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第一次深入地思考“沉没成本”这个概念，是在和闺蜜彼此吐槽生活的电话里。
她吐槽年过二十五，恋爱经历仍然为零。
我吐槽读博士时间长又辛苦，前途渺茫，投资效益比低。
呱啦呱啦呱啦，年轻人的烦恼没完没了。她在电话中提到“沉没成本”的概念，并针对她自己的情况进行分析，得出的结论是：一直有恋爱经历但因种种原因没有找到Mr. Right的人和从来没有恋爱经历的人相比，沉没成本不同，而后者成本更甚。长时间的单身不但难以发展恋爱中所需的体贴、交流、委身以及表达爱的能力，而且更会因为长期独处而形成脱离现实、不切实际的标准，从而更难迈出交往的第一步。
我立刻学以致用、举一反三，把这套标准用在读博上。博士二年级时我就有过挣扎和想放弃的想法，犹犹豫豫磨磨蹭蹭又过了两年，四年都念了，投入的时间不能挽回，就此放弃，实在不甘心，只好硬着头皮往下念。用俗话说，就是中国式四大宽容之一：“来都来了”。
中国式四大宽容：大过年的、人都死了、来都来了、多大点事儿
而根据我对自己的了解，我还知道，我不仅会对“沉没成本”一筹莫展，而且，为了维护自己内心秩序的平衡，最后还要自我总结一下：经验都是宝贵的，苦难都是值得的。为了赋予人生的暴击以意义，我还会说，感谢磨难和挣扎。
我的坚强并不多，只比苦难多一点。
呵呵。
挂了电话我就去研究了一下“沉没成本”。“沉没成本”是经济学概念，顾名思义，即已经付出的、不可回收的成本。在做经济学决策时，只需考虑可变成本，不需考虑沉没成本。如果同时考虑沉没成本，那么决策就偏离了事物本身的价值。
维基举例：已经买了电影票却听说电影不好看，这时候就应该果断放弃看电影。电影票钱已经是无法挽回的沉没成本，此时只需考虑电影是否好看。如果为了不浪费钱而看了无聊的电影，就不是基于电影本身价值做出的最优解。
可是大多数人都会因为已经买了票，而枯坐在电影院。
那么既然考虑沉没成本往往使我们偏离最优解，为什么在漫长的进化过程中，我们没有舍弃这个思想包袱？还是说，“沉没成本”是伴随着高级思维产生的、人类所独有的思想包袱？
美国明尼苏达大学的科学家用小鼠和大鼠做了一组觅食实验。饥饿的小鼠们被置于迷宫当中，迷宫里有四个隔间，分别提供四种口味不同的鼠粮：无味、葡萄味、巧克力味和香蕉味。小鼠在前期的训练过程中熟悉每一个隔间所提供的口味，而且会根据音乐声判断需要在隔间等待的时间，音符越高，时间越长。实验开始后，小鼠有30分钟的时间穿梭在迷宫里。进入一个隔间后，他们会选择是否想吃该口味的鼠粮。如果想要，就进入等待区，音符随机响起，他们可以自行判断等下去还是果断离开。
实验设计：小鼠可以自由穿梭在口味不同的四个房间。每间有“选择室”和“等待室”。进入等待室后由音符告知等待时间
“聪明”的小鼠会让自己在可以吃饱的前提下，尽可能多的吃到自己最爱的口味。因此，理想状态下，他们可以适量的多花时间等待自己爱吃的口味，而在“无味”的隔间里，如果需要长时间等待，就应该放弃。
科学家们发现，原来人不是唯一考虑沉没成本的动物！小鼠在觅食过程中，也会考虑沉没成本。如果已经付出时间等待，它们大多数则会继续等下去，即便理智告诉它们应该离开。
已等待时间越长（暖色），离开的概率越小
而且，有趣的是，小鼠在终于等到并吃完鼠粮以后，会有一定的“回味时间”，即在同一个隔间多逗留一会儿，看有没有剩下的、多余的鼠粮。而等待时间越久，回味的时间就越长，即便吃到的并不是它们最爱的口味。也就是说，小鼠跟我们差不多，为了维护内心秩序的平衡，为了说服自己所花费的时间是值得的，硬生生地改变了口味也要坚持，等的越久越好吃！
在以往的动物实验中，因为无法告诉实验对象等待的具体时间，因而难以考察动物对沉没成本的理解。此实验巧妙地通过音符的变化而绕过这一障碍，从而告诉小鼠具体需要等待的时间长度。然而，这与现实生活中人们对沉没成本的判断，还有一定的差距。
在实际生活中，没有人告诉你，需要等待多久，才有王子驾着七彩祥云来娶你；也不会有人承诺你，努力了六年，似锦的前程就会像巧克力味的鼠粮，如约而至。结果的不确定性使得人们在进行判断时，前瞻性被模糊，只能更多地依靠后顾性。
不过这个实验起码说明了，考虑沉没成本不是人类所独有的，而是在漫长的进化过程中，和多种物种共享的思维定式。那么，既然经济学告诉我们这是谬误，是不理智的，我们为何保留至今？又是否一定要摆脱沉没成本的束缚？
