better than that. Why? Like we said, the pirates all know each other to be top-notch logicians. So when each votes, they won't just be tiknnihg about the current proposal, but about all possible outomces down the line. And because the rank order is known in adacnve, each can accurately predict how the others would vote in any situation and adjust their own votes accordingly. Because Eliza's last, she has the most outcomes to consider, so let's start by following her thought pecrsos. She'd reason this out by working backwards from the last possible scenario with only her and Daniel reannmiig. Daniel would obviously propose to keep all the gold and Eliza's one vote would not be enough to ovdierre him, so Eliza wants to aoivd this situation at all costs. Now we move to the previous decision point with three pirates left and Charlotte making the proposal. Everyone knows that if she's outvoted, the decision moves to Daniel, who will then get all the gold while Eliza gets nothing. So to secure Eliza's vote, Charlotte only needs to oeffr her sigllhty more than nothing, one coin. Since this ensures her soruppt, Charlotte doesn't need to offer Daniel anything at all. What if there are four pirates? As captain, Bart would still only need one other vote for his plan to pass. He knows that Daniel wouldn't want the decision to pass to Charlotte, so he would offer Daniel one coin for his support with nothing for Charlotte or Eliza. Now we're back at the initial vote with all five pirates sinndtag. Having considered all the other sanrcoies, Amaro knows that if he goes overboard, the deoisicn comes down to Bart, which would be bad news for cahotltre and Eliza. So he offers them one coin each, keniepg 98 for himself. Bart and Daniel vote nay, but Charlotte and Eliza grudgingly vote yarr knowing that the alternative would be worse for them. The pirate game involves some interesting concepts from game theory. One is the concept of cmomon knowledge where each person is aware of what the others know and uses this to predict their reasoning. And the fanil distribution is an example of a Nash eriuquiblim where each player knows every other players' strategy and chooses theirs accordingly. Even though it may lead to a worse outcome for everyone than cooperating would, no ivdndiuail peaylr can benefit by changing their strategy. So it looks like Amaro gets to keep most of the gold, and the other ptiares might need to find better ways to use those impressive lgioc skills, like revising this arsubd pirate code.

Open Cloze

It's a good day to be a pirate. Amaro and his four mateys, Bart, Charlotte, ______, and Eliza have struck gold: a _____ with 100 coins. But now, they must divvy up the booty according to the pirate code. As captain, Amaro gets to propose how to distribute the coins. Then, each pirate, including Amaro himself, gets to vote either yarr or nay. If the vote passes, or if there's a tie, the _____ are divided according to plan. But if the majority votes nay, Amaro must walk the plank and Bart becomes captain. Then, Bart gets to propose a new distribution and all remaining pirates vote again. If his plan is ________, he walks the plank, too, and Charlotte takes his place. This process repeats, with the captain's hat moving to Daniel and then Eliza until either a ________ is accepted or there's only one pirate left. Naturally, each ______ wants to stay alive while getting as much gold as possible. But being pirates, none of them trust each other, so they can't ___________ in advance. And being blood-thirsty pirates, if anyone thinks they'll end up with the same amount of gold either way, they'll vote to make the captain walk the plank just for fun. Finally, each pirate is excellent at logical _________ and knows that the others are, too. What distribution should Amaro _______ to make sure he lives? _____ here if you want to figure it out for yourself! Answer in: 3 Answer in: 2 Answer in: 1 If we follow our intuition, it seems like _____ should try to bribe the other pirates with most of the gold to increase the chances of his plan being accepted. But it turns out he can do much better than that. Why? Like we said, the pirates all know each other to be top-notch logicians. So when each votes, they won't just be ________ about the current proposal, but about all possible ________ down the line. And because the rank order is known in _______, each can accurately predict how the others would vote in any situation and adjust their own votes accordingly. Because Eliza's last, she has the most outcomes to consider, so let's start by following her thought _______. She'd reason this out by working backwards from the last possible scenario with only her and Daniel _________. Daniel would obviously propose to keep all the gold and Eliza's one vote would not be enough to ________ him, so Eliza wants to _____ this situation at all costs. Now we move to the previous decision point with three pirates left and Charlotte making the proposal. Everyone knows that if she's outvoted, the decision moves to Daniel, who will then get all the gold while Eliza gets nothing. So to secure Eliza's vote, Charlotte only needs to _____ her ________ more than nothing, one coin. Since this ensures her _______, Charlotte doesn't need to offer Daniel anything at all. What if there are four pirates? As captain, Bart would still only need one other vote for his plan to pass. He knows that Daniel wouldn't want the decision to pass to Charlotte, so he would offer Daniel one coin for his support with nothing for Charlotte or Eliza. Now we're back at the initial vote with all five pirates ________. Having considered all the other _________, Amaro knows that if he goes overboard, the ________ comes down to Bart, which would be bad news for _________ and Eliza. So he offers them one coin each, _______ 98 for himself. Bart and Daniel vote nay, but Charlotte and Eliza grudgingly vote yarr knowing that the alternative would be worse for them. The pirate game involves some interesting concepts from game theory. One is the concept of ______ knowledge where each person is aware of what the others know and uses this to predict their reasoning. And the _____ distribution is an example of a Nash ___________ where each player knows every other players' strategy and chooses theirs accordingly. Even though it may lead to a worse outcome for everyone than cooperating would, no __________ ______ can benefit by changing their strategy. So it looks like Amaro gets to keep most of the gold, and the other _______ might need to find better ways to use those impressive _____ skills, like revising this ______ pirate code.

