Financial Intelligence - Counterintuitive Pattern 1: Proportion VS Absolute Value

Counterintuitive Pattern 1: Proportion VS Absolute Value


The first counterintuitive pattern is about how the human mind perceives proportion and absolute value. Essentially, our brain excels at recognising absolute value when the number is small, but it automatically shifts to thinking about proportion when the number is large. Let’s use a concrete example to illustrate this.

Imagine you’re making two purchases today. First, you need to buy a $200 printer from the local office supply store, as your partner has asked. Second, you’re buying a new car. After weeks of searching, you’ve chosen a white Honda CR-V from a local dealer. You have $20,000 in cash, freshly withdrawn from the bank, and you’re ready to pay the dealer and drive the CR-V home.

When you picked up the printer from the office supply store, you noticed a sign at the checkout stating that anyone using the Bravo Loyalty card, which you are, would receive a 10% discount on any printer purchase. Delighted, you showed the cashier your Bravo Loyalty card, paid $180, and left with your new printer.

After dropping the printer off at home, you took an Uber to the local car dealer to finalise the purchase of the CR-V. Upon arrival, Paul, whom you had met during previous test drives and negotiations, greeted you warmly. Before you could express your readiness to pay, Paul handed you an envelope with a secret smile. Intrigued, you opened it to find a paper printed in charming fonts: “Congratulations! You are the 1000th customer of this store! You will receive a 10% discount on your CRV!” What a delightful surprise! Shortly after, you took $2000 out of the $20,000 in your pocket and handed $18,000 to Paul, who then gave you the car keys. Deal done! It was a great day, saving $20 on the printer and $2000 on the car!

Now, let’s analyse the feeling. Which discount brings you more happiness, the printer or the car? Naturally, it’s the car discount, as it’s a significantly larger amount. But consider this: how many times more joy does the car discount provide compared to the printer discount? Take your time to assess your perception of the joy each brings truly. Your answer might be three, five, or even ten, but it’s unlikely to be 100. In other words, a $2000 discount probably won’t bring you 100 times more joy than a $20 discount.

This illustrates how our minds perceive numbers, a concept frequently used in finance. Due to our limited ability to grasp large numbers, we often think in terms of proportions or percentages to simplify calculations. In the example above, our minds unconsciously converted both discounts to 10%, which is essentially the same. Our conscious minds adjust this perception by applying a multiplying factor, knowing $2000 is much more than $20. After this adjustment, our perceived joy from the discounts is anchored between 3 to 10 times. In other words, when dealing with discounts, growth, multiplication, division, or any financial calculation involving proportions, we tend to focus on the proportion and overlook the absolute number.

This counterintuitive tendency to misjudge proportions and absolute numbers is often exploited in advertising. When the absolute number is low, percentages are used to make it appear larger. For instance, “This popcorn has 10% less salt than the previous version.” In reality, it’s only 0.5 grams less, as the total salt per pack is 5 grams. Another example: “This fruit bar has 20% extra fibre than average fruit bars!” This translates to just 2 grams of extra fibre, less than the fibre in two apple seeds you might accidentally chew while eating an apple. We’ll discuss nutrition intelligence in a later chapter, where fibre will be mentioned again.

Conversely, absolute values are commonly used when the number is large, even if it doesn’t make a significant difference. For example, kitchen and bathroom renovation shops often advertise a few thousand dollars in cash back. It seems substantial, but compared to the typical renovation spending of hundreds of thousands, it’s merely 1% to 3%, likely a fraction of what you pay in sales tax. Another example is political propaganda for public project cost savings: “The People Party has launched a new software program, saving more than 3 million dollars on public construction projects!” While 3 million sounds like a lot of tax dollars, it’s only 0.0015% of the 200 billion yearly spending on public construction, likely insignificant enough that it wasn’t included in the yearly budget planning.

How can we enhance our financial intelligence by consciously adjusting this pattern of absolute and proportional values? The answer is to think quickly when making decisions about small numbers, and slowly when dealing with large numbers. When making a significant purchase, force yourself to slow down, ask many questions, conduct thorough research, and compare various options. This approach reminds us, “I’m about to make a big purchase; however, my brain might incorrectly think proportionally rather than in absolute terms, so I need to slow down to focus on the absolute value.” For example, when buying a million-dollar property, any potential 0.1% savings opportunity, whether on buying agent costs, tax benefits, or compliance spending, could amount to $1000. This $1000 saving might be worthwhile, but you might not bother to explore it if you think, “Nah, just a tiny difference on a million-dollar deal.”

On the other hand, we can consciously speed up when making small transactions. When buying the printer in the scenario above —a $200 deal —consider how much time and energy you want to invest in it and stick to that budget. A chance to collect three different vouchers and save up to 10%? Thanks, but no, since 10% would only be $20, which might not justify the time needed to collect those vouchers.

