Is the Perfect Really the Enemy of the Good?

I’ve recently heard the phrase “the perfect is the enemy of the good” quoted in several statistics talks. The speakers were discussing situations in which it was difficult to obtain a high-quality designed sample that is representative of the population, and were arguing that the statistics from their conveniently available data were “fit for use” even though they were “imperfect.

In this post, I argue that in fact we do want to strive for perfection when producing or disseminating statistics — but that entails defining what a “perfect” statistic is.

First, though, let’s look at where the phrase “the perfect is the enemy of the good” came from and how its common usage — that we shouldn’t aspire to perfection but settle for something that is “good enough” — is not at all what the French philosopher Voltaire intended.

Voltaire’s Poem

The phrase comes Voltaire’s 1772 poem “La Bégueule,” which can be roughly translated as “The Prude.” The poem is a fairy tale about Madame Arsène, who had everything a woman could want (in Voltaire’s opinion) — youth, beauty, an eager-to-please husband, wealth, leisure — but was nevertheless always unhappy. The more people tried to please her the more disdainful she became. Finally she begs her fairy godmother Aline to take her to Aline’s magical palace. There, la belle Arsène is given power despotique to order things as she chooses and her every wish is granted. If she is hungry, a hundred dishes are brought; twenty chariots shine with rubies and sapphires; a thousand birds fill the air with their sweet chirping. Still, she remains unhappy and bored. She leaves the palace, finds herself in a desert surrounded by howling bears and panthers, and is rescued by a coalman (un vilain charbonnier) who kisses her. At this point the fairy godmother reappears (“perhaps a little too late,” Voltaire informs us, whatever that is supposed to mean). “You see,” says Aline, “you were a prude. My dear child, there is nothing so perilous as to leave the good to try to obtain better.” Aline then returns Madame Arsène to her house, where she is now gentle, attentive, polite, lively, and prudent. And, having taken a new discreet young lover (a coalman!), Madame Arsène is finally, according to Voltaire, “an accomplished woman.”*

Voltaire calls La Bégueule a “moral tale.” The moral, that “the best is the enemy of the good,” is stated in the first stanza:**

Dans ses écrits un sage Italien
Dit que le mieux est l’ennemi du bien ;
Non qu’on ne puisse augmenter en prudence,
En bonté d’âme, en talents, en science ;
Cherchons le mieux sur ces chapitres-là ;
Partout ailleurs évitons la chimère.
Dans son état heureux qui peut se plaire,
Vivre à sa place, et garder ce qu’il a !***

In context, it is clear that Voltaire meant that one should not throw away the goodness in one’s life in a chimerical quest to obtain more possessions. He did not mean that one should tolerate sloppiness in one’s work or settle for “good enough” in scientific endeavors. On the contrary, in the rest of the stanza Voltaire says that of course we should strive for “the best” in prudence, goodness, talent, and science.

Perfect Statistics

Voltaire’s (or, I should say, the Italian sage’s) aphorism therefore cannot be used to justify sloppy statistics. The first stanza of the poem in fact states that perfection is our goal in science (including statistical science).

But what does it mean to have a perfect statistic? This does not mean that a statistic has to be exact. The discipline of statistics was developed precisely because all statistics are inexact. The statistician’s goal is to provide measures of the accuracy of statistics produced so that users know how close the estimated unemployment rate is to the true percentage of people who are unemployed, or know the amount of uncertainty surrounding a conclusion that the five-year survival rate with cancer treatment A is higher than the rate with treatment B.

We can judge the quality of a statistic by looking at how it was produced and by assessing the validity of the measures of accuracy.**** A high quality statistic is accompanied by:

A technical methodology report that gives details of how the data were collected, how the concepts were measured, and how the statistics were calculated. The methods in the report must be supported by sound statistical theory.
A margin of error or confidence interval that accurately reflects the amount of uncertainty about the statistic.
A document or web page aimed a nontechnical reader that explains the information in the technical methodology report. This includes an interpretation of the statistics and their accuracy, a description of caveats and limitations of the data collection, and other information that readers need to assess the suitability of the statistic for their uses.

It is possible to strive for perfection in statistics. This comes from producing statistics that have the accuracy claimed for them. Thus, if producing 95 percent confidence intervals, you should be able to demonstrate mathematically or empirically that 95 percent of those intervals capture the true value of the quantity being estimated.

But let’s not support statistical sloppiness by misquoting Voltaire. If one doesn’t strive for perfection, then flawed statistics can become the enemy of the good.

Footnotes and References

*Sicco (2018) argues that La Bégueule also promotes Voltaire’s ideas that women find their fulfillment in love and that happiness comes from listening to and satisfying the voice of nature. Hence, in the poem, Madame Arsène is only “accomplished” after she takes a lover.

**Candide has a similar moral. The protagonists experience war, famine, the Portuguese Inquisition, rape, disembowelment, and being (partially) cannibalized — all while being assured by Dr. Pangloss that this is “the best of all possible worlds” — until they come to the realization that this optimism is unfounded and the best they can do is to cultivate their own garden.

***The stanza can be roughly translated (although of course it loses its poetry in the translation) as:

In his writings a wise Italian
Says that the best is the enemy of the good;
Not that one cannot increase in prudence,
In kindness, in talents, in science;
Let us seek the best in these areas;
Everywhere else let us avoid the chimera.
In the happy state that is pleasing,
Let us live in our place, and look after what we have!

****See also my eight questions to ask when judging the quality of a statistic in Measuring Crime: Behind the Statistics.

Sicco, D. (2018). Les contes en vers de Voltaire: le merveilleux comme véhicule d’un message moral. Studi Francesi, 186, 433-442.

Sharon LohrAugust 7, 2023