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第一次深入地思考“沉沒成本”這個概念，是在和閨蜜彼此吐槽生活的電話里。
她吐槽年過二十五，戀愛經(jīng)歷仍然為零。
我吐槽讀博士時間長又辛苦，前途渺茫，投資效益比低。
呱啦呱啦呱啦，年輕人的煩惱沒完沒了。她在電話中提到“沉沒成本”的概念，并針對她自己的情況進行分析，得出的結(jié)論是：一直有戀愛經(jīng)歷但因種種原因沒有找到Mr. Right的人和從來沒有戀愛經(jīng)歷的人相比，沉沒成本不同，而后者成本更甚。長時間的單身不但難以發(fā)展戀愛中所需的體貼、交流、委身以及表達愛的能力，而且更會因為長期獨處而形成脫離現(xiàn)實、不切實際的標準，從而更難邁出交往的第一步。
我立刻學以致用、舉一反三，把這套標準用在讀博上。博士二年級時我就有過掙扎和想放棄的想法，猶猶豫豫磨磨蹭蹭又過了兩年，四年都念了，投入的時間不能挽回，就此放棄，實在不甘心，只好硬著頭皮往下念。用俗話說，就是中國式四大寬容之一：“來都來了”。
而根據(jù)我對自己的了解，我還知道，我不僅會對“沉沒成本”一籌莫展，而且，為了維護自己內(nèi)心秩序的平衡，最后還要自我總結(jié)一下：經(jīng)驗都是寶貴的，苦難都是值得的。為了賦予人生的暴擊以意義，我還會說，感謝磨難和掙扎。
我的堅強并不多，只比苦難多一點。
呵呵。
掛了電話我就去研究了一下“沉沒成本”。“沉沒成本”是經(jīng)濟學概念，顧名思義，即已經(jīng)付出的、不可回收的成本。在做經(jīng)濟學決策時，只需考慮可變成本，不需考慮沉沒成本。如果同時考慮沉沒成本，那么決策就偏離了事物本身的價值。
維基舉例：已經(jīng)買了電影票卻聽說電影不好看，這時候就應該果斷放棄看電影。電影票錢已經(jīng)是無法挽回的沉沒成本，此時只需考慮電影是否好看。如果為了不浪費錢而看了無聊的電影，就不是基于電影本身價值做出的最優(yōu)解。
可是大多數(shù)人都會因為已經(jīng)買了票，而枯坐在電影院。
那么既然考慮沉沒成本往往使我們偏離最優(yōu)解，為什么在漫長的進化過程中，我們沒有舍棄這個思想包袱？還是說，“沉沒成本”是伴隨著高級思維產(chǎn)生的、人類所獨有的思想包袱？
美國明尼蘇達大學的科學家用小鼠和大鼠做了一組覓食實驗。饑餓的小鼠們被置于迷宮當中，迷宮里有四個隔間，分別提供四種口味不同的鼠糧：無味、葡萄味、巧克力味和香蕉味。小鼠在前期的訓練過程中熟悉每一個隔間所提供的口味，而且會根據(jù)音樂聲判斷需要在隔間等待的時間，音符越高，時間越長。實驗開始后，小鼠有30分鐘的時間穿梭在迷宮里。進入一個隔間后，他們會選擇是否想吃該口味的鼠糧。如果想要，就進入等待區(qū)，音符隨機響起，他們可以自行判斷等下去還是果斷離開。
“聰明”的小鼠會讓自己在可以吃飽的前提下，盡可能多的吃到自己最愛的口味。因此，理想狀態(tài)下，他們可以適量的多花時間等待自己愛吃的口味，而在“無味”的隔間里，如果需要長時間等待，就應該放棄。
科學家們發(fā)現(xiàn)，原來人不是唯一考慮沉沒成本的動物！小鼠在覓食過程中，也會考慮沉沒成本。如果已經(jīng)付出時間等待，它們大多數(shù)則會繼續(xù)等下去，即便理智告訴它們應該離開。
而且，有趣的是，小鼠在終于等到并吃完鼠糧以后，會有一定的“回味時間”，即在同一個隔間多逗留一會兒，看有沒有剩下的、多余的鼠糧。而等待時間越久，回味的時間就越長，即便吃到的并不是它們最愛的口味。也就是說，小鼠跟我們差不多，為了維護內(nèi)心秩序的平衡，為了說服自己所花費的時間是值得的，硬生生地改變了口味也要堅持，等的越久越好吃！
在以往的動物實驗中，因為無法告訴實驗對象等待的具體時間，因而難以考察動物對沉沒成本的理解。此實驗巧妙地通過音符的變化而繞過這一障礙，從而告訴小鼠具體需要等待的時間長度。然而，這與現(xiàn)實生活中人們對沉沒成本的判斷，還有一定的差距。
在實際生活中，沒有人告訴你，需要等待多久，才有王子駕著七彩祥云來娶你；也不會有人承諾你，努力了六年，似錦的前程就會像巧克力味的鼠糧，如約而至。結(jié)果的不確定性使得人們在進行判斷時，前瞻性被模糊，只能更多地依靠后顧性。
不過這個實驗起碼說明了，考慮沉沒成本不是人類所獨有的，而是在漫長的進化過程中，和多種物種共享的思維定式。那么，既然經(jīng)濟學告訴我們這是謬誤，是不理智的，我們?yōu)楹伪Ａ糁两?？又是否一定要擺脫沉沒成本的束縛？
既然沉沒成本是經(jīng)濟學概念，那么一切脫離了經(jīng)濟的考慮就是耍流氓。已知有兩個項目，一個已投資50萬，若再投資50萬，收益150萬。另一個若投資80萬，收益200萬。此時應該果斷放棄已經(jīng)投入的，而選擇效益高的。在錢的世界里，把成本賺回來了就回到原點，剩余的則可算為收益。在人的世界里則不然。
因為人投入的是時間、感情、精力、心血，一旦付出，便再也回不到原點。這聽起來像是詛咒，但其實也是祝福。
