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

翻译人员: yifei wang 校对人员: Helen Chang

After much debate, the fantasy realm you call home

多轮辩后，你的国家幻想之国觉得 赛龙也许不是选择领袖的最好方式

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

and has begun transitioning to democracy.

于是从赛龙这种方式逐渐过渡到了民主

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

候选人们是一个橙色巨人 和一棵经验丰富的树政治家

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

一个全能的眉毛雇用 你的公司‘‘老虎窗投票公司’’

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

来调查地区居民，推断赢家

There’s a lot riding on this:

干这个的压力很大呀

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

如果有什么差错， 有人的脑袋，嗯...你的脑袋

will quite literally roll.

就要掉在地上滚了

Your job is to go from door to door,

你的工作是挨家挨户地

asking voters whether they prefer the troll or the treefellow

询问投票者是支持巨人还是树

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

然后运用投票的结果来决定选举的结果

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

你的子民们会想要你成功 他们会向你吐露心声

but there’s a problem.

但是还有个问题

Few are willing to admit they support the troll

由于巨人饱受争端的生活方式

on account of his controversial life choices.

只有那么区区几个会承认他们支持巨人

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

如果你去问巨人的支持者 她们应该选择谁

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

有很大的几率她会告诉你 说她支持的是树

skewing your results.

这就让你采集的结果非常不可靠

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

正当你打算开始用这个不可靠的方式 采集投票结果时：

一个神秘人向你提供了一个神秘的建议

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

‘’这是一个能让你能保住脑袋的问题： 你口袋里装的是什么？“

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

你伸手去你的口袋里掏... 原来是一枚硬币

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

硬币正面有着现任国王的头像， 反面是国王的尾巴

How can you use it to conduct an accurate poll?

你怎么用这枚硬币 得到一个准确的大选结果呢？

Pause here to figure it out yourself. Answer in 3

按暂停然后自己想想 3

Answer in 2

2

Answer in 1

1

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

方法就是用硬币来增加 支持巨人的票数的随机性

to your interaction that will give troll supporters deniability.

因为有些人不是不敢投巨人吗

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

换种说法就是，你要找一种体制， 当人们在这个体制中投票给巨人

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

可以是因为这个硬币让他们这样做

or because they actually support the troll—

也可以是因为他们的确想投给巨人

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

但是你无法判断

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

你还需要知道这枚硬币打乱结果的频率

so you can account for it in your calculations.

最后你就可以通过以上的信息 来计算大选结果

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

那么办法就是，每个投票的人 回房间里去抛硬币

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

如果正面朝上，他们就必须支持巨人

whether or not they actually support him.

不管他们是不是真正的支持巨人

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

如果是反面朝上， 他们就必须说出真实的想法

Here’s what happens:

那么以下的局面就会发生：

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

你采集了200个人的投票选择 130个人说要投给巨人

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

那么大约50% 或者200人里的100个人

抛出来的硬币正面朝上

So you can subtract 100 troll votes off his total,

所以你就可以用 巨人得到的总票数减去100

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

得到真正支持巨人的是3比7 显然巨人要落选啊

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

大选正在进行 但当结果确定下来之前

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

有个第三方突然出现 然后把参加大选的树烧成了渣渣

The freshly signed and deeply flawed constitution mandates that this challenger

刚刚完工，漏洞百出的宪法规定 这个第三方挑战者

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

能代替他的受害人去参加新的大选

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

你的老虎窗投票公司 又派你和你可靠的硬币去调查大选

Only this time no one is comfortable admitting their preference:

只是这次没有人愿意说出 他们真正的想法了

supporting the troll is still shameful,

因为：支持巨人还是一件很羞耻的事

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

而且没有人想在明面上 支持一个靠着谋杀成为候选人的龙

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

但是你的工作还是得做啊 在该怎么得到最公平准确的结果呢？

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

按暂停然后自己想想 3

Answer in 2

2

Answer in 1

1

This time, instead of masking just one candidate preference,

这次与上次不一样，你不只是要模糊 群众对一个候选人的喜好

you need some way to disguise both.

你要同时模糊两个 同时增加票数随机性

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

与此同时， 你还要留点空间 让某一部分的人

polled to express their true preference.

去表达他们真正的意愿

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

但是一枚硬币只有着正反两面 两种可能性... 对吧？

Suppose you have everyone flip the coin twice—

假设你让所有人都抛两次硬币

now there are four possible results.

那么现在就有4种结果

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

你可以让抛硬币结果是 “两次都是正面”的人

to report support for the troll;

说他们支持巨人

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

两次都是反面的人说她们支持龙

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

让那些一正一反的吐露他们的心声

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

抛到相同面，两正或两反的几率是

are 50% times 50%— or 25%.

50%乘50%--->25%

Subtracting that proportion of the total respondents

减去总人数的25%

from each candidate’s score should give you something close

每个候选人的投票结果就应该

to the real distribution.

和真实的结果比较相近了

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

这次，有105个人投了巨人

and 95 for the dragon.

95人投了龙

Out of the total, the coin will make 25%

硬币的结果会让总人数的25%

or 50 respond troll and another 50 respond dragon.

也就是50人，投给巨人 再有另外50人投给龙

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

用巨人和龙获得的票数各减去50 我们发现选民似乎更喜欢巨人

by a margin of about 55 to 45.

大概是55比45这样的结果

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

虽然是险胜，但是巨人还是 照预测的那样赢得了选举

and you live to poll another day.

而你又能活着去调查下一个选举了