More strictly, and in reference to an arbitrary element (e.g. a human, an object, a computer), within a well-defined set (called the "anonymity set"), "anonymity" of that element refers to the property of that element of not being identifiable within this set. If it is not identifiable, then the element is said to be "anonymous".
The term "anonymous message" typically refers to message (which is, for example, transmitted over some form of a network) that does not carry any information about its sender and its intended recipient. It is therefore unclear if multiple such messages have been sent by the same sender or if they have the same intended recipient.
Sometimes it is desired that a person can establish a long-term relationship (such as a reputation) with some other entity, without his/her personal identity being disclosed to that entity. In this case, it may be useful for the person to establish a unique identifier, called a pseudonym, with the other entity. Examples of pseudonyms are nicknames, credit card numbers, student numbers, bank account numbers, and IP addresses. A pseudonym enables the other entity to link different messages from the same person and, thereby, the maintenance of a long-term relationship. Although typically pseudonyms do not contain personally identifying information, communication that is based on pseudonyms is often not classified as "anonymous", but as "pseudonymous" instead. Indeed, in some contexts, anonymity and pseudonymity are separate concepts.
However, in other contexts what matters is that both anonymity and pseudonymity are concepts that are, among other things, concerned with hiding a person's legal identity. In such contexts people may not distinguish between anonymity and pseudonymity.
The problem of determining whether or not the identity of a communication partner is the same as one previously encountered is the problem of authentication.
Anonymity is not an absolute. That is, the degree of anonymity one enjoys may vary. In the above example, if Carol has an ironclad alibi at the time of the perpetration, then we may deduce that it must have been either Alice or Bob who opened the safe. That is, the probability of the elements {Alice, Bob, Carol} of being the perpetrator is now 1/2, 1/2, and 0 respectively. This clearly amounts to a reduction of the perpetrator's anonymity (i.e. although the perpetrator still remains anonymous, it is now more likely than before that (s)he is either Alice or Bob).
In some cases, anonymity is reached unintentionally, as is often the case with victims of crimes or war battles, when a body is discovered in such a state that the physical features used to identify someone are no longer present. Anonymity is not always found in such morbid situations, however. As an example, a winner of a lottery jackpot is anonymous (one of however many play the lottery) until that person turns in the winning lottery ticket.
There are many reasons why a person might choose to obscure their identity and become anonymous. Several of these reasons are legal and legitimate - many acts of charity are performed anonymously, as benefactors do not wish, for whatever reason, to be acknowledged for their action. Someone who feels threatened by someone else might attempt to hide from the threat behind various means of anonymity, a witness to a crime can seek to avoid retribution, for example, by anonymously calling a crime tipline. There are also many illegal reasons to hide behind anonymity. Criminals typically try to keep themselves anonymous either to conceal the fact that a crime has been committed, or to avoid capture. However, the saying that there is no honor among thieves implies that criminals may also snitch on each other for various reasons.
In conversational settings, anonymity may allow people to reveal personal history and feelings without fear of later embarrassment. Electronic conversational media can provide physical isolation, in addition to anonymity. This prevents physical retaliation for remarks, and prevents negative or taboo behavior or discussion from tarnishing the reputation of the speaker. This can be beneficial when discussing very private matters, or taboo subjects or expressing views or revealing facts which may put someone in physical, financial, or legal danger (such as illegal activity, or unpopular or outlawed political views).
With few perceived negative consequences, anonymous or semi-anonymous forums often provide a soapbox for disruptive conversational behavior. The term Internet troll is sometimes used to refer to those who do this online.
Relative anonymity is often enjoyed in large crowds. Different people have different psychological and philosophical reactions to this development, especially as a modern phenomenon. This anonymity is an important factor in crowd psychology.
Anonymous commercial transactions can protect the privacy of consumers. Some consumers prefer to use cash when buying everyday goods (like groceries or tools), to prevent sellers from aggregating information or soliciting them in the future. Credit cards are linked to a person's name, and can be used to discover other information, such as postal address, phone number, etc. The ecash system was developed to allow secure anonymous transactions. When purchasing taboo goods and services, anonymity makes many potential consumers more comfortable with or more willing to engage in the transaction. Many loyalty programs use cards which personally identify the consumer engaging in each transaction (possibly for later solicitation, or for redemption or security purposes), or which act as a numerical pseudonym, for use in data mining.
