# The Numerosity Heuristic

As a three-time CEO, I’ve had a lot of experience with incentive stock options and have been appalled by how poorly they are understood by the average employee. Many employees fixated on the number of shares they were granted, rather than the percentage of shares outstanding. They would multiply their number of shared granted by some arbitrary share price to determine how much money they might make. “All my shares for \$10” was a common refrain.

One example stands out to me, even though it happened more than a decade ago. After a poor first year, our company had to raise additional capital.  Because the terms of the new money were much worse than the previous capital round, we had to dramatically increase the number of shares issued from 10M to 40M. The board realized that this 4X dilution could be devastating on employee morale and tried to partially mitigate the impact by issuing new options to all employees.

After I explained the situation at an All Hands meeting, a senior engineer came to my office to thank me for the additional grant which increased his ownership from 40K to 60K shares. In his mind, he now had a greater likelihood of buying a house in Silicon Valley.  I tried to explain to him that his ownership had gone from 0.4% to 0.15% but he didn’t agree. In his mind, the 40M shares showed that the company was more valuable and therefore his shares were also worth more.

Although I didn’t know it at the time, that engineer was exhibiting the numerosity heuristic. People tend to equate bigger numbers with bigger quantities, even if they have different denominations.  According to the authors,

When consumers evaluate the difference between two attribute levels, they may pay more attention to the number of units rather than the type of units, such that they appreciate a 24-month warranty difference more than a two-year warranty difference because they rely on the number of units rather than their type.

In “How to Make a 29% Increase Look Bigger: Numerosity Effects in Option Comparisons”, Pandelaere and Briers use a series of experiments to systematically show that numerosity can impact consumer preference. We will likely pay more for a 7-day vacation than a one week vacation, and we will complain less about a flight that is delayed for 1 hour than for 60 mins.  We even believe that there is a larger quality difference between two items rated 700 and 830 (on a 1000 point scale) than the same items rated 7.0 and 8.3 (on a 10 point scale).

Marketers, take note. Numbers can persuade and apparently size does matter.

Oh, yeah. And I’m to start giving out annual bonuses in pennies rather than dollars.

### 8 Responses to The Numerosity Heuristic

1. Arun Krishnaswamy June 19, 2011 at 8:35 pm #

Interesting Jonathan. One possible takeaway could be in before-after bake-offs: if a technology does what took 25 hours in 25 secs… are we better off saying ‘what took 90000 secs now takes 25 secs’ ? It does seem more impressive however in this specific example since the ’25’ is the same, the ‘hours to seconds’ is certainly impactful. I guess in other cases where one cannot reduce it so nicely (without being untruthful to facts), the Numerosity Heuristic works better. I have wondered why countdowns (to an important event) happen in small units.. it makes the number look big but rapidly counting down to zero. And explains why Indonesia has so many millionaires (in rupiah of course!)

• Jonathan June 20, 2011 at 9:27 am #

Arun, I agree. 25 mins to 25 secs likely to be memorable since the numerator is the same whereas numerosity suggests that 10 mins to 25 secs is not likely to be.

2. Nancy Fessatidis June 20, 2011 at 11:10 am #

True story – Last year we acheived a 150% improvement in one of our marketing experiments. No one seemed to get too excited until one day I decided to report a 2.5X improvement. Everyone wanted to know what we did and what we could do to repeat this phenomenal success. Interesting how expressing the same results differently can elicit such different reactions.

• Alpesh June 21, 2011 at 4:35 am #

2.5X would that not be 250% improvement?

if you started with 100 meters and you know have 250 meters that is an improvement of 150 meters 🙂

• Anonymous June 21, 2011 at 7:53 pm #

Good catch Alpesh. What i meant to say was results went from x to 2.5x which sounded more impressive.

Irregardless, I think the point I was trying to make … around how expressing the same result differently can often elicit different reactions still holds true.

cheers

3. Julie Barrier June 20, 2011 at 6:53 pm #

Jonathan,
Numerosity meets Musicality.

I can’t help but break into song on this one. From Rent (the musical): “Five hundred twenty-five thousand six hundred minutes…how do you measure, measure a year.”…

PS: I’d prefer my bonus in dollars (actually, how about euros? 😉

4. Robert E July 5, 2011 at 9:56 am #

The “Becher Buck” replaced by the Becher 100 pennies? Don’t think that would work well.