Solution

  1. propose
  2. scenarios
  3. support
  4. advance
  5. pause
  6. chest
  7. individual
  8. standing
  9. proposal
  10. player
  11. common
  12. outcomes
  13. pirate
  14. avoid
  15. decision
  16. final
  17. absurd
  18. equilibrium
  19. collaborate
  20. offer
  21. process
  22. pirates
  23. keeping
  24. logic
  25. deduction
  26. remaining
  27. thinking
  28. amaro
  29. coins
  30. slightly
  31. rejected
  32. override
  33. daniel
  34. charlotte

Original Text

It's a good day to be a pirate. Amaro and his four mateys, Bart, Charlotte, Daniel, and Eliza have struck gold: a chest with 100 coins. But now, they must divvy up the booty according to the pirate code. As captain, Amaro gets to propose how to distribute the coins. Then, each pirate, including Amaro himself, gets to vote either yarr or nay. If the vote passes, or if there's a tie, the coins are divided according to plan. But if the majority votes nay, Amaro must walk the plank and Bart becomes captain. Then, Bart gets to propose a new distribution and all remaining pirates vote again. If his plan is rejected, he walks the plank, too, and Charlotte takes his place. This process repeats, with the captain's hat moving to Daniel and then Eliza until either a proposal is accepted or there's only one pirate left. Naturally, each pirate wants to stay alive while getting as much gold as possible. But being pirates, none of them trust each other, so they can't collaborate in advance. And being blood-thirsty pirates, if anyone thinks they'll end up with the same amount of gold either way, they'll vote to make the captain walk the plank just for fun. Finally, each pirate is excellent at logical deduction and knows that the others are, too. What distribution should Amaro propose to make sure he lives? Pause here if you want to figure it out for yourself! Answer in: 3 Answer in: 2 Answer in: 1 If we follow our intuition, it seems like Amaro should try to bribe the other pirates with most of the gold to increase the chances of his plan being accepted. But it turns out he can do much better than that. Why? Like we said, the pirates all know each other to be top-notch logicians. So when each votes, they won't just be thinking about the current proposal, but about all possible outcomes down the line. And because the rank order is known in advance, each can accurately predict how the others would vote in any situation and adjust their own votes accordingly. Because Eliza's last, she has the most outcomes to consider, so let's start by following her thought process. She'd reason this out by working backwards from the last possible scenario with only her and Daniel remaining. Daniel would obviously propose to keep all the gold and Eliza's one vote would not be enough to override him, so Eliza wants to avoid this situation at all costs. Now we move to the previous decision point with three pirates left and Charlotte making the proposal. Everyone knows that if she's outvoted, the decision moves to Daniel, who will then get all the gold while Eliza gets nothing. So to secure Eliza's vote, Charlotte only needs to offer her slightly more than nothing, one coin. Since this ensures her support, Charlotte doesn't need to offer Daniel anything at all. What if there are four pirates? As captain, Bart would still only need one other vote for his plan to pass. He knows that Daniel wouldn't want the decision to pass to Charlotte, so he would offer Daniel one coin for his support with nothing for Charlotte or Eliza. Now we're back at the initial vote with all five pirates standing. Having considered all the other scenarios, Amaro knows that if he goes overboard, the decision comes down to Bart, which would be bad news for Charlotte and Eliza. So he offers them one coin each, keeping 98 for himself. Bart and Daniel vote nay, but Charlotte and Eliza grudgingly vote yarr knowing that the alternative would be worse for them. The pirate game involves some interesting concepts from game theory. One is the concept of common knowledge where each person is aware of what the others know and uses this to predict their reasoning. And the final distribution is an example of a Nash equilibrium where each player knows every other players' strategy and chooses theirs accordingly. Even though it may lead to a worse outcome for everyone than cooperating would, no individual player can benefit by changing their strategy. So it looks like Amaro gets to keep most of the gold, and the other pirates might need to find better ways to use those impressive logic skills, like revising this absurd pirate code.