Anonymity can also be used as a protection against legal prosecution. For example, when committing a robbery, many criminals will obscure their faces to avoid identification. In organized crime, groups of criminals may collaborate on a certain project without revealing to each other their names or other personally identifiable information. The movie The Thomas Crown Affair depicted a fictional collaboration by people who had never previously met and did not know who had recruited them. The anonymous purchase of a gun or knife to be used in a crime helps prevent linking an abandoned weapon to the identity of the perpetrator.
Attempts at anonymity are not always met with support from society. There is a trend in society to mistrust someone who makes an effort to maintain their anonymity. This is often summed up in the statement, "You wouldn't want to stay anonymous unless you had something to hide." The implication is that there is no legitimate reason to obscure one's identity from the world as a whole.
Anonymity sometimes clashes with the policies and procedures of governments or private organizations. In the United States, disclosure of identity is required to be able to vote. In airports in most countries, passengers are not allowed to board flights unless they have identified themselves to some sort of airline or transportation security personnel, typically in the form of the presentation of an identification card.
On the other hand, some policies and procedures require anonymity. According to the Universal Declaration of Human Rights, "... periodic and genuine elections which shall be by universal and equal suffrage ... shall be held by secret vote or by equivalent free voting procedures."
When it is necessary to refer to someone who is anonymous, it is typically necessary to create a type of pseudo-identification for that person. In literature, the most common way to state that the identity of an author is unknown is to refer to them as simply "Anonymous." This is usually the case with older texts in which the author is long dead and unable to claim authorship of a work. When the work claims to be that of some famous author the pseudonymous author is identified as "Pseudo-", as in Pseudo-Dionysius the Areopagite, an author claiming—and long believed—to be Dionysius the Areopagite, an early Christian convert.
Anonymus, in its Latin spelling, generally with a specific city designation, is traditionally used by scholars in the humanities to refer to an ancient writer whose name is not known, or to a manuscript of their work. Very many such writers have left valuable historical or literary records: an incomplete list of such Anonymi is at Anonymus.
In the history of art, many painting workshops can be identified by their characteristic style and discussed and the workshop's output set in chronological order. Sometimes archival research later identifies the name, as when the "Master of Flémalle"—defined by three paintings in the Städelsches Kunstinstitut in Frankfurt— was identified as Robert Campin. The 20th-century art historian Bernard Berenson methodically identified numerous early Renaissance Florentine and Sienese workshops under such sobriquets as "Amico di Sandro" for an anonymous painter in the immediate circle of Sandro Botticelli.
In legal cases, a popularly accepted name to use when it is determined that an individual needs to maintain anonymity is "John Doe". This name is often modified to "Jane Doe" when the anonymity-seeker is female. The same names are also commonly used when the identification of a dead person is not known. The semi-acronym Unsub is used as law enforcement slang for "Unknown Subject of an Investigation".
The military often feels a need to honor the remains of soldiers for whom identification is impossible. In many countries, such a memorial is named the Tomb of the Unknown Soldier.
The history of anonymous expression in political dissent is both long and with important effect is human history, as in the Letters of Junius or Voltaire's Candide, or scurrilous as in pasquinades. In the tradition of anonymous British political criticism, the Federalist Papers were anonymously authored. Without the public discourse on the controversial contents of the U.S. Constitution, ratification would likely have taken much longer as individuals worked through the issues. The United States Declaration of Independence, however, was not anonymous. If it had been unsigned, it might well have been less effective. John Perry Barlow, Joichi Ito, and other US bloggers express a very strong support for anonymous editing as one of the basic requirements of open politics as conducted on the Internet. Saipansucks.com is an example of an anonymously written website that socially and politically criticizes the United States' Commonwealth of the Northern Mariana Islands, and UticaSux.com politically criticizes the local government of Utica, New York, in the United States.
Anonymity is directly related to the concept of obscurantism or pseudonymity, where an artist or group attempts to remain anonymous, for various reasons, not limited to: adding an element of mystique to themselves and/or their work, attempting to avoid what is know as the "cult of personality" or hero worship, where the charisma, good looks, wealth and/or other unrelated or mildly related aspects of the person(s) is the main reason for interest in their work, rather than the work itself; also the ability to break into a field or area of interest normally dominated by males, such as James Tiptree, Jr, the famous science fiction author who was actually a woman named Alice Bradley Sheldon, as seems to also be the case with JT LeRoy. The reasons for choosing this approach vary. Some, such as Thomas Pynchon, and J. D. Salinger who seem to want to avoid the "limelight" of popularity or simply want to live private lives. Some others include The Residents, and until 2004, musician Jandek.