Imagine we want to build a new space port at one of four recently settled Martian bases, and are holding a vote to determine its location.

想像一下，我們想在四個新殖民的火星基地之一建立新的太空港，因此舉辦投票來決定新太空港的地點。

Of the hundred colonists on Mars, 42 live on West Base, 26 on North Base, 15 on South Base, and 17 on East 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 位住在南基地，17 位則是住在東基地。

For our purposes, let's assume that everyone prefers the space port to be as close to their base as possible, and will vote accordingly.

為了方便討論我們的主題，先假設大家都希望太空港離自己的基地越近越好，也會依此偏好來投票。

What is the fairest way to conduct that vote?

如何進行投票才是最公平的方式？

The most straightforward solution would be to just let each individual cast a single ballot, and choose the location with the most votes.

最直接的解決方案是讓每個人投一票，並選擇得票最高的地點。

This is known as plurality voting, or "first past the post."

這就是多數制，或「領先者當選」。

In this case, West Base wins easily, since it has more residents than any other.

在這種情況下，西基地很容易勝出，因為那裡的居民比其他基地多。

And yet, most colonists would consider this the worst result, given how far it is from everyone else.

但是，大部分的殖民地居民會認為這是最糟糕的結果，因為西基地離其他人都很遠。

So, is plurality vote really the fairest method?

所以，多數制真的是最公平的投票方式嗎？

What if we tried a system like instant runoff voting, which accounts for the full range of people's preferences rather than just their top choices?

我們是否可以嘗試像排序複選制的制度，把大家所有偏好納入考量，而不只是他們的首選？

Here's how it would work.

這種制度的運作方式是這樣進行的。

First, voters rank each of the options from 1 to 4, and we compare their top picks.

首先，投票者將所有選項從第 1 名排至第 4 名，我們再來比較他們的首選票數。

South receives the fewest votes for first place, so it's eliminated.

南基地得到的首選票數最少，所以將它排除。

Its 15 votes get allocated to those voters' second choice — East Base — giving it a total of 32.

投給南基地的這 15 票就會被重新分配到那些投票者的第二選擇 — 東基地 — 讓它的總得票數變成 32 票。

We then compare top preferences and cut the last place option again.

接著，我們再次比較首選票數，並將最後一名排除。

This time, North Base is eliminated.

這次北基地被排除了。

Its residents' second choice would've been South Base, but since that's already gone, the votes go to their third choice.

北基地居民的第二個選擇本來是南基地，但是南基地早就被排除了，所以他們的票被分配到第三選擇。

That gives East 58 votes over West's 42, making it the winner.

於是，東基地總共有 58 票，超過西基地的 42 票，導致東基地勝出。

But this doesn't seem fair either.

但這樣似乎也不公平。

Not only did East start out in second-to-last place, but a majority ranked it among their two least preferred options.

東基地不但一開始就是倒數第二名，大多數人也都將它排在最後兩名的順位。

Instead of using rankings, we could try voting in multiple rounds, with the top two winners proceeding to a separate runoff.

我們可以不用排名，改用多輪的投票，讓前兩名的選項接著進入獨立的決選。

Normally, this would mean West and North winning the first round, and North winning the second.

通常，這就表示西基地和北基地會在第一輪勝出，而北基地會贏得第二輪。

But the residents of East Base realize that while they don't have the votes to win, they can still skew the results in their favor.

但是，東基地的居民知道，即便他們的票數不足以贏，仍然可以影響結果，讓結果偏向他們的喜好。

In the first round, they vote for South Base instead of their own, successfully keeping North from advancing.

在第一輪，他們投給南基地而不是投給自己的基地，成功讓北基地無法進入第二輪。

Thanks to this "tactical voting" by East Base residents, South wins the second round easily, despite being the least populated.

因為東基地居民的這種「戰略式投票」，人口最少的南基地在第二輪輕鬆獲勝。

Can a system be called fair and good if it incentivizes lying about your preferences?

如果制度本身鼓勵投票者在偏好上作假，還能夠說它是公平的好制度嗎？

Maybe what we need to do is let voters express a preference in every possible head-to-head matchup.

也許我們需要做的是讓投票者針對每種可能性的兩兩競賽來選出他們的偏好。

This is known as the Condorcet method.

這就是孔多塞制 (雙序制)。

Consider one matchup: West versus North.

假設有這樣的競賽：西基地對北基地。

All 100 colonists vote on their preference between the two.

(火星上的) 100 位殖民地居民都要在兩者間選出他們的偏好。

So that's West's 42 versus the 58 from North, South, and East, who would all prefer North.

結果是，西基地的 42 票對北基地的 58 票，因為北、南、東基地的居民都偏好北基地。

Now do the same for the other five matchups.

針對其他五組競賽進行同樣的流程。

The victor will be whichever base wins the most times.

贏得最多次的基地就是最後的贏家。

Here, North wins three and South wins two.

最後，北基地贏得三次，南基地則贏得兩次。

These are indeed the two most central locations, and North has the advantage of not being anyone's least preferred choice.

這兩個選項的確都是最中心的地點，而北基地的優勢在於大家最排斥的選項不是它。

So, does that make the Condorcet method an ideal voting system in general?

這是否代表孔多塞制就是一般情況下最理想的投票制度？

Not necessarily.

不見得。

Consider an election with three candidates.

假設有三位候選人的選舉。

If voters prefer A over B, and B over C, but prefer C over A, this method fails to select a winner.

如果投票者喜歡 A 勝過 B，喜歡 B 勝過 C，但喜歡 C 勝過 A，這個方法就選不出贏家。

Over the decades, researchers and statisticians have come up with dozens of intricate ways of conducting and counting votes, and some have even been put into practice.

數十年以來，研究者和統計學家已經提出了數十種複雜的方法來投票和計票，甚至有些已經被實際應用過。

But whichever one you choose, it's possible to imagine it delivering an unfair result.

但是，無論你選擇使用哪一種投票制度，都有可能造成不公平的結果。

It turns out that our intuitive concept of fairness actually contains a number of assumptions that may contradict each other.

事實上，我們對於公平的直覺觀念，其實已經包含了幾個互相矛盾的假設。

It doesn't seem fair for some voters to have more influence than others.

若某些投票者的影響力比其他投票者大，似乎並不公平。

But nor does it seem fair to simply ignore minority preferences, or encourage people to game the system.

但是，忽略少數人的偏好或鼓勵投票者利用制度耍技倆，似乎也不公平。

In fact, mathematical proofs have shown that for any election with more than two options, it's impossible to design a voting system that doesn't violate at least some theoretically desirable criteria.

事實上，已經有數學證據指出，只要選舉的選項超過兩個，無論如何設計，投票系統都有可能違反一些理論上的理想標準。

So while we often think of democracy as a simple matter of counting votes, it's also worth considering who benefits from the different ways of counting them.

雖然我們經常認為民主只是計票這麼簡單的事，我們也需要思考不同計票方式下誰會受益。

The United States' use of the electoral college to elect presidents instead of the popular vote has become increasingly contentious in recent years.

近幾年，美國利用選舉人團選出總統而不是普選的方式逐漸引起爭議。

How exactly does this system work?

這個制度到底是如何運作？

And is it fair? Or antiquated.

這個制度公平嗎？還是已經過時了？

Find out here.

看下一支影片了解更多。