February 4, 2011

The Simple Math Underlying Why We Hate To Lose

“The only thing I hate more than not winning is losing”—something Yogi Berra could have said, even if he didn’t

Net Cost =1 Smile/Image: Michael Moffa

Although our reactions to losing a job, a client or a wallet seem transparently “natural” and negative, there is something strange about our attitudes towards losses and gains that is revealed when we are asked which matters more: not losing any of these, or gaining their equivalent?

Which matters to you more: getting a client or a job, or not losing one? Here, if we were talking about dollars, rather than their sources (jobs, clients or wallets), “what matters more” can be rephrased as, “Which will give you more pleasure: gaining \$10 or not losing \$10?” Alternatively, “Which will give you more pain: not gaining \$10 or losing \$10?”

[Clearly, positive pleasure and the relief of anxiety are not psychologically or viscerally the same—being respectively labeled “positive reinforcement” and “negative reinforcement” in Psychology 101; however, here they will be treated as mathematically commensurable, when measured in terms of “utility”. This means that even though discovering you’ve inherited \$1,000 feels very different from having discovered you haven’t lost \$1,000, those feelings are to be measured by the same quantitative yardstick and as positive, but not necessarily equal.]

Not Exactly Like Losing a Daughter, Gaining a Son-in-Law

This loss-gain choice can also be phrased this way: “To which would you respond more strongly (even if differently)—losing X or gaining X?” Think: “Losing a daughter, gaining a son-in-law”—assuming these are equivalent. Which, for all dads, they are not.

Some people seem to be negatively affected more by losing something than by not gaining something equivalent. An example would be a stock broker who hates losing his stock options more than being denied additional and equivalent new ones. Following apparently equivalent “emotional logic”, that should mean the same stock broker would feel better, more positive about not losing his stock options than about getting an equivalent increase in them. On the other hand, another stock broker might feel that the lost prospective gain matters more than the loss of the earlier gain.

Now why is that? Why would many—but not all—people feel worse about a loss than good about an equivalent gain?—assuming that this can be quantified, which, indeed is possible, using a mathematical tool called an “indifference lottery”—which I recommend you investigate on your own, if you are curious..

Cusp Catastrophes Aside

One simple mathematical explanation that occurred to me regarding why many people hate a loss more than they love an identical gain is this: People who are more “cost-sensitive” than “benefit-sensitive” may unconsciously be utilizing something like a mathematical proof that supports their cost-sensitivity. Here’s the argument: If you have \$100 and are asked, “Which matters to you more: gaining another \$10 or losing \$10?”, which will you choose?

Of course, in some scenarios, e.g., where you must have \$110 when you have only \$100 or go to jail, it’s a no-brainer. That’s because the \$110-level is a threshold for something qualitatively significantly different, viz., sleeping in a jail cell instead of your own bed. But such “catastrophe bifurcation points” aside, when the utilities curves change more smoothly, such threshold-triggered responses will not play a part.

So, assume no such looming threats, obligations, other constraints, etc. Then what may happen is this: You notice that as a percentage of what you will have after the gain or loss, the \$10 represents a bigger proportion of your holdings after the loss, viz., \$10/\$90 or 1/9, than it does after the gain, viz., \$10/\$110 1/11.

Hence, the relative or proportional value of \$10, viewed from the perspective of someone who has just lost that amount, is greater than the relative or proportional value of the \$10 from the perspective of someone who has just gained that amount. In other words, the marginal utility of \$10 relative to the new post-loss holdings of \$90 is greater than the marginal utility of the same \$10 relative to the new post-gain \$110.

The Math of December-May Match-Ups and Toddler Impatience

The decisive consideration is usually (although not always) not how much the \$10 means relative to what you started with. It is how much it means relative to what you have now.

Imagine a man of 50 infatuated with a young woman of 25. The age difference, viewed from either of their perspectives is exactly and identically 25. Yet somehow, for her, and even though they do not disagree on what the age difference is, it is much bigger deal than it is for him—bigger in the sense that emotionally positively or negatively it somehow seems like a bigger difference to her than to him. She might, for example, see him as much more mature or older than he sees himself. Why?

Because she is right, in a way: Although the difference between them is the same irrespective of whether it is measured from her perspective or his, there is a key ratio that is not the same. That ratio is the ratio of the age difference to total age, i.e., D/A. In his case 25/50, which is ½ or 50%, whereas in her case the ratio is 25/25=100%.

Hence, for her, the marginal utility or relative weight of those 25 years, measured against her 25-year-old yardstick is 100%–a very big deal indeed. For him it’s much less and therefore not such a big deal. In dollar terms, he is more like Bill Gates, she, like Bill Gate’s housekeeper, upon being told that she’s getting an extra \$25/hour.

This mathematical logic also explains why 4-year-old children are so impatient and overwhelmed by the idea of turning 5. The one year is 25% of their 4-year lifetime-calibrated yardstick, a tiny fraction of yours. So, wait one year before getting a pony?! Become 25% older?! Scary.

