Definition: In any decision, there are two ways to be right and two ways to be wrong. A false positive is acting when one should not have: an error of commission. A false negative is not acting when one should have: an error of omission. The key, in any decision, is to minimize both.
Consequence: Behaviorally, a false positive leads to an actual negative consequence, whereas a false negative leads to a missed positive consequence. Emotionally, a false positive leads to guilt and resentment, whereas a false negative leads to regret. Psychologists find that people regret actions more in the short term and inactions more over a lifetime [1].
Cause: The future is unknown. Outcomes may be desired or undesired, expected or unexpected, intended or unintended. We plan for the desired, expected, intended outcome and may face the undesired, unexpected, unintended one. Hope is the expectation of the former; fear is the anticipation of the latter. Therefore, hope drives false positives and fear drives false negatives.
Trade-off: For fixed evidence, the two errors trade off. Lowering the threshold for action reduces false negatives and increases false positives; raising it does the reverse. Neyman and Pearson formalized this trade-off in 1933 [2], and signal detection theory generalized it in 1954 [3]. Precision and recall express the same trade-off in the vocabulary of machine learning. Note that moving the threshold only converts one error into the other; training a network sharpens the evidence and reduces both.
Levers: There are three levers. First, better evidence reduces both errors. Second, the threshold trades one error for the other; the optimal rule is to act when the probability of being right exceeds the cost of a false positive divided by the sum of the two costs [4]. Third, the cost of an error can itself be changed: a reversible decision makes a false positive cheap, and an open option makes a false negative cheap.
Costs: The costs of the two errors depend on context. A false negative diagnosis of a disease is far more expensive to an individual than a false positive, which leads to additional testing. A false positive in a missile defense system may lead to annihilation, and a false negative may as well. The law sets the ratio explicitly: it is better that ten guilty persons escape than that one innocent suffer [5]. Warren Buffett follows the same ratio in investing: an investor cannot be called out for letting a pitch pass [7]. Yet, when he counts his mistakes, the omissions run to billions [8].
Institutions: In a large organization, false positives are more expensive than false negatives. There is much to lose, commission is blamed, and omission is invisible. In a startup, false negatives are more expensive than false positives. There is little to lose, everything to find, and omission is usually fatal. Note that large organizations overshoot: they apply the caution appropriate to irreversible decisions to reversible ones, and slow down [6].
Deadline: There is a third error, indecision. Waiting to avoid both errors becomes an omission once the option expires. Every decision has a deadline.
Silicon: I learned this on silicon. A tape-out is irreversible; a false positive costs a year and the budget. Therefore, the discipline is to verify until a false positive is survivable, and then to commit. My colleagues and I created three first-time-right silicon chips: Golden Gate, TrueNorth, and NorthPole [9]. That is the third lever in practice.
Rule: Take care of the downside, and with that backstop, seek the upside. In these terms: make the false positives survivable first, and then reduce the false negatives.
References
[1] Thomas Gilovich and Victoria Husted Medvec, “The experience of regret: What, when, and why,” Psychological Review 102(2), 1995. https://pubmed.ncbi.nlm.nih.gov/7740094/
[2] Jerzy Neyman and Egon Pearson, “On the problem of the most efficient tests of statistical hypotheses,” Philosophical Transactions of the Royal Society A 231, 1933.
[3] Wilson Tanner and John Swets, “A decision-making theory of visual detection,” Psychological Review 61(6), 1954.
[4] Charles Elkan, “The foundations of cost-sensitive learning,” IJCAI 2001. Act on a positive prediction when p > C_FP / (C_FP + C_FN). https://dl.acm.org/doi/10.5555/1642194.1642224
[5] William Blackstone, Commentaries on the Laws of England, Book IV (1769): “It is better that ten guilty persons escape than that one innocent suffer.” https://en.wikipedia.org/wiki/Blackstone%27s_ratio
[6] Jeff Bezos, Amazon 2015 letter to shareholders (April 2016): one-way and two-way doors. https://www.aboutamazon.com/about-us/shareholder-letters
[8] Warren Buffett, Berkshire Hathaway 2004 annual meeting (from meeting notes): “The main mistakes we’ve made … are: 1) Ones when we didn’t invest at all, even when we understood it was cheap; and 2) Starting in on an investment and not maximizing it”; on Walmart, “I cost us about $10 billion.” And the 2007 letter: the Dallas-Fort Worth NBC station offered at $35 million and declined, “bringing its total earnings since I turned down the deal to at least $1 billion,” with “a capital value of about $800 million.” The same letter names a commission as his single worst: “To date, Dexter is the worst deal that I’ve made” (cost to shareholders “$3.5 billion” in Berkshire stock). https://www.berkshirehathaway.com/letters/2007ltr.pdf
[7] Warren Buffett, Berkshire Hathaway 1997 letter to shareholders: “Unlike Ted, we can’t be called out if we resist three pitches that are barely in the strike zone.” https://www.berkshirehathaway.com/letters/1997.html
[9] Dharmendra Modha, “The Long Arc: Twenty-Two Years of Brain-inspired Computing at IBM Research,” modha.org, July 16, 2026. https://modha.org/2026/07/the-long-arc-twenty-two-years-of-brain-inspired-computing-at-ibm-research/