跟張三戀愛三年，期間一直有波折。此時有兩個選擇。第一，放棄張三，再尋李四?？墒且欢ㄓ欣钏膯?？李四一定比張三好嗎？李四不需要磨合嗎？放棄張三損失的是穩(wěn)定性，得著的是自己內(nèi)心的安寧和舒暢，以及再遇李四王五的可能性。第二種選擇，因為已經(jīng)投入了感情而繼續(xù)和張三磨合。這或許要放棄一些自主性，出讓一些主權和空間?？墒瞧鋵嵢魏谓?jīng)歷過親密關系的人都明白，人之相與，就是要不斷的磨合、妥協(xié)、遷就、忍讓，從而練就美好的品格。愛是恒久忍耐。因此人生的吊詭之處就在，無論怎么選，都是失去?？扇松拿烂钪幰舱诖耍簾o論怎么選，都能得著。
最近我開始用游山玩水的心情對待求學之路。任何學科的深入學習都要經(jīng)歷初極狹，才通人的階段，而誰又能預料，復行數(shù)十步，豁然開朗，土地平曠，屋舍儼然。王安石曾經(jīng)在辭職回家的路上路過褒禪山，與朋友游一山洞有感：世界上美麗的東西都很難得，需要毅力（世之奇?zhèn)ァ⒐骞郑浅Ｖ^，常在于險遠，而人之所罕至焉，故非有志者不能至也）。有毅力，又不隨波逐流，但沒有體力、精力，也得不到（有志矣，不隨以止也，然力不足者，亦不能至也）。有毅力、體力、精力，不人云亦云，但行至幽暗處，沒有可借助的工具，也不能到達（有志與力，而又不隨以怠，至于幽暗昏惑而無物以相之，亦不能至也）。如果萬事俱備，仍然半途而棄，不但別人恥笑，自己也要后悔（然力足以至焉，于人為可譏，而在己為有悔）；可是盡了心力卻沒有到達，自己問心無愧，別人又能說些什么呢（盡吾志也而不能至者，可以無悔矣，其孰能譏之乎）？
入之愈深，其進愈難，而其見愈奇，這是“進”的得著。盡吾志也而不能至者，可以無悔矣。問心無愧，這是“退”的饋贈。
人生是一個把可能性越過越少的過程。選了單身貴族，就少了油鹽醬醋；選了遠走高飛，就少了承歡膝下；選了挑燈夜讀，就少了觥籌交錯。所以我們羨慕青春，因為青春充滿了可能性?？汕∏∫驗槭篱g沒有雙全法，每一次選擇都有遺憾，才使得每一個選擇厚重而有分量。倘若事事兩全，實則事事無趣。因而這些成本無一沉沒，因為這點點滴滴的選擇堆聚成了獨一無二的我們，迷惘的、沉思的、沸騰的。
所有的小鼠都愛巧克力，鼠類愛甜，這并無特別?？捎幸恢恍∈髸驗榈却撕芫茫瑘猿终f自己口味很淡，愛無味的鼠糧。因為這個選擇，他不再是萬千小鼠中的一個，他有了自己的故事。
聽說電影很不好看，但因為第一次約會，你和TA都堅持看完了。后來你們一起看了很多有質(zhì)量的電影，都忘了，唯有這第一個無趣的電影、枯坐的尷尬，變成了一輩子的笑料和甜蜜的回憶。
"一代傾城逐浪花，吳宮空自憶兒家。效顰莫笑東鄰女，頭白溪邊仍浣紗。"(1)
西施貌美，卻因貌美而離家千里，離家又收獲了吳王的寵愛。東施其貌不揚，卻現(xiàn)世安穩(wěn)。誰能說怎樣的人生更精彩呢？
讓經(jīng)濟學的歸經(jīng)濟學，生命的歸生命。生命里沒有沉沒成本，只有獨一無二的故事。
The first time I heard of the term “sunk cost” was in a phone call with a close friend. We both felt the need to vent and lament, she over her state of singleness, and I over a seemingly interminable Ph.D.
The thought of quiting my PhD had crept into my mind a few years ago, but while I sat around being indecisive, time twirled and leapt and danced forward. Before I knew it, I was caught in an awkward and uncompromising state: two years of work I might’ve given up, but four years? Five years?
“That”, pronounced my friend over the phone, “is making bad decisions on the sunk cost fallacy”.
As for herself, the sunk cost of having been single the entire 26 years of her life is profound. All the caution and work that had went into waiting now makes it extremely difficult to let others into her life.
After we hung up, I googled “sunk cost”. It is a term coined in economics and business, meaning “a cost that has already been incurred and can not be recovered”. It is contrasted with “prospective costs”, meaning future costs which may be incurred.