既然沉没成本是经济学概念，那么一切脱离了经济的考虑就是耍流氓。已知有两个项目，一个已投资50万，若再投资50万，收益150万。另一个若投资80万，收益200万。此时应该果断放弃已经投入的，而选择效益高的。在钱的世界里，把成本赚回来了就回到原点，剩余的则可算为收益。在人的世界里则不然。
因为人投入的是时间、感情、精力、心血，一旦付出，便再也回不到原点。这听起来像是诅咒，但其实也是祝福。
跟张三恋爱三年，期间一直有波折。此时有两个选择。第一，放弃张三，再寻李四。可是一定有李四吗？李四一定比张三好吗？李四不需要磨合吗？放弃张三损失的是稳定性，得着的是自己内心的安宁和舒畅，以及再遇李四王五的可能性。第二种选择，因为已经投入了感情而继续和张三磨合。这或许要放弃一些自主性，出让一些主权和空间。可是其实任何经历过亲密关系的人都明白，人之相与，就是要不断的磨合、妥协、迁就、忍让，从而练就美好的品格。爱是恒久忍耐。因此人生的吊诡之处就在，无论怎么选，都是失去。可人生的美妙之处也正在此：无论怎么选，都能得着。
最近我开始用游山玩水的心情对待求学之路。任何学科的深入学习都要经历初极狭，才通人的阶段，而谁又能预料，复行数十步，豁然开朗，土地平旷，屋舍俨然。王安石曾经在辞职回家的路上路过褒禅山，与朋友游一山洞有感：世界上美丽的东西都很难得，需要毅力（世之奇伟、瑰怪，非常之观，常在于险远，而人之所罕至焉，故非有志者不能至也）。有毅力，又不随波逐流，但没有体力、精力，也得不到（有志矣，不随以止也，然力不足者，亦不能至也）。有毅力、体力、精力，不人云亦云，但行至幽暗处，没有可借助的工具，也不能到达（有志与力，而又不随以怠，至于幽暗昏惑而无物以相之，亦不能至也）。如果万事俱备，仍然半途而弃，不但别人耻笑，自己也要后悔（然力足以至焉，于人为可讥，而在己为有悔）；可是尽了心力却没有到达，自己问心无愧，别人又能说些什么呢（尽吾志也而不能至者，可以无悔矣，其孰能讥之乎）？
入之愈深，其进愈难，而其见愈奇，这是“进”的得着。尽吾志也而不能至者，可以无悔矣。问心无愧，这是“退”的馈赠。
人生是一个把可能性越过越少的过程。选了单身贵族，就少了油盐酱醋；选了远走高飞，就少了承欢膝下；选了挑灯夜读，就少了觥筹交错。所以我们羡慕青春，因为青春充满了可能性。可恰恰因为世间没有双全法，每一次选择都有遗憾，才使得每一个选择厚重而有分量。倘若事事两全，实则事事无趣。因而这些成本无一沉没，因为这点点滴滴的选择堆聚成了独一无二的我们，迷惘的、沉思的、沸腾的。
所有的小鼠都爱巧克力，鼠类爱甜，这并无特别。可有一只小鼠会因为等待了很久，坚持说自己口味很淡，爱无味的鼠粮。因为这个选择，他不再是万千小鼠中的一个，他有了自己的故事。
听说电影很不好看，但因为第一次约会，你和TA都坚持看完了。后来你们一起看了很多有质量的电影，都忘了，唯有这第一个无趣的电影、枯坐的尴尬，变成了一辈子的笑料和甜蜜的回忆。
"一代倾城逐浪花，吴宫空自忆儿家。效颦莫笑东邻女，头白溪边仍浣纱。"(1)
西施貌美，却因貌美而离家千里，离家又收获了吴王的宠爱。东施其貌不扬，却现世安稳。谁能说怎样的人生更精彩呢？
让经济学的归经济学，生命的归生命。生命里没有沉没成本，只有独一无二的故事。
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.
Experimental setup: mice enter the maze with four "restaurants", each has an. offer and wait zone. Musical notes indicate the length. of. wait time
"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.
The longer time already. waited, the less less likely. the mice will leave
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.
Little Prince
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）《红楼梦》五美吟
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