has decided dragon jousting may not be the best way to choose its leaders,

已經決定龍爭虎鬥可能不是選擇領導人的最佳方式。

and has begun transitioning to democracy.

並已開始向民主過渡。

The candidates are a giant orange troll and an experienced tree statesman.

候選人是一個巨大的橙色巨魔和一個經驗豐富的樹木政治家。

An all-powerful eyebrow has hired your company— The Dormor Polling Agency—

一個全能的眉毛僱傭了你的公司--多摩爾民調機構。

to survey the citizens of the land and predict who will win.

以調查這塊土地上的公民，並預測誰將獲勝。

There's a lot riding on this:

這上面有很多東西

if you get it wrong, heads— well, your head—

如果你弄錯了，人頭... ... 好吧，你的頭... ...

will quite literally roll.

將相當字面滾。

Your job is to go from door to door,

你的工作就是挨家挨戶的走訪。

asking voters whether they prefer the troll or the treefellow

問選民是喜歡巨魔還是喜歡樹人？

and to use the results to project how the election will go.

並用結果來推測選舉的走勢。

Your fellow citizens want you to succeed and would tell you the truth...

你的同胞們希望你成功，會告訴你真相... ...

but there's a problem.

但有一個問題。

Few are willing to admit they support the troll

很少有人願意承認他們支持巨魔。

on account of his controversial life choices.

因為他有爭議的人生選擇。

If you were to ask a troll supporter who she'll vote for,

如果你要問一個巨魔的支持者，她會投給誰。

there's a good chance that she'll claim to support the treeman,

她很有可能會聲稱支持樹人。

skewing your results.

歪曲你的結果。

You're about to begin your rounds when a stranger offers you some cryptic advice:

你正準備開始巡視時，一個陌生人給了你一些神祕的建議。

“Here's the question that will save your neck: what have you got in your pocket?”

"這裡有一個能拯救你脖子的問題：你口袋裡有什麼？"

You reach into your pocket and pull out... a silver coin,

你伸手到口袋裡掏出... 一枚銀幣。

which has the current king's head on one side and his tail on the other.

其中一邊是現任國王的頭，一邊是他的尾巴。

How can you use it to conduct an accurate poll?

如何利用它來進行準確的投票？

Pause here to figure it out yourself.

在這裡暫停一下，自己想辦法。

Answer in 3

3個回答

Answer in 2

答覆2

Answer in 1

回答1

The trick here is to use the coin to add random chance

這裡的訣竅是用硬幣來增加隨機機率。

to your interaction that will give troll supporters deniability.

到你的互動，會給巨魔的支持者否認。

In other words, you're looking for a system where when someone says “troll,”

換句話說，你在尋找一個系統，當有人說 "巨魔"

it could either be because the coin somehow told them to,

也可能是因為硬幣以某種方式告訴他們。

or because they actually support the troll—

還是因為他們真的支持巨魔

and you'd have no way to tell the difference.

而你卻無從得知其中的區別。

You'll also need to know how frequently the coin skewed the results,

你還需要知道硬幣傾斜結果的頻率。

so you can account for it in your calculations.

這樣你就可以在計算時考慮到它。

One solution is to have every pollee go into their house and flip the coin.

有一個辦法是讓每一個波利人都到自己家裡去拋硬幣。

If it lands heads, they should tell you “troll,”

如果是人頭，他們應該告訴你 "巨魔"。

whether or not they actually support him.

不管他們是否真的支持他。

If it lands tails, they should tell you their actual preference.

如果落在尾巴上，他們應該告訴你他們的實際喜好。

Here's what happens:

下面是發生了什麼。

you pull 200 voters, and 130 say they'll vote for the troll.

你拉了200個選民，130個說他們會投給巨魔。

For about 50%, or 100 of them, the coin will have landed heads.

大約有50%，也就是100個，硬幣就會落到頭。

So you can subtract 100 troll votes off his total,

所以你可以從他的總票數中減去100張巨魔票。

and know the troll's real support is 30 to 70, and he's very likely to lose.

並知道巨魔的真實支持率是30比70，他很可能會輸。

The election comes around, but before the results can be certified

選舉來了，但在選舉結果還沒有得到認證之前

a third party candidate swoops in and burns the treefellow to a crisp.

第三方候選人突然襲擊，把樹人燒成了焦炭。

The freshly signed and deeply flawed constitution mandates that this challenger

新近簽署的漏洞百出的憲法規定，這個挑戰者

gets to take his victim's place in a new election.

可以在新的選舉中取代受害者的位置。

The Dormor Polling Agency sends you back out on the streets with your trusty coin.

多摩爾民調機構派你帶著你信任的硬幣回到街上。

Only this time no one is comfortable admitting their preference:

只不過這次沒有人願意承認自己的喜好。

supporting the troll is still shameful,

支持巨魔還是很可恥的。

and nobody wants to express support of a dragon who murdered his way into the race.

沒有人願意表示支持一條龍誰謀殺了他的方式進入比賽。

But your job is your job. How do you conduct an accurate poll now?

但你的工作就是你的工作。 你現在如何進行準確的民意調查？

Pause here to figure it out for yourself.

這裡暫停一下，自己想辦法。

Answer in 3

3個回答

Answer in 2

答覆2

Answer in 1

回答1

This time, instead of masking just one candidate preference,

這一次，不是隻掩蓋一個候選人的喜好。

you need some way to disguise both.

你需要一些方法來掩飾兩者。

At the same time, you also need to leave space for some portion of the people

同時，你還需要給一部分人留出空間。

polled to express their true preference.

受訪者表達了他們的真實喜好。

But a coin toss only has two possible outcomes... right?

但擲硬幣只有兩種可能的結果，對嗎？

Suppose you have everyone flip the coin twice—

假設你讓每個人都拋兩次硬幣--。

now there are four possible results.

現在有四種可能的結果。

You can tell the people who flip heads twice in a row

你可以告訴那些連續兩次翻臉的人。

to report support for the troll;

來報告支持巨魔。

those who get tails twice in a row to report dragon;

那些連續兩次得到尾巴的人去舉報龍。

and those with any other combination to declare their true preference.

和其他任何組合的人宣佈他們的真實偏好。

The chances of getting either two heads or two tails in a row

連續獲得兩個頭或兩個尾的機會。

are 50% times 50%— or 25%.

是50%乘以50%-或25%。

Subtracting that proportion of the total respondents

減去佔答覆者總數的這一比例

from each candidate's score should give you something close

從每個考生的分數中應該可以得到一些接近於

to the real distribution.

到實際分佈。

This time, 105 respondents announced themselves in favor of the troll

這次有105名受訪者宣佈支持巨頭的做法。

and 95 for the dragon.

和95的龍。

Out of the total, the coin will make 25%

其中，硬幣將佔25%。

or 50 respond troll and another 50 respond dragon.

或50個響應巨魔，另50個響應龍。

Subtracting 50 from each result reveals that voters seem to prefer the troll

從每項結果中減去50，發現選民似乎更喜歡巨魔。

by a margin of about 55 to 45.

以約55比45的差距。

It's close, but as predicted, the troll wins the election,

雖然很接近，但正如預測的那樣，巨魔贏得了選舉。

and you live to poll another day.

你還能活到明天