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After much debate, the fantasy realm you call home has decided dragon jousting may not be the best way to choose its leaders, and has begun transitioning to democracy.
经过大量辩论，你的家园梦幻王国认定龙上骑枪比武可能不是选出领袖的最佳方式，并开始朝向民主改革。
The candidates are a giant orange troll and an experienced tree statesman.
候选人包括一个橘色巨怪和一位有经验的树政治家。
An all-powerful eyebrow has hired your company -- The Dormor Polling Agency -- to survey the citizens of the land and predict who will win.
全能的眉毛雇用了你的公司--多魔民调机构--对全国公民进行调查，预测谁会赢。
There's a lot riding on this: if you get it wrong, heads -- well, your head -- will quite literally roll.
这件事攸关生死：如果你预测错了，人头--嗯，你的头--真的就会落地。
Your job is to go from door to door, asking voters whether they prefer the troll or the treefellow and to use the results to project how the election will go.
你的工作是要挨家挨户拜访，问选民他们比较偏好巨怪或树人，并用这些资料来预测选举的结果。
Your fellow citizens want you to succeed and would tell you the truth... but there's a problem.
你的同胞都希望你成功，因此会告诉你实话...但有一个问题。
Few are willing to admit they support the troll on account of his controversial life choices.
很少有人会肯承认他们支持巨怪，因为巨怪的人生选择十分争议。
If you were to ask a troll supporter who she'll vote for, there's a good chance that she'll claim to support the treeman, skewing your results.
如果你去问巨怪支持者会投给谁，很有可能她会宣称她支持树人，让你的结果有偏差。
You're about to begin your rounds when a stranger offers you some cryptic advice: "Here's the question that will save your neck: what have you got in your pocket?"
就在你即将开始巡访时，一个陌生人给你神秘的建议：“这个问题可以保住你的头颅：你的口袋里有什么？”
You reach into your pocket and pull out... a silver coin, which has the current king's head on one side and his tail on the other.
你把手伸进口袋，拿出了...一个硬银币，一面是现任国王的头像，另一面是他的尾巴。
How can you use it to conduct an accurate poll?
你要如何用这个银币来进行准确的民调？
The trick here is to use the coin to add random chance to your interaction that will give troll supporters deniability.
这里的密诀，是用银币在你的互动中增加一个随机的可能性，让支持巨怪的人可以做出否认。
In other words, you're looking for a system where when someone says "troll,"
换言之，你想设计这样的系统：当对方说“巨怪”时，
it could either be because the coin somehow told them to, or because they actually support the troll -- and you'd have no way to tell the difference.
可能是因为银币要他们说巨怪，或者因为他们真的支持巨怪--而你分不出两者的差别。
You'll also need to know how frequently the coin skewed the results, so you can account for it in your calculations.
你也需要知道银币让结果偏差的频率，这样你在计算时才能一并考虑进去。
One solution is to have every pollee go into their house and flip the coin.
一种解决方案是请每位受访者进到他们的房子里去掷硬币。
If it lands heads, they should tell you "troll," whether or not they actually support him.
如果是正面，他们就要告诉你“巨怪”，不论他们实际上是否支持巨怪。
If it lands tails, they should tell you their actual preference.
如果是反面，他们就要告诉你他们真正支持谁。
Here's what happens: you poll 200 voters, and 130 say they'll vote for the troll.
实际经过如下：你调查了两百位选民，其中一百三十位说他们会投给巨怪。
For about 50%, or 100 of them, the coin will have landed heads.
大约50%的人，或大约一百人，会掷出正面。
So you can subtract 100 troll votes off his total, and know the troll's real support is 30 to 70, and he's very likely to lose.
所以你可以把巨怪的总票数减掉一百票，真正支持巨怪的有三十票，对手七十票，巨怪非常可能会输。
The election comes around, but before the results can be certified a third party candidate swoops in and burns the treefellow to a crisp.
选举开始进行，但在结果能被证实之前，第三方候选人突然袭击，将树人烧成松脆的焦木。
The freshly signed and deeply flawed constitution mandates that this challenger gets to take his victim's place in a new election.
根据才刚签署且满是瑕疵的宪法，这位挑战者可以在新选举中取代他的受害者。
The Dormor Polling Agency sends you back out on the streets with your trusty coin.
多魔民调机构要你带着你那可靠的硬币再次回到街头。
Only this time no one is comfortable admitting their preference:
不过这一次，没有人愿意承认他们支持谁：
supporting the troll is still shameful, and nobody wants to express support of a dragon who murdered his way into the race.
支持巨怪仍然是件可耻的事，也没有人会想表示自己支持靠谋杀进入选战的龙。
But your job is your job. How do you conduct an accurate poll now?
但你的工作还是要做。现在，你要如何进行准确的民调？
This time, instead of masking just one candidate preference, you need some way to disguise both.
这次，不能只掩饰对一位候选人的支持。你得想办法伪装对两位候选人的支持。
At the same time, you also need to leave space for some portion of the people polled to express their true preference.
同时，你还得保留些空间，因为有部分人会在民调中表达出他们真正的支持意愿。
But a coin toss only has two possible outcomes... right?
但掷硬币只会有两种结果...对吧？
Suppose you have everyone flip the coin twice -- now there are four possible results.
假设你让每个人都掷两次硬币--现在就有四种可能结果了。
You can tell the people who flip heads twice in a row to report support for the troll;
你可以告诉两次都掷出正面的人，回报说他们支持巨怪；
those who get tails twice in a row to report dragon; and those with any other combination to declare their true preference.
两次都掷出反面的人，回报支持龙；掷出剩下其他组合的人要说出真正支持的对象。
The chances of getting either two heads or two tails in a row are 50% times 50% -- or 25%.
连续掷出两次正面或两次反面的机率是50%乘以50%，即25%。
Subtracting that proportion of the total respondents from each candidate's score should give you something close to the real distribution.
把每位候选人的总票数减掉这个比例的人数，应该就可以得出近似真实情况的选票分布。
This time, 105 respondents announced themselves in favor of the troll and 95 for the dragon.
这次，有一百零五位受访者说他们支持巨怪，九十五位支持龙。
Out of the total, the coin will make 25% or 50 respond troll and another 50 respond dragon.
硬币会让总人数中25%的人或者五十个人必须回答巨怪，另外五十人回答龙。
Subtracting 50 from each result reveals that voters seem to prefer the troll by a margin of about 55 to 45.
把每位候选人的总票数减掉五十，显示选民似乎比较支持巨怪，比数为五十五比四十五。
It's close, but as predicted, the troll wins the election, and you live to poll another day.
票数很接近，但如预测，巨怪赢了选战，你则没有送命，可以继续做民调。
