The Independence of Irrelevant Alternatives (IIA) is a principle in voting theory and social choice theory that stipulates that the choice between two options should depend only on those two options and not be affected by the presence or preference for other alternatives.

The mathematical theory of democracy applies mathematical concepts and tools to study and analyze democratic systems, decisions, and outcomes. It encompasses various aspects, including social choice theory, voting systems, and the mechanics of collective decision-making. Here are some key components: 1. **Social Choice Theory**: This area investigates how individual preferences can be aggregated into a collective decision. It addresses questions such as how to fairly represent individual votes in a group decision.

May's Theorem is a result in social choice theory, particularly regarding voting systems and preferences. It addresses the behavior of the majority rule method in elections with more than two candidates. Specifically, May's Theorem states that in a majority rule voting system, the only function that satisfies certain axioms (unanimity, independence of irrelevant alternatives, and non-dictatorship) is the simple majority rule.

Ebenezer Child appears to refer to a few different contexts, but it is most commonly associated with Ebenezer Scrooge's character from Charles Dickens' "A Christmas Carol," wherein "child" might refer to various themes of childhood, innocence, and redemption represented in the story. However, there may also be other specific references or uses of the name in literature, music, or other media.

Elkanah Kelsey Dare (1850–1933) was an American painter known for his work in the late 19th and early 20th centuries. His contributions were primarily in the fields of landscape painting and portraiture. Dare was part of the artistic community during a time when many American artists were beginning to establish their unique styles, influenced by both European techniques and American subjects. He often depicted natural landscapes that highlighted the beauty of the American scenery.

"Harmonia Sacra" is a collection of sacred music, specifically a series of compositions and hymns. The term is often associated with the work of the 17th-century composer and music theorist John Playford, who published a collection under this title in 1678. The collection contains various hymns, psalms, and sacred songs, arranged for vocal parts and often accompanied by instruments.

Jacob Kimball Jr. was an American businessman and politician from Massachusetts in the 19th century. He was notably involved in the textile industry and served as a member of the Massachusetts House of Representatives. Jacob Kimball Jr. is often recognized for his contributions to local commerce and governance during his time. If you meant something else by "Jacob Kimball Jr.

Jesse B. Aikin does not appear to be a widely recognized figure or concept based on the data available up to October 2023. It's possible that he could be a private individual, a lesser-known professional, or a newly emerging figure in a specific field.

John Gill Landrum is a figure known for various contributions throughout his life, but to provide a more specific answer, I would need clarification on the context in which you are referring to him. He may be associated with academia, literature, or other fields.

Joseph Funk (1778-1862) was an American composer, music educator, and publisher known primarily for his contributions to shape note singing and choral music in the United States. He is best known for his compilation of "The Southern Harmony," a shape note hymn book published in 1835. This book played a significant role in the development of folk and religious music traditions in the South and contributed to the shape note singing tradition that became popular in the 19th century.

Kentucky Harmony is a historic shape-note singing book published in 1816 by the American Baptist minister and composer, John G. D. G. R. Knox. It is significant in the tradition of American Sacred Harp and shape-note music, which uses a system of shapes to denote different musical notes, making it easier for people, particularly those without formal musical training, to read and sing music.

The National Gospel Singing Convention is an event that celebrates gospel music and its various forms. It typically features performances by gospel choirs, solo artists, and other musicians from across the country. These conventions are often a gathering place for artists, fans, and those involved in the gospel music industry, providing a platform for worship, fellowship, and sharing of musical talent. The convention might include workshops, seminars, and opportunities for networking, as well as opportunities for attendees to participate in singing or other musical activities.

Nehemiah Shumway refers to a historical figure who was a prominent member of the Shaker community in the 19th century. Shakers are a religious group known for their communal lifestyle, pacifism, and distinct style of worship that includes dance. Nehemiah Shumway is most well-known for his contributions to the Shaker community in places like New Hampshire and Massachusetts, particularly in the areas related to agriculture and craftsmanship.

The Larger Sieve, commonly known in the context of number theory, refers to an advanced mathematical technique used for determining the properties of integers, particularly in relation to prime numbers. It is an extension of the Sieve of Eratosthenes and is particularly useful in analytic number theory and areas dealing with the distribution of prime numbers.

In the context of sieve theory, the "parity problem" generally refers to questions about the distribution of prime numbers. More specifically, sieve theory involves methods that can help determine how many integers in a given set meet certain criteria, often in relation to being prime or composite. The parity problem in sieve theory can typically involve exploring the even and odd behavior of prime numbers or their residues modulo some integer. One classic observation related to parity and primes is that all prime numbers except for 2 are odd.

"Shenandoah Harmony" is a collection of shape-note hymns and sacred music, primarily associated with the Southern United States cultural tradition. The term "shape-note" refers to a musical notation system that uses shapes to represent different pitches, making it easier for singers—especially those who may not be formally trained—to read music and sing together.

The term "Southern Harmony" can refer to different concepts, but it most commonly relates to a few key areas: 1. **Southern Harmony (book)**: Published in 1835 by William Walker, "The Southern Harmony" is a shape note hymn book that contributed to American music, particularly in the Southern United States. Shape notes use different shapes to represent different musical pitches, making it easier for people to learn and sing hymns, especially in religious settings.

As of my last knowledge update in October 2023, "Supply Belcher" does not appear to be a widely recognized term or concept in any mainstream context. It's possible that it could refer to a specific term in a niche industry, a local business, or perhaps a concept that has emerged more recently.

"The Christian Harmony" refers to a shape-note hymn book created by William Walker, first published in 1835. It is significant in the American sacred music tradition, particularly in the Southern United States. Walker's book features a simpler music notation system designed to aid congregations and choirs in singing hymns. Shape-note music uses different shapes to represent different musical notes, making it easier for singers—especially those who may not have formal music training—to learn and perform hymns.

Thomas Commuck (c. 1810–1856) was a notable figure in American history, recognized as one of the first known Native American composers and musicians. He belonged to the Narragansett tribe in Rhode Island and is primarily remembered for his contributions to music during the 19th century. Commuck composed several works that reflected his cultural heritage and experiences as a Native American in a rapidly changing society. His pieces often incorporated themes relevant to Indigenous life and perspectives.