到底哪个投票制度才是最好的?Alex Gendler Alex Gendler: Which voting system is the best?

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演员: Alex Gendler


台词
Imagine we want to build a new space port
假如我们想在四个最新的火星基地
at one of four recently settled Martian bases,
建立一个新的太空港,
and are holding a vote to determine its location.
并通过投票来决定 新太空港的地点。
Of the hundred colonists on Mars, 42 live on West Base, 26 on North Base,
在火星上的 100 名殖民地居民中, 有 42 位住在西基地,26 位住在北基地,
15 on South Base, and 17 on East Base.
15 位住在南基地,17 位住在东基地。
For our purposes, let’s assume that everyone prefers the space port
介于此次的目的, 先假设所有人都希望
to be as close to their base as possible, and will vote accordingly.
太空港离他们的基地越近越好, 并且会以此为参考进行投票。
What is the fairest way to conduct that vote?
怎样举行投票才是最公平的?
The most straightforward solution would be to just let each individual
最直接的方案 就是让每一个人投一票,
cast a single ballot, and choose the location with the most votes.
然后选出得票最多的地点。
This is known as plurality voting, or "first past the post."
这就是多数制(plurality voting), 或“领先者当选”(first past the post)。
In this case, West Base wins easily,
在这个情况下, 西基地很容易胜出,
since it has more residents than any other.
因为那里的居民多于其他的基地。
And yet, most colonists would consider this the worst result,
可是,大多数的居民会认为 这是最差的结果,
given how far it is from everyone else.
因为西基地离其他所有人都很远。
So is plurality vote really the fairest method?
那么,多数制投票 真的是最公平的方法吗?
What if we tried a system like instant runoff voting,
我们是否也可以尝试 “排序复选制”(instant runoff voting),
which accounts for the full range of people’s preferences
即考虑大家所有的偏向,
rather than just their top choices?
而不只是他们的第一选择?
Here’s how it would work.
排序复选制的规则是这样的:
First, voters rank each of the options from 1 to 4,
首先,投票者将 把他们的选择按优先级排序,
and we compare their top picks.
我们会比较他们的第一选择。
South receives the fewest votes for first place, so it’s eliminated.
南基地收到的投票最少, 所以最先将它排除。
Its 15 votes get allocated to those voters’ second choice—
投给它的 15 票会被重新分配给 投票者的第二选择——
East Base— giving it a total of 32.
东基地——那么它的总票数会是 32。
We then compare top preferences and cut the last place option again.
然后,我们再次比较 首选并且排除最后一名。
This time North Base is eliminated.
这次北基地会被排除。
Its residents’ second choice would’ve been South Base,
该基地居民的第二选择 本来会是南基地,
but since that’s already gone, the votes go to their third choice.
但是南基地已经被排除了, 票数会分配到他们的第三选择。
That gives East 58 votes over West’s 42, making it the winner.
这样,东基地 58 票比西基地 42 票, 东基地胜出。
But this doesn’t seem fair either.
但这似乎也不太公平。
Not only did East start out in second-to-last place,
东基地不仅一开始是倒数第二名,
but a majority ranked it among their two least preferred options.
并且,在大多数人的排序中, 它都位列最后两名。
Instead of using rankings, we could try voting in multiple rounds,
不过,我们也可以不用排名, 而尝试改用多轮投票。
with the top two winners proceeding to a separate runoff.
前两名的选择直接 进入独立的决选。
Normally, this would mean West and North winning the first round,
通常来说,这意味着 西和北基地在第一轮胜出,
and North winning the second.
北基地在第二轮胜出。
But the residents of East Base realize
但是东基地的居民认识到,
that while they don’t have the votes to win,
虽然他们的票数不足以让他们胜出,
they can still skew the results in their favor.
他们仍然可以让结果偏向他们的喜好。
In the first round, they vote for South Base instead of their own,
在第一轮,他们投给南基地, 而不是他们自己的东基地,
successfully keeping North from advancing.
以成功地阻止北基地胜出。
Thanks to this "tactical voting" by East Base residents,
因为东基地居民的“战略性投票”,
South wins the second round easily, despite being the least populated.
尽管拥有最少的居民, 南基地在第二轮轻松胜出。
Can a system be called fair and good if it incentivizes lying
如果一个系统鼓励谎报偏好的话,
about your preferences?
它还能被称为一个公平的系统吗?
Maybe what we need to do is let voters express a preference
也许我们需要让投票者针对 所有可能的两两配对做出选择,
in every possible head-to-head matchup.
由此选出他们的喜好。
This is known as the Condorcet method.
这就是康德西法 (Condorcet method,即双序制)。
Consider one matchup: West versus North.
比如:西基地对北基地。
All 100 colonists vote on their preference between the two.
所有 100 名殖民地居民都要 在两者中选出他们的偏好。
So that's West's 42 versus the 58 from North, South, and East,
结果是西基地的 42 票对 北基地的 58 票,
who would all prefer North.
因为其他三个基地都偏向于北。
Now do the same for the other five matchups.
现在对其他五个组合也进行一样的流程,
The victor will be whichever base wins the most times.
胜出者将会是赢得最多次的基地。
Here, North wins three and South wins two.
北基地赢得三次,南基地两次。
These are indeed the two most central locations,
它们确实是最靠近中心的地点,
and North has the advantage of not being anyone’s least preferred choice.
并且北基地的优势是, 它不是任何一方最排斥的选择。
So does that make the Condorcet method an ideal voting system in general?
那么,这意味着康德西方法 总会是最理想的投票制度吗?
Not necessarily.
不一定。
Consider an election with three candidates.
假设在一场选举中 有三位候选人。
If voters prefer A over B, and B over C, but prefer C over A,
如果投票者们喜欢 A 胜过 B, 喜欢 B 胜过 C,但喜欢 C 胜过 A,
this method fails to select a winner.
那么,这个方法就无法选出一个赢家。
Over the decades, researchers and statisticians have come up with
数十年来,研究者 和统计学家已经提出过
dozens of intricate ways of conducting and counting votes,
数十种复杂的方法来投票和计票,
and some have even been put into practice.
有些甚至已经被投入实际应用。
But whichever one you choose,
但不论你选择哪个,
it's possible to imagine it delivering an unfair result.
都可以想得出 某种结果不公平的情况。
It turns out that our intuitive concept of fairness
其实,我们对公平的直觉观念
actually contains a number of assumptions that may contradict each other.
已经包含了数个 也许互相矛盾的假设。
It doesn’t seem fair for some voters to have more influence than others.
若某些投票者的影响力 比其他投票者大,似乎就不太公平。
But nor does it seem fair to simply ignore minority preferences,
但忽略少数人的偏好, 或鼓励投票者利用制度耍小伎俩,
or encourage people to game the system.
似乎也不公平。
In fact, mathematical proofs have shown that for any election
事实上,已经有数学证明指出,
with more than two options,
只要选举的选项超出两个,
it’s impossible to design a voting system that doesn’t violate
那么设计出的投票制度 就一定会违反
at least some theoretically desirable criteria.
某些理论前提下的理想标准。
So while we often think of democracy as a simple matter of counting votes,
虽然我们经常认为民主 只是数一数票那么简单的事,
it’s also worth considering who benefits from the different ways of counting them.
但我们也应该认真思考, 在不同的计票方式下,谁会收益。