The Anna Karenina principle was popularized by Jared Diamond

Jared Diamond

Jared Mason Diamond is an American scientist and author whose work draws from a variety of fields. He is currently Professor of Geography and Physiology at UCLA...

 in his book Guns, Germs and Steel to describe an endeavor in which a deficiency in any one of a number of factors dooms it to failure. Consequently, a successful endeavor (subject to this principle) is one in which every last one of the possible deficiencies has been avoided.

The name of the principle derives from Leo Tolstoy

Leo Tolstoy

Lev Nikolayevich Tolstoy was a Russian writer who primarily wrote novels and short stories. Later in life, he also wrote plays and essays. His two most famous works, the novels War and Peace and Anna Karenina, are acknowledged as two of the greatest novels of all time and a pinnacle of realist...

's book Anna Karenina

Anna Karenina

Anna Karenina is a novel by the Russian writer Leo Tolstoy, published in serial installments from 1873 to 1877 in the periodical The Russian Messenger...

, which begins:

Happy families are all alike; every unhappy family is unhappy in its own way.

Diamond uses this principle to illustrate why so few wild animals have been successfully domesticated throughout history, as a deficiency in any one of a great number of factors can render a species undomesticable. Therefore all successfully domesticated species are not so because of a particular positive trait, but because of a lack of any number of possible negative traits.

From chapter 9 of Guns, Germs and Steel, six groups of reasons for failed domestication of animals are:

• Diet - To be a candidate for domestication, a species must be easy to feed. Finicky eaters make poor candidates. Non-finicky omnivores make best candidates.
• Growth Rate - The animal must grow fast enough to be economically feasible. An elephant farmer, for example, would wait perhaps 12 years for his herd to reach adult size.
• Problems of Captive Breeding - The species must breed well in captivity. Species having mating
  Mating
  In biology, mating is the pairing of opposite-sex or hermaphroditic organisms for copulation. In social animals, it also includes the raising of their offspring. Copulation is the union of the sex organs of two sexually reproducing animals for insemination and subsequent internal fertilization...
  
   rituals prohibiting breeding in a farm-like environment make poor candidates for domestication. These rituals could include the need for privacy or long, protracted mating chases.
• Nasty Disposition - Some species are too mean and nasty to be good candidates for domestication. The farmer must not be at risk of life or injury every time he enters the animal pen. The zebra
  Zebra
  Zebras are several species of African equids united by their distinctive black and white stripes. Their stripes come in different patterns unique to each individual. They are generally social animals that live in small harems to large herds...
  
   is of special note in the book, as it was recognized by local cultures and Europeans alike as extremely valuable and useful to domesticate, but it proved impossible to tame. Horses in Africa proved to be susceptible to disease and attack by a wide variety of animals, while the very characteristics that made the zebra hardy and survivable in the harsh environment of Africa also made it fiercely independent.
• Tendency to Panic - Species are genetically predisposed to react to danger in different ways. A species that immediately takes flight is a poor candidate for domestication. A species that freezes, or mingles with the herd for cover in the face of danger, is a good candidate. Deer
  Deer
  Deer are the ruminant mammals forming the family Cervidae. Species in the Cervidae family include white-tailed deer, elk, moose, red deer, reindeer, fallow deer, roe deer and chital. Male deer of all species and female reindeer grow and shed new antlers each year...
  
   in North America have proven almost impossible to domesticate and have difficulty breeding in captivity. Horses, however, immediately thrived from the time they were introduced to North America in the 17th century.
• Social Structure - Species of lone, independent animals make poor candidates. A species that has a strong, well defined social hierarchy is more likely to be domesticated. A species that can imprint
  Imprinting (psychology)
  Imprinting is the term used in psychology and ethology to describe any kind of phase-sensitive learning that is rapid and apparently independent of the consequences of behavior...
  
   on a human as the head of the hierarchy is best. Different social groups must also be tolerant of one another.

The term is also used in science.

• In statistics
  Statistics
  Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
  
  , the term is used to describe significance tests: there are any number of ways in which a dataset may violate the null hypothesis
  Null hypothesis
  The practice of science involves formulating and testing hypotheses, assertions that are capable of being proven false using a test of observed data. The null hypothesis typically corresponds to a general or default position...
  
   and only one in which all the assumptions are satisfied.
• In ecology
  Ecology
  Ecology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...
  
   and in particular ecological risk assessment
  Risk assessment
  Risk assessment is a step in a risk management procedure. Risk assessment is the determination of quantitative or qualitative value of risk related to a concrete situation and a recognized threat...
  
  :

Successful ecological risk assessments are all alike; every unsuccessful ecological risk assessment fails in its own way. Tolstoy posited a similar analogy in his novel Anna Karenina : "Happy families are all alike; every unhappy family is unhappy in its own way." By that, Tolstoy meant that for a marriage to be happy, it had to succeed in several key aspects. Failure on even one of these aspects, and the marriage is doomed . . . the Anna Karenina principle also applies to ecological risk assessments involving multiple stressors.

See also

After a failed attempt to assassinate the British prime minister, Margaret Thatcher, the IRA

Irish Republican Army

The Irish Republican Army was an Irish republican revolutionary military organisation. It was descended from the Irish Volunteers, an organisation established on 25 November 1913 that staged the Easter Rising in April 1916...

 said: "Today we were unlucky, but remember we only have to be lucky once. You will have to be lucky always."

Aristotle

Aristotle

Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

 states the same principle in the Nichomachean Ethics (Book 2, translation by W. D. Ross

W. D. Ross

Sir David Ross KBE was a Scottish philosopher, known for work in ethics. His best known work is The Right and the Good , and he is perhaps best known for developing a pluralist, deontological form of intuitionist ethics in response to G.E. Moore's intuitionism...

 http://classics.mit.edu/Aristotle/nicomachaen.2.ii.html):

Again, it is possible to fail in many ways (for evil belongs to the class of the unlimited, as the Pythagoreans conjectured, and good to that of the limited), while to succeed is possible only in one way (for which reason also one is easy and the other difficult -- to miss the mark easy, to hit it difficult); for these reasons also, then, excess and defect are characteristic of vice, and the mean of virtue; For men are good in but one way, but bad in many.

Order in chaos of maladaptation

Many experiments and observations of groups of humans, animals, trees, grassy plants, stockmarket prices, and changes in the banking sector proved the modified Anna Karenina principle.

By studying the dynamics of correlation and variance in many systems facing external, or environmental, factors, we can typically, even before obvious symptoms of crisis appear, predict when one might occur, as correlation between individuals increases, and, at the same time, variance (and volatility) goes up. ... All well-adapted systems are alike, all non-adapted systems experience maladaptation in their own way,... But in the chaos of maladaptation, there is an order. It seems, paradoxically, that as systems become more different they actually become more correlated within limits.

This effect is proved for many systems: from the adaptation of healthy people to a change in climate conditions to the analysis of fatal outcomes in oncological and cardiological clinics.
The same effect is found in the stock market.

Interesting Facts

Vladimir Arnold

Vladimir Arnold

Vladimir Igorevich Arnold was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable Hamiltonian systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory,...

in his book "Catastrophe Theory" describes "The Principle of Fragility of Good Things" which in a sense supplements the Principle of Anna Karenina: "good" systems must meet simultaneously a number of requirements; therefore, they are more fragile:

... for systems belonging to the singular part of the stability boundary a small change of the parameters is more likely to the send the system into the unstable region than into the stable region. This is a manifestation of a general principle stating that all good things (e.g. stability) are more fragile than bad things. It seems that in good situations a number of requirements must hold simultaneously, while to call a situation bad even one failure suffices.