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Voting

Voting is a method by which a group, such as a meeting or an electorate, convenes together for the purpose of making a collective decision or expressing an opinion usually following discussions, debates or election campaigns. Democracies elect holders of high office by voting. Residents of a jurisdiction represented by an elected official are called "constituents", and the constituents who choose to cast a ballot for their chosen candidate are called "voters." There are different systems for collecting votes, but while many of the systems used in decision-making can also be used as electoral systems, any which cater to proportional representation can only be used in elections.

In smaller organizations, voting can occur in many different ways: formally via ballot to elect others for example within a workplace, to elect members of political associations, or to choose roles for others; or informally with a spoken agreement or a gesture like a raised hand, or electronically.

In politics
In a democracy, the government is elected by the people who vote in an election: a way for an electorate to elect, i.e., choose, among several different candidates. It is more than likely that elections will be between two opposing parties. These two will be the most established and most popular parties in the country. For example, in the US, the competition is between the Republicans and the Democrats. In an indirect democracy, voting is the method by which the person elected (in charge) represents the people, whilst making decisions. Direct democracy is the complete opposite, the people make the policy decisions directly without selecting a representative to do it for them.

A majority vote is when more than half of voters vote for the same person or party. However, whilst it is usually said each individual's vote does count, many countries use a combination of factors to decide who has power, not the at-large "popular vote". Most influential of these factors are districts that divide the electorate. For example, in the UK a party winning plurality in a majority of constituencies wins majority government, but they may not always have the most individual votes (i.e. they may have lose the popular vote but still win the seat count). (It is also possible for a party to win plurality in a minority of constituencies (but more than any other one party) and thus win minority government.)

Many liberal democracies use what is called a secret ballot, hoping to prevent individuals from becoming influenced by other people and to protect their political privacy. The objective of secret ballots is to try to achieve the most authentic outcome, without any risk of peer pressure, threat, or services linked to one's vote: the person votes for their actual preferred choice.

Voting often takes place at a polling station but voting can also be done remotely by mail or using internet voting (such as in Estonia). Voting is voluntary in some countries, like the UK, but it may be compulsory in others, such as Australia.

Because countries have different rules about whether or not voting is compulsory, statistics showing how voting has changed will differ.

Decision-making systems
Voters seek one outcome: a government majority who will vote in favor of a decision or a prioritization that the voter cares about. Voters and/or elected representatives may seek in several way to identify what the majority opinion is. Three types include the simple, weighted, or consociational majority vote. Other multi-option procedures include two-round voting, the alternative vote (AV) - also known as instant run-off voting (IRV) - and the single transferable vote (STV), approval voting, the Borda Count (BC), the Modified Borda Count (MBC), and the Condorcet method, nearly all of which are also used as electoral systems. They are outlined below.

Electoral systems
There are many electoral methods. The purpose of an election may be to choose one person, such as a president, or a group, such as a committee or a parliament. In electing a parliament, either each of many small constituencies can elect a single representative, as in Britain; or each of a lesser number of multi-member constituencies may elect two or more representatives, as in Ireland; or multi-member districts and some single-member districts can be used; or the entire country can be treated as one "at-large" district, as in The Netherlands.

Different voting systems use different ballot designs. Some ballots allow only one choice to be selected (single X voting); others allow ranking or selecting multiple options (Ranked ballots).

Different voting systems allow each voter to cast a different number of votes - only one (single voting as in First-past-the-post voting, Single non-transferable voting and Single transferable voting); as many as are being elected in a multiple-member district (multiple voting as used in Plurality block voting; more than one but fewer than are being elected in a multiple-member district (Limited voting). Most allow a voter to put just one vote on each candidate, but others allow a voter's votes to be piled on to one candidate.

Different voting systems require different levels of support to be elected. Plurality voting (First-past-the-post voting) elects the candidate with more votes than any other single candidate. It does not require the winner to achieve a voting majority, to have more than half of the total votes cast. In First-past-the-post voting, when more than two candidates run, the winner commonly has less than half of the vote, as few as 18 percent was recorded in 2014 in Toronto. In Instant-runoff voting, a candidate must have a majority of votes to be elected, although presence of exhausted votes may mean that the majority at time of final count is not majority of votes cast.