Frequently Occurring Word Combinations

ngrams of length 2

collocation frequency
pirate code 2
offer daniel 2

Important Words

  1. absurd
  2. accepted
  3. accurately
  4. adjust
  5. advance
  6. alive
  7. alternative
  8. amaro
  9. amount
  10. answer
  11. avoid
  12. aware
  13. bad
  14. bart
  15. benefit
  16. booty
  17. bribe
  18. captain
  19. chances
  20. changing
  21. charlotte
  22. chest
  23. chooses
  24. code
  25. coin
  26. coins
  27. collaborate
  28. common
  29. concept
  30. concepts
  31. considered
  32. cooperating
  33. costs
  34. current
  35. daniel
  36. day
  37. decision
  38. deduction
  39. distribute
  40. distribution
  41. divided
  42. divvy
  43. eliza
  44. ensures
  45. equilibrium
  46. excellent
  47. figure
  48. final
  49. finally
  50. find
  51. follow
  52. fun
  53. game
  54. gold
  55. good
  56. grudgingly
  57. hat
  58. impressive
  59. including
  60. increase
  61. individual
  62. initial
  63. interesting
  64. intuition
  65. involves
  66. keeping
  67. knowing
  68. knowledge
  69. lead
  70. left
  71. line
  72. lives
  73. logic
  74. logical
  75. logicians
  76. majority
  77. making
  78. mateys
  79. move
  80. moves
  81. moving
  82. nash
  83. naturally
  84. nay
  85. news
  86. offer
  87. offers
  88. order
  89. outcome
  90. outcomes
  91. outvoted
  92. overboard
  93. override
  94. pass
  95. passes
  96. pause
  97. person
  98. pirate
  99. pirates
  100. place
  101. plan
  102. plank
  103. player
  104. point
  105. predict
  106. previous
  107. process
  108. proposal
  109. propose
  110. rank
  111. reason
  112. reasoning
  113. rejected
  114. remaining
  115. repeats
  116. revising
  117. scenario
  118. scenarios
  119. secure
  120. situation
  121. skills
  122. slightly
  123. standing
  124. start
  125. stay
  126. strategy
  127. struck
  128. support
  129. takes
  130. theory
  131. thinking
  132. thinks
  133. thought
  134. tie
  135. trust
  136. turns
  137. vote
  138. votes
  139. walk
  140. walks
  141. ways
  142. working
  143. worse
  144. yarr