Can you solve the pirate riddle? - Alex Gendler

譯者: William Yen 審譯者: Sylvia He

It's a good day to be a pirate.

現在是做海盜的好時機

Amaro and his four mateys,

阿馬羅和他四個夥伴

Bart,

巴特

Charlotte,

Daniel,

夏洛特

丹尼爾

and Eliza

和伊麗莎

have struck gold:

碰上了大好事：

a chest with 100 coins.

他們挖到一個裝著一百枚金幣的箱子

But now, they must divvy up the booty according to the pirate code.

但是現在，他們必須要遵守 海盜分金的分配規則

As captain, Amaro gets to propose how to distribute the coins.

身為船長，阿馬羅 得以提出金幣的分配方案

Then, each pirate, including Amaro himself,

然後每位海盜，包括阿馬羅本人

gets to vote either yarr or nay.

可以表決贊成或否決

If the vote passes, or if there's a tie, the coins are divided according to plan.

如果表決通過或正反方平手， 就按照金幣分配方案進行

But if the majority votes nay,

但是如果表決沒通過

Amaro must walk the plank

阿馬羅將會被入大海餵鯊魚

and Bart becomes captain.

而巴特成為船長

Then, Bart gets to propose a new distribution

然後，巴特可以提出新的金幣分配方案

and all remaining pirates vote again.

然後剩下的海盜可以再次表決

If his plan is rejected, he walks the plank, too,

如果巴特的提案沒過半， 他也要被投入大海

and Charlotte takes his place.

而夏洛特就會取代他當船長

This process repeats,

重覆這程序

with the captain's hat moving to Daniel and then Eliza

接著是丹尼爾，然後是伊麗莎當船長

until either a proposal is accepted or there's only one pirate left.

直到一個方案被接受或只剩一位海盜

Naturally, each pirate wants to stay alive while getting as much gold as possible.

當然， 每位海盜都想要活著 並且得到最大的利益

But being pirates, none of them trust each other,

但身為海盜，他們不信任彼此

so they can't collaborate in advance.

所以他們無法事先溝通

And being blood-thirsty pirates,

他們又是殺人不眨眼的海盜

if anyone thinks they'll end up with the same amount of gold either way,

如果他們覺得表決後都還是 會拿一樣數量的金幣

they'll vote to make the captain walk the plank just for fun.

他們就會故意惡整船長， 把他投入大海餵鯊魚

Finally, each pirate is excellent at logical deduction

最後一點， 每位海盜都是 邏輯推論高手

and knows that the others are, too.

也同時知道其他人也是

What distribution should Amaro propose to make sure he lives?

阿馬羅應該要如何提出分配規則 才能確保他的性命?

Pause here if you want to figure it out for yourself!

按暫停如果想自己計算答案！

Answer in: 3

解答 3 秒後會出現

Answer in: 2

解答：再 2 秒

Answer in: 1

解答：再 1 秒

If we follow our intuition,

如果我們按照直覺考慮

it seems like Amaro should try to bribe the other pirates with most of the gold

阿馬羅似乎要把大多數的黃金 拿來賄賂其他海盜

to increase the chances of his plan being accepted.

來增加他的方案被接受的機率

But it turns out he can do much better than that. Why?

但其實他可以給自己留更多黃金。

為什麼呢？

就像之前說的， 海盜都知道別人是邏輯高手

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,

所以投票時他們不只會考慮當下的提案

but about all possible outcomes down the line.

也會考慮之後所有可能的情況

And because the rank order is known in advance,

因為提案的排序已經事先知道

each can accurately predict how the others would vote in any situation

每位都能預測其他人 在任何情況下會如何投票

and adjust their own votes accordingly.

並且根據這些推論調整自己的選擇

Because Eliza's last, she has the most outcomes to consider,

因為伊麗莎排在最後，她的顧慮也最多

so let's start by following her thought process.

讓我們從分析她的思考程序開始

She'd reason this out by working backwards from the last possible scenario

她從最後的可能性情境往回推

with only her and Daniel remaining.

也就是只剩丹尼爾和她

Daniel would obviously propose to keep all the gold

丹尼爾當然會提議自己擁有所有的寶藏

and Eliza's one vote would not be enough to override him,

而伊麗莎的一票否決並不能推翻他的提案

so Eliza wants to avoid this situation at all costs.

所以伊麗莎會不惜一切代價避免這個狀況

Now we move to the previous decision point

現在我們先到前一個投票點

with three pirates left and Charlotte making the proposal.

剩下三位海盜，且輪到夏洛特提案

Everyone knows that if she's outvoted, the decision moves to Daniel,

大家都知道如果她被多數票否決， 決定權就給丹尼爾

who will then get all the gold while Eliza gets nothing.

他就會拿到所有的黃金， 同時伊麗莎甚麼都沒有拿到

So to secure Eliza's vote,

所以如果要保障伊麗莎的贊成

Charlotte only needs to offer her slightly more than nothing, one coin.

夏洛特只要給予微薄的利益， 甚至是一枚金幣

Since this ensures her support,

這樣就能保障她的支持

Charlotte doesn't need to offer Daniel anything at all.

夏洛特不需要分給丹尼爾任何黃金

What if there are four pirates?

如果剩四位海盜呢？

As captain, Bart would still only need one other vote for his plan to pass.

身為船長，巴特也只多需要 一票來讓他的提案通過

He knows that Daniel wouldn't want the decision to pass to Charlotte,

他知道丹尼爾不會想要 讓提案權輪到夏洛特手上

so he would offer Daniel one coin for his support

所以他會給丹尼爾一個金幣 以換取他的支持

with nothing for Charlotte or Eliza.

而不分給夏洛特及伊麗莎任何東西

Now we're back at the initial vote with all five pirates standing.

現在我們回到最初的表決， 而五位海盜都在

Having considered all the other scenarios,

考慮了所有其他情況

Amaro knows that if he goes overboard,

阿馬羅知道如果他落水

the decision comes down to Bart,

巴特就會有提案權

which would be bad news for Charlotte and Eliza.

將會對夏洛特和伊麗莎不利

So he offers them one coin each, keeping 98 for himself.

所以他發給她們每位一枚金幣， 給自己保留 98 枚金幣

Bart and Daniel vote nay,

巴特和丹尼爾會表示否決

but Charlotte and Eliza grudgingly vote yarr

但是夏洛特和伊麗莎勉強同意

knowing that the alternative would be worse for them.

因為她們知道否決的替代方案 只會對他們更加不利

The pirate game involves some interesting concepts from game theory.

海盜遊戲涉及一些有趣遊戲理論概念

One is the concept of common knowledge

一個就是基本常識的概念

where each person is aware of what the others know

每個人都知道其他人所知道的

and uses this to predict their reasoning.

並用它來預測他們的推理

And the final distribution is an example of a Nash equilibrium

而最後的分配是個 「奈許均衡點」的例子

where each player knows every other players' strategy

每個人都知道彼此的策略

and chooses theirs accordingly.

並相應地做他們的選擇

Even though it may lead to a worse outcome for everyone

雖然有可能每個人得到的結果

than cooperating would,

比起合作更糟

no individual player can benefit by changing their strategy.

但沒有人因為改變策略而受益

So it looks like Amaro gets to keep most of the gold,

所以看來阿馬羅保留了大部分的金幣

and the other pirates might need to find better ways

而其他海盜可能需要找更好的途徑

to use those impressive logic skills,

來使用他們優秀的邏輯

like revising this absurd pirate code.

例如修改這荒謬的海盜金錢分配規則