In STV, any candidate who takes quota (usually set at much less than half of the votes) is elected; others without quota (but with more votes than any other single candidate) may be declared elected as well.

Side effects of First-past-the-post voting include a waste of votes due to vote splitting, a two-party system and political polarization due to electing candidates that do not support centrism. To understand why a race using First-past-the-post voting tends to favor less-centric candidates, consider a simple lab experiment where students in a class vote for their favorite marble. If five marbles are assigned names and are placed "up for election", and if three of them are green, one is red, and one is blue, then a green marble will rarely win the election. The reason for the green's lack of success is vote splitting. The three green marbles will split the votes of those who prefer green. In fact, in this analogy, the only way that a green marble is likely to win is if more than three-fifths of the voters prefer green. If the same number of people prefer green as those who prefer red and blue, that is to say, if one-third of the voters prefer green, one-third prefer blue, and one-third prefer red, then each green marble will only get one-ninth of the vote, if the green marbles each take same number of votes, while the red and blue marbles will each get one-third, putting the green marbles at a serious disadvantage. If the experiment is repeated with other colors, the color that is in the majority (if the majority is split among multiple choices) will still rarely win. In other words, from a purely mathematical perspective, a single-winner system tends to favor a winner that is different from the majority, if the majority runs multiple candidates, and if the minority group runs just one candidate. This minority rule success can also result if multiple winners are elected and voters cast multiple votes (Plurality block voting). But even if the majority is split among multiple candidates, proportionate results can still be produced if votes can be transferred, as under STV, or if multiple winners are elected and each voter has just one vote.

Alternatives to First-past-the-post voting include approval voting, two-round, proportional representation, and instant-runoff voting. With approval voting, voters are encouraged to vote for as many candidates as they approve of, so the winner is much more likely to be any one of the five marbles because people who prefer green will be able to vote for every one of the green marbles. With two-round elections, the field of candidates is thinned prior to the second round of voting. In most cases, the winner must receive a majority of the votes, which is more than half. If no candidate obtains a majority in the first round, then the two candidates with the most significant plurality run again for the second round of voting. Variants exist regarding these two points: the requirement for being elected at the first round is sometimes less than 50%, and the rules for participation in the runoff may vary.

With single-round ranked voting, such as instant-runoff voting system as used in some elections in Australia and the United States, voters rank each candidate in order of preference (1,2,3,4 etc.). Votes are distributed to each candidate according to the first preferences. If no single candidate has 50% of the vote, then the candidate with the fewest votes is excluded and their votes are redistributed according to the voter's nominated order of preference. The process repeats itself until a candidate has 50% or more votes. The system is designed to produce the same result as an exhaustive ballot but using only a single round of voting.

Ranked voting is also used in a PR format. PR-STV is used in Australia, Ireland and Malta. Quota is calculated. In say a four-seat constituency, quota (if Droop quota is used) is 20 percent of the valid vote plus 1. Every candidate with quota (of 1st preferences alone or combination of first preferences and later preferences) will be elected. If a candidate has more than a quota and seats are yet to be filled, his/her surplus will be distributed to the other candidates in proportion to all of that candidate's 2nd preferences, in line with secondary preferences marked on the vote if any. If there are still candidates to be elected and no surplus votes to be transferred, the least-popular is eliminated, as above in AV or IRV, and the process continues until four candidates have reached a quota or are declared elected when the field of candidates is thinned to the number of remaining open seats.

In the Quota Borda System (QBS), the voters also cast their preferences, 1,2,3,4... as they wish. In the analysis, all 1st preferences are counted; all 2nd preferences are counted; after these preferences have been translated into points per the rules of a Modified Borda Count (MBC), the candidates' points are also counted. Seats are awarded to any candidates with a quota of 1st preferences; to any pair of candidates with two quotas of 1st/2nd preferences; and if seats are still to be filled, to those candidates with the highest MBC scores.