反直觉模式一：比例 vs 绝对值

第一个反直觉模式，涉及人类如何感知比例与绝对值。本质上，当数字较小时，我们的大脑更擅长理解绝对值；但当数字变大时，大脑会自动转向用“比例”来思考。我们用一个具体的例子来说明这一点。

假设你今天要进行两笔消费。第一笔，你需要按照伴侣的要求，在本地办公用品店购买一台价值200美元的打印机。第二笔，你准备购买一辆新车。经过数周的寻找，你选中了一辆本地车行的白色本田CR-V。你从银行取出了2万美元现金，准备直接付款，把车开回家。

当你在办公用品店拿起打印机结账时，你注意到收银台有一个提示：凡是使用Bravo会员卡的顾客，购买打印机可享受10%的折扣。你正好是会员，于是开心地出示了会员卡，以180美元付款，带着新打印机离开。

把打印机送回家后，你叫了一辆Uber前往车行，准备完成CR-V的购买。到达后，之前试驾和谈价时认识的销售Paul热情地接待了你。在你准备付款之前，他带着一丝神秘的微笑递给你一个信封。你打开一看，上面用精美字体写着：“恭喜！您是本店第1000位顾客！购买CR-V可享受10%折扣！”这是个令人愉快的惊喜！很快，你从口袋里的2万美元中拿出2000美元，只支付了18000美元，Paul把车钥匙交到你手中。交易完成！这是美好的一天——你在打印机上省了20美元，在汽车上省了2000美元！

现在我们来分析一下你的感受。哪个折扣让你更开心，是打印机还是汽车？显然是汽车，因为金额更大。但再进一步思考：汽车折扣带来的快乐，是打印机折扣的多少倍？你可以认真感受一下这种“快乐的差距”。你的答案可能是3倍、5倍，甚至10倍，但很少会是100倍。换句话说，2000美元的折扣，通常不会带来比20美元多100倍的快乐。

这正体现了我们大脑处理数字的方式，这也是金融领域中常见的一个现象。由于我们对大数字的感知能力有限，大脑会倾向于用比例或百分比来简化理解。在这个例子中，大脑无意识地把两个折扣都转换成了10%，于是它们在“感觉上”变得相似。随后，我们的意识再进行一定调整，知道2000美元远大于20美元，于是把感受放大到大约3到10倍之间。也就是说，当面对折扣、增长、乘除等涉及比例的计算时，我们更容易关注比例，而忽略绝对数值。

这种对比例和绝对值的误判，常常被广告所利用。当绝对数值较小时，商家会使用百分比来让它看起来更大。例如：“这款爆米花比上一代减少了10%的盐。”实际上只是少了0.5克，因为每包总共只有5克盐。再比如：“这款水果棒的膳食纤维比普通水果棒多20%！”实际上只多了2克纤维，甚至还不如你吃苹果时不小心咬到的两颗苹果籽中的纤维含量。我们会在后面的营养智能章节中再次提到膳食纤维。

相反，当数字较大时，人们更倾向于使用绝对值，即使它的实际意义并不大。例如，厨房或浴室装修商常常宣传“返现几千美元”，听起来很多，但相对于动辄几十万的装修费用，这通常只占1%到3%，甚至可能只是你所支付销售税的一小部分。再比如政治宣传中常见的说法：“人民党推出新软件，为公共建设项目节省了300万美元！”听起来是很大一笔纳税人的钱，但如果对比每年2000亿美元的公共建设支出，这只占0.0015%，可能小到在年度预算中都不会被单独列出。

那么，我们该如何通过主动调整这种认知模式，来提升自己的财务智能呢？一个简单的原则是：面对小金额时，快速决策；面对大金额时，放慢决策。当你进行一笔重大消费时，刻意放慢节奏，多问问题，做充分调研，对比不同选项。提醒自己：“这是一笔大额交易，但我的大脑可能会错误地用比例来思考，我需要放慢速度，关注绝对数值。”例如，在购买一套价值100万美元的房产时，哪怕只是0.1%的节省，无论来自中介费用、税务优化还是合规支出，都相当于1000美元。这1000美元是有价值的，但如果你只是想着“对100万美元来说，这点差异很小”，你可能就不会去深入挖掘这些机会。

相反，对于小额消费，我们可以有意识地加快决策节奏。例如在上述购买打印机的场景中，这是一笔200美元的交易，你可以提前设定好愿意投入的时间和精力预算。比如有人告诉你可以通过收集三种优惠券来获得10%的折扣，你可以礼貌拒绝——因为10%也只是20美元，可能不值得花时间去折腾这些优惠券。