Which voting system is the best? - Alex Gendler

譯者: Lilian Chiu 審譯者: Pui-Ching Siu

Imagine we want to build a new space port

想像一下，我們想在 四個新殖民的火星基地

at one of four recently settled Martian bases,

其中一個建立新的太空港，

and are holding a vote to determine its location.

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,

在火星上的 100 名殖民地居民中，

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 位住在東基地。

For our purposes, let’s assume that everyone prefers the space port

為了討論我們的主題， 先假設大家都希望

太空港離他們的基地越近越好，

to be as close to their base as possible, and will vote accordingly.

且會依此偏好來投票。

What is the fairest way to conduct that vote?

怎樣進行投票才是最公平的？

The most straightforward solution would be to just let each individual

最直接的解決方案， 就是讓每個人投一票，

cast a single ballot, and choose the location with the most votes.

並選擇得票最多的地點。

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,

在這個情況下， 西基地很容易勝出，

since it has more residents than any other.

因為那裡的居民比其他基地多。

And yet, most colonists would consider this the worst result,

但，大部分的殖民地居民 會認為這是最糟糕的結果，

given how far it is from everyone else.

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 最公平的投票方法嗎？

What if we tried a system like instant runoff voting,

我們是否可以嘗試 像排序複選制這樣的制度，

which accounts for the full range of people’s preferences

把大家的所有偏好納入考量，

rather than just their top choices?

而不只是他們的第一選擇？

Here’s how it would work.

這種制度的運作方式是：

First, voters rank each of the options from 1 to 4,

首先，投票者為所有選項排名， 從第 1 名到第 4 名，

and we compare their top picks.

我們再來比較首選。

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—

投給它的這 15 票就會被重新 分配到那些投票者的第二選擇——

East Base— giving it a total of 32.

東基地——讓它的總得票數變成 32。

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

接著，我們再次比較首選， 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,

其居民的第二選擇本來是南基地，

but since that’s already gone, the votes go to their third choice.

但南基地早就被排除， 他們的票被轉入第三選擇。

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， 東基地勝出。

But this doesn’t seem fair either.

但那似乎也不公平。

Not only did East start out in second-to-last place,

東基地不但一開始 就只是倒數第二名，

but a majority ranked it among their two least preferred options.

而且大多數人都 將它排在最後兩名。

Instead of using rankings, we could try voting in multiple rounds,

我們可以不要用排名， 改用多輪的投票，

with the top two winners proceeding to a separate runoff.

讓前兩名的選項再接著 進入獨立的決選。

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

通常，那就表示西基地 和北基地會在第一輪勝出，

and North winning the second.

北基地會贏得第二輪。

But the residents of East Base realize

但，東基地的居民知道

that while they don’t have the votes to win,

雖然他們的票數不足以贏，

they can still skew the results in their favor.

但仍然可以影響結果， 讓結果偏向他們的喜好。

In the first round, they vote for South Base instead of their own,

在第一輪，他們投給南基地 而不是他們自己的基地，

successfully keeping North from advancing.

成功讓北基地無法進入第二輪。

Thanks to this "tactical voting" by East Base residents,

因為東基地居民的 這種「戰略式投票」，

South wins the second round easily, despite being the least populated.

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

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？

about your preferences?

Maybe what we need to do is let voters express a preference

也許我們需要做的是讓投票者

針對每種可能的兩兩配對 來選出他們的偏好。

in every possible head-to-head matchup.

This is known as the Condorcet method.

這就是康德西法（雙序制）。

Consider one matchup: West versus North.

想想這種配對：西基地對北基地。

All 100 colonists vote on their preference between the two.

所有 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,

最後西基地的 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。

who would all prefer North.

Now do the same for the other five matchups.

針對其他五組配對進行同樣的流程。

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， 南基地兩次。

These are indeed the two most central locations,

的確，這兩個選項 都是最中心的地點，

and North has the advantage of not being anyone’s least preferred choice.

且北基地的優勢在於 大家最排斥的選項不是它。

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

這是否表示康德西法就是 一般情況下最理想的投票制度？

Not necessarily.

不見得。

Consider an election with three candidates.

想想有三位候選人的選舉。

If voters prefer A over B, and B over C, but prefer C over A,

如果投票者喜歡 A 勝過 B，

喜歡 B 勝過 C，但喜歡 C 勝過 A，

this method fails to select a winner.

這個方法就選不出贏家。

Over the decades, researchers and statisticians have come up with

數十年來，研究者 和統計學家已經提出了

dozens of intricate ways of conducting and counting votes,

數十種複雜的方法來投票和計票，

and some have even been put into practice.

甚至有些已經被實際應用。

But whichever one you choose,

但，不論你選擇哪一種，

it's possible to imagine it delivering an unfair result.

都有可能造成結果不公平的情況。

It turns out that our intuitive concept of fairness

結果發現，我們對於 公平的直覺觀念，

actually contains a number of assumptions that may contradict each other.

其實已經包含有 數個彼此矛盾的假設。

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,

但忽略少數人的偏好 或鼓勵投票者利用制度耍技倆，

or encourage people to game the system.

似乎也都不公平。

In fact, mathematical proofs have shown that for any election

事實上，已經有數學證據指出，

只要選舉的選項超過兩個，

with more than two options,

it’s impossible to design a voting system that doesn’t violate

不論如何設計，設計出的投票系統

都不可能不違反任何一種 理論上的理想標準。

at least some theoretically desirable criteria.

So while we often think of democracy as a simple matter of counting votes,

雖然我們經常認為民主 就只是計票這麼簡單的事，

it’s also worth considering who benefits from the different ways of counting them.

我們也值得好好思考一下， 不同計票方式下誰會受益。