In a voting system that uses multiple votes (Plurality block voting), the voter can vote for any subset of the running candidates. So, a voter might vote for Alice, Bob, and Charlie, rejecting Daniel and Emily. Approval voting uses such multiple votes.

In a voting system that uses a ranked vote, the voter ranks the candidates in order of preference. For example, they might mark a preference for Bob in the first place, then Emily, then Alice, then Daniel, and finally Charlie. Ranked voting systems, such as those used in Australia and Ireland, use a ranked vote.

In a voting system that uses a scored vote (or range vote), the voter gives each alternative a number between one and ten (the upper and lower bounds may vary). See cardinal voting systems.

Some "multiple-winner" systems such as the Single Non-Transferable Vote, SNTV, used in Afghanistan and Vanuatu give a single vote or one vote per elector per available position.

STV uses single ranked votes; block voting (Plurality-at-large voting) are often used for at-large positions such as on some city councils.

Finally, the Condorcet rule is used (sometimes) in decision-making. The voters or elected representatives cast their preferences on one, some, or all options, 1,2,3,4... as in PR-STV or QBS. In the analysis, option A is compared to option B, and if A is more popular than B, then A wins this pairing. Next, A is compared with option C, then D, and so on. Likewise, B is compared with C, D, etc. The option which wins the most pairings, (if there is one), is the Condorcet winner.

Referendums
When the citizens of a country are invited to vote, they are participating in an election. However, people can also vote in referendums and initiatives. Since the end of the eighteenth century, more than five hundred national referendums (including initiatives) were organized in the world; among them, more than three hundred were held in Switzerland. Australia ranked second with dozens of referendums.

Most referendums are binary. The first multi-option referendum was held in New Zealand in 1894, and most of them are conducted under a two-round system. New Zealand had a five-option referendum in 1992, while Guam had a six-option plebiscite in 1982, which also offered a blank option, in case some voters wanted to (campaign and) vote for a seventh option.

Fair voting
The results of an election may lead to confusion, and in extreme cases, could lead to violence and even a civil war. Many alternatives may fall in the latitude of indifference—they are neither accepted nor rejected.

There are social choice theory definitions of seemingly reasonable criteria that are a measure of the fairness of certain aspects of voting, including non-dictatorship, unrestricted domain, non-imposition, Pareto efficiency, and independence of irrelevant alternatives. However, Arrow's impossibility theorem states that no voting system can meet all these standards.

To ensure fair voting and to prevent the misuse of its microblogging platform, Twitter announced that it was going to be adding a feature for its users to be able to report content that misleads voters.

Negative voting
Negative voting allows a vote that expresses the people's disapproval of a candidate. For explanatory purposes, consider a hypothetical voting system that uses negative voting. In this system, one vote is allowed, with the choice of either for a candidate or against a candidate. Each positive vote adds one to a candidate's overall total, while a negative vote subtracts one, arriving at a net favorability. The candidate with the highest net favorability is the winner. Not only is a negative total possible, but also, a candidate may even be elected with 0 votes if enough negative votes are cast against their opponents.

Under this implementation, negative voting is no different from a positive voting system, when only two candidates are on the ballot. However, in the case of three or more candidates, each negative vote for a candidate counts positively toward all of the other candidates.

Consider the following example:

Three candidates are running for the same seat. Two hypothetical election results are given, contrasting positive and negative voting. (The illustration assumes perfect polling accuracy and total voter turnout.)

Election results with positive voting: A-voters, with the clear advantage of 40%, logically vote for Candidate A. B-voters, unconfident of their candidate's chances, split their votes exactly in half, giving both Candidates A and C 15% each. C-voters, also logically vote for their candidate. A is the winner with 55%, C at 45%, and B at 0%.