The example given by Wikipedia to illustrate “sunk cost” is investment by a company in a power plant. $20 million has been spent already but the current value of the plant is 0 because it is incomplete. The company can either spend another $10 million to complete the power plant, or invest $5 million in another equally profitable facility. The rational decision-maker in this case should disregard sunk costs ($20 million already invested) and invest in the new project.
This is all very well. But it doesn’t take much for sunk costs to be extended to other life decisions. Can’t give up watching a bad movie because you’ve already purchased the ticket? Cut your losses, get up and go! Made up your mind to picnic but it starts to rain as you head out? Smart people turn back. Spent four years in university on a subject you find out you don’t care for? Run from it as fast as you can!
The theory posits that if people were rational and smart all the time, they will disregard sunk costs and move on. But in reality, we are all too easy prey to this fallacy. Most people will wait out a bad movie, head out for the picnic hoping the rain will stop, and explore cautiously related areas of study.
A team of researchers at the University of Minnesota recently reported that when it comes to making decisions, humans are not the only species that are all too aware of irrecoverable costs. It seems that even mice and rats are sensitive to sunk costs.
To research this, scientists designed a maze with four different "restaurants", each offering different flavored kibbles: plain, grape, banana or chocolate. Mice and rats that are familiar with these rooms and kibbles were then allowed to forage for half an hour on an empty stomach. As they come to a "restaurant", they will first linger in an "offer zone", in which they need to make a decision regarding whether they want to commit to waiting for a particular flavor. If so, they will then move into the "waiting room". After the decision of commitment and entrance into the waiting room, a musical note will play at random, indicating the amount of time they will have to wait for the kibbles to be dispensed. High-pitched notes meant longer waiting times.
