Can you solve the fantasy election riddle? - Dennis E. Shasha

譯者: Lilian Chiu 審譯者: Helen Chang

After much debate, the fantasy realm you call home

經過大量辯論，

你的家園夢幻王國認定

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

龍上槍術比賽可能不是 選出領袖的最佳方式，

and has begun transitioning to democracy.

並開始朝向民主改革。

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

候選人包括一個橘色巨怪

和一位有經驗的樹政治家。

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

全能的眉毛僱用了你的公司——

多魔民調機構——

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

對全國公民進行調查，預測誰會贏。

There’s a lot riding on this:

這件事攸關生死：

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

如果你預測錯了，人頭—— 嗯，你的頭——

will quite literally roll.

真的就會落地。

Your job is to go from door to door,

你的工作是要挨家挨戶拜訪，

asking voters whether they prefer the troll or the treefellow

問選民他們比較偏好巨怪或樹人，

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

並用這些資料來預測選舉的結果。

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

你的同胞都希望你成功，

因此會告訴你實話…… 但有一個問題。

but there’s a problem.

Few are willing to admit they support the troll

很少有人會肯承認他們支持巨怪，

on account of his controversial life choices.

因為巨怪的人生選擇十分爭議。

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

如果你去問巨怪支持者會投給誰，

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

很有可能她會宣稱她支持樹人，

skewing your results.

讓你的結果有偏差。

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

就在你即將開始巡訪時，

一個陌生人給你神秘的建議：

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

「這個問題可以保住你的頭顱：

你的口袋裡有什麼？」

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

你把手伸進口袋，拿出了……

一個硬銀幣，

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

一面是現任國王的頭像，

另一面是他的尾巴。

How can you use it to conduct an accurate poll?

你要如何用這個銀幣 來進行準確的民調？

Pause here to figure it out yourself. Answer in 3

若要自行解題，請在此暫停。 答案即將公佈：三。

Answer in 2

答案即將公佈：二。

Answer in 1

答案即將公佈：一。

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

這裡的密訣，

是用銀幣在你的互動中 增加一個隨機的可能性，

to your interaction that will give troll supporters deniability.

讓支持巨怪的人可以做出否認。

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

換言之，

你想設計這樣的系統： 當對方說「巨怪」時，

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

可能是因為銀幣要他們說巨怪，

or because they actually support the troll—

或者因為他們真的支持巨怪——

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

而你分不出兩者的差別。

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

你也需要知道

銀幣讓結果偏差的頻率，

so you can account for it in your calculations.

這樣你在計算時才能一併考量進去。

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

一種解決方案是請每位受訪者

進到他們的房子裡去擲硬幣。

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

如果是正面，他們就要 告訴你「巨怪」，

whether or not they actually support him.

不論他們實際上是否支持巨怪。

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

如果是反面，

他們就要告訴你他們真正支持誰。

Here’s what happens:

實際經過如下：

you poll 200 voters, and 130 say they’ll vote for the troll.

你調查了兩百位選民，

其中一百三十位說他們會投給巨怪。

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

大約 50% 的人，或大約一百人，

會擲出正面。

So you can subtract 100 troll votes off his total,

所以你可以把巨怪的 總票數減掉一百票，

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

真正支持巨怪的 有三十票，對手七十票，

巨怪非常可能會輸。

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

選舉開始進行，

但在結果能被證實之前，

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

第三方候選人突然襲擊，

將樹人燒成鬆脆的焦木。

The freshly signed and deeply flawed constitution mandates that this challenger

根據才剛簽署且滿是瑕疵的憲法，

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

這位挑戰者可以在新選舉中 取代他的受害者。

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

多魔民調機構要你帶著 你那可靠的硬幣再次回到街頭。

Only this time no one is comfortable admitting their preference:

不過這一次，

沒有人願意承認他們支持誰：

supporting the troll is still shameful,

支持巨怪仍然是件可恥的事，

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

也沒有人會想表示自己支持

靠謀殺進入選戰的龍。

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

但，你的工作還是要做。

現在，你要如何進行準確的民調？

Pause here to figure it out for yourself. Answer in 3

自行解題，請在此暫停。 答案即將公佈：三。

Answer in 2

答案即將公佈：二。

Answer in 1

答案即將公佈：一。

This time, instead of masking just one candidate preference,

這次，不能只掩飾 對一位候選人的支持。

you need some way to disguise both.

你得想辦法偽裝 對兩位候選人的支持。

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

同時，

你還得保留些空間， 因為有部分人會在民調中

polled to express their true preference.

表達出他們真正的支持意願。

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

但擲硬幣只會有兩種結果……對吧？

Suppose you have everyone flip the coin twice—

假設你讓每個人都擲兩次硬幣——

now there are four possible results.

現在就有四種可能結果了。

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

你可以告訴兩次都擲出正面的人，

to report support for the troll;

回報說他們支持巨怪；

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

兩次都擲出反面的人，回報支持龍；

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

擲出剩下其他組合的人

要說出真正支持的對象。

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

連續擲出兩次正面或兩次反面的機率

are 50% times 50%— or 25%.

是 50% 乘以 50%，

即 25%。

Subtracting that proportion of the total respondents

把每位候選人的總票數

from each candidate’s score should give you something close

減掉這個比例的人數，

應該就可以得出近似 真實情況的選票分佈。

to the real distribution.

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

這次，有一百零五位受訪者

說他們支持巨怪，

and 95 for the dragon.

九十五位支持龍。

Out of the total, the coin will make 25%

硬幣會讓總人數中 25% 的人

or 50 respond troll and another 50 respond dragon.

或者五十個人必須回答巨怪，

另外五十人回答龍。

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

把每位候選人的總票數減掉五十，

顯示選民似乎比較支持巨怪，

by a margin of about 55 to 45.

比數為五十五比四十五。

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

票數很接近，但如預測，

巨怪贏了選戰。

and you live to poll another day.

你則沒有送命，可以繼續做民調。