The relevance to the gain-loss analysis is that the role the \$10 or the one year wait plays in calculating the ratio using the current or updated yardstick matters more than its role as an absolute amount.

The mention of Bill Gates, when combined with the jail threshold illustration, does serve to make an important point: If you are not confronted by such turning points that hinge on your gaining or losing money, e.g., if you are incalculably wealthy, there should be no difference as to which “matters more” to you, gaining or losing \$10. Probably neither will matter to you at all.

Have Your Placement Numbers Really Recovered?

Here is another reason ratios of gains and losses count more than the amounts: Consider a recruiter whose placements in numbers or dollars increased this month by the same amount or percentage they decreased last month. Has he fully recovered? Should he or will he feel as good this month as he felt bad last month?

You may be tempted to argue that from a percentage standpoint he certainly should not feel better or good. That’s because last month he was reduced to 90% of his performance, because of the 10% drop. Now, measured against that previous month’s yardstick, the “restored” 10% only brings him up to 99% of his pre-loss performance. Hence, in both percentage and the implied absolute amounts, he is not where he started. So, you may conclude, the recruiter should feel bad.

That’s because the increase in marginal utility of the 10% recovery calculated on the basis of his diminished performance is not enough to fully cover his losses over the two months. True, a 10% gain relative to the 99% yardstick used now is more than 10% of the original 100%; however, it is less than the 10% loss relative to the 90% base.

What about arguing that, at worst, he should feel neutral: down 10%, up 10%?  That would be like arguing that every lottery ticket has a 50-50 chance of being a winner, since it will be a winning ticket or a losing ticket. Wrong in both cases, because of incorrectly assigning equal weights to the two outcomes.

Finally, what about absolute placement numbers or dollar amounts, rather than percentages? Say that the number of candidates you, as a recruiter, placed last month decreased by 10, but recovered by the same amount this month. Should you feel bad, glad or neither? Here the outcome seems to be reversed.

Assume you had 100 placements at the beginning of last month (which made 100 your yardstick). You lost 10 during last month, so you were down to 90 (your first updated, revised yardstick). Now, this month, you have regained 10 placements (resulting in an updated second updated yardstick of 100). Using—as unconsciously many, if not most, people will—90 as your base, you have gained 1/9—which is more than the 1/10 you lost.

So, it should not be surprising that you feel good, not because you are in fact—and unlike the percentage-based case in which you are “in the red”—back to where you started, but because, unconsciously, you feel you are somehow better off! In using these absolute numbers, you found that you felt better using the most positive yardstick—the 90 level—than you would using the most recent, which would have indicated only a 1/10 gain, rather than a 1/9 gain. It also feels better than simply noting you are merely back where you started.

Those who are basing their feelings entirely on such mathematical, often opportunistic calculations are doing so on the basis of the marginal utility yardsticks that matter to them most. These are usually the most recent yardstick, but sometimes they are the yardstick that makes them feel best or worst, depending upon whether they want to pat their own backs,whip them or flog others—much as politicians and economists will choose their statistical baselines to flog their agendas or their opposition.

Implications for Economic Recovery

The profound relevance of this math to macro-economic history and psychology is obvious: In connection with recovery from an economic recession or depression, such “recovery euphoria” upon merely recovering a percentage or, in absolute amounts, no more than what was lost, may be disproportionate, because the glow may be based on the gain relative to the worst, most recent performance, not relative to the initial baseline.

Exactly the same analysis applies to employment-figure headlines: “Jobs up 10%!”—however, only after a 20% or  a still comparatively bad 10% decline.

In all examples cited throughout this discussion, the unconsciously understood weight of a gain or a loss relative to the most recently updated or most emotionally most important yardstick is the or at least one decisive factor that determines the emotional response to the gain or loss.

In many instances, whether one feels good or bad will depend on whether one uses a pre-loss/gain yardstick or the post-gain/loss yardstick as the calculation base.

All Math Aside

These mathematical considerations aside, there are also psychological reasons why perhaps in general we hate losing more than we like winning equivalent amounts. One is that many people hate being seen as “losers” more than they love being seen as “winners”. (Yes, despite GW Bush “you-are-with-us-or-with-them” logic or the forced outcomes of Yogi Berra’s game of baseball, they could be seen as neither.)

To them being stigmatized seems to psychologically and socially matter more than being lionized does. In contrast, the stockbroker who hates losing a gain than gaining a loss of stock options may be motivated by a belief that “winning” matters more than anything—even more than losing, because “everybody loves a winner”.

Accordingly, in virtue of being more “gain-sensitive” than “loss-sensitive”, over the years, as he tallies his gains and losses, he is likely to emotionally weigh gains more heavily than equivalent losses, even if only to prop up his (self-) image as and desire to be a winner.

As for the gains and losses associated with this article, it would have bothered me more to have lost your interest than not to have gained it at all. But since we are not only on the same page, but also on the same line, I feel pretty good.