"Smart" animals should decide to leave quickly if they enter a room that pairs a less-preferred flavor with a long wait time. However, across individuals and experiments, mice and rats both showed a tendency to stick with their commitments, regardless of their preferences. Typical sunk costs bias! And the longer the wait, the stronger the bias.
Whew, so we are not the only ones making non-optimal decisions in life, though the satisfaction gained from finding out that mice think just like us (or we think just like mice???) is minimal at most. But one does begin to wonder, if considering sunk costs leads to bad decision-making, even in survival situations like foraging, why hasn't evolution weeded this bias out?
This experiment was elegantly designed to study sunk costs in animals, because teaching the animals to correlate wait times with musical notes helped them assess the amount of future investments needed. In past animal experiments, information uncertainty has led to some inconsistent results. However, lack of information is perhaps a more realistic illustration of real-world situations. We don't know how long it will take for our efforts to pay off! When future costs are difficult to evaluate, we have nothing to base our decisions off of except past efforts, and to pray hard that they will pay off.
Even more interestingly, scientists were able to measure how much the rodents appreciated their kibbles by measuring the amount of times they lingered in a particular "restaurant" after they had already consumed what was offered. The longer they lingered, perhaps hoping for more or looking for bits they might've missed, the more they valued the reward. And funnily enough, the longer they've waited for their reward, the more they valued it, regardless of their original flavor preferences! It's kind of the human version of #worthit. The need to psychologically console and make peace with our inner selves was also passed down in evolution. So then... is it really necessary to avoid decision making based on sunk costs now?
As an economic concept, sunk costs has its own relevance in the monetary world. Once investment pays off, in terms of bank accounts, we basically turned the clock back to day 0. Therefore, an equally profitable facility that costs $5 million is a much better choice than spending an additional $10 million on top of the $20 million already invested in the half-complete power plant.
But in the world of careers, love, relationships, life experiences, we will never EVER come back to day 0 again, which, in some ways, is a lamentable loss, but in other ways, a tremendous blessing.
Robert Frost, in “The Road Less Traveled”, described two roads that diverged in a wood, and like any traveler he was faced with a choice: the choice of saying “yes” or “no”, the choice of persisting or quitting, and when push comes to shove, in all life choices, we MUST choose, and we can only make one choice.
And both that morning equally lay
In leaves no step had trodden black.
Oh, I kept the first for another day!
Yet knowing how way leads on to way,
I doubted if I should ever come back.
Perhaps we consider the decision wrong after we had traveled along the second road for a while, perhaps the scenery is not to our taste. But knowing woods, and lives, there will be other roads, other forks, other choices. We will never come to the same spot twice. And there lies the magnitude, and beauty, of choices.
But as we walked down the second road, even though we imagine the first to be better (how will we ever know?), we learned the names of the strange mushrooms that dotted the path, we befriended a stray fox that wanders those parts, we watched the sunset crown the trees. The second road, and the choice to go along it, made us who we are:
I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I—
I took the one less traveled by,
And that has made all the difference.
Mice tend to like chocolate-flavored kibbles, no surprises there. But because one mouse once decided to wait for grape-flavored kibbles, and spent a long time waiting, he will tell a different story. And so he is forever set apart.
Being single means losing out a bit on companionship, getting to know people, practicing the skills of communication and love. But one day when Mr. Right finally shows up (fashionably late of course), who’s to say the joy of courting one’s first love won’t make the wait worth it? And it works the other way too.
The Little Prince said of the rose he worked hard to take care of, “It is the time you have wasted for your rose that makes your rose so important.” And that rings true for PhDs, for families, for life in general.
So render onto Caesar the things that are Caesar’s, and to God the things that are God’s. Let sunk costs stay in economics and business decision making, and let life proceed unconfounded.
References
B.M. Sweis el al., "Sensitivity to 'sunk costs' in mice, rats, and humans," Science (2018)
（1）《紅樓夢》五美吟
中英文皆原創(chuàng)，禁止轉(zhuǎn)載