Election results with negative voting: A-voters again, with the clear advantage of 40%, logically vote for Candidate A. B-voters, split exactly in half. Each B-voter decides to vote negatively against their least favourite candidate, with the reasoning that this negative vote allows them to express approval for the two other candidates. C-voters also decide to vote negatively against Candidate A, reasoning along similar lines. Candidate B is the winner with 0 votes. Enough negative votes were cast against Candidate B's opponents, resulting in negative totals. Candidate A, despite having polled at 40%, winds up with -5%, offset due to the aggregate 45% of negative votes cast by B and C voters. Candidate C ends up with -15%.

Proxy voting
Proxy voting is a form of voting in which a registered citizen who can legally vote passes on his or her vote to a different voter or electorate who will vote in his stead.

Anti-voting
In South Africa, there is a strong presence of anti-voting campaigns by poor citizens. They make the structural argument that no political party truly represents them. This resulted in the "No Land! No House! No Vote!" campaign, which becomes very prominent each time the country holds elections. The campaign is prominent among three of South Africa's largest social movements: the Western Cape Anti-Eviction Campaign, Abahlali baseMjondolo, and the Landless Peoples Movement.

Other social movements in other parts of the world also have similar campaigns or non-voting preferences. These include the Zapatista Army of National Liberation and various anarchist-oriented movements.

It is possible to make a blank vote, carrying out the act of voting, which may be compulsory, without selecting any candidate or option, often as an act of protest. In some jurisdictions, there is an official none of the above option and it is counted as a valid vote. Usually, blank and null votes are counted (together or separately) but are not considered valid.

Voting and information
Modern political science has questioned whether average citizens have sufficient political knowledge to cast meaningful votes. A series of studies coming out of the University of Michigan in the 1950s and 1960s argued that many voters lack a basic understanding of current issues, the liberal–conservative ideological dimension, and the relative ideological dilemma that are important to understand when making political decisions. Studies from other institutions have suggested that the physical appearance of candidates is a criterion upon which voters base their decision. Voting advice applications can increase political knowledge enabling to cast informed votes.

Religious views
Christadelphians, Jehovah's Witnesses, Old Order Amish, Rastafarians, the Assemblies of Yahweh, and some other religious groups, have a policy of not participating in politics and this extends to voting. Rabbis from all Jewish denominations encourage voting and some even consider it a religious obligation.

Meetings and gatherings
Whenever several people who do not all agree need to make some decision, voting is a very common way of reaching a decision peacefully. The right to vote is usually restricted to certain people. Members of a society or club, or shareholders of a company, but not outsiders, may elect its officers, or adopt or change its rules, in a similar way to the election of people to official positions. A panel of judges, either formal judicial authorities or judges of the competition, may decide by voting. A group of friends or members of a family may decide which film to see by voting. The method of voting can range from formal submission of written votes, through show of hands, voice voting or audience response systems, to informal noting which outcome seems to be preferred by more people.

Voting basis
According to Robert's Rules of Order, a widely used guide to parliamentary procedure, the bases for determining the voting result consists of two elements: (1) the number of votes that are required for a proposal to be adopted or for a candidate to be elected (e.g. more than half, two-thirds, three-quarters, etc., of the total); and (2) the set of members to which the proportion applies (e.g. the members present and voting, the members present, the entire membership of the organization, the entire electorate, etc.). An example of this concept is the need for a majority vote of the members present and voting.

Alternatively, a decision could be made without a formal vote by using unanimous consent.

A voting method is the way in which people cast their votes in an election or a referendum. There are several different methods in use around the world.

Voting methods in deliberative assemblies
Deliberative assemblies—bodies that use parliamentary procedure to arrive at decisions—use several methods when voting on motions (formal proposals by a member or members of a deliberative assembly). The regular methods of voting in such bodies are a voice vote, a rising vote, and a show of hands. Additional forms of voting include a recorded vote and balloting. The assembly can decide on the voting method by adopting a motion on it.

Paper-based methods
The most common voting method uses paper ballots on which voters mark their preferences. This may involve marking their support for a candidate or party listed on the ballot, or a write-in where they write out the name of their preferred candidate (if it is not listed).

An alternative method that is still paper-based known as ballot letters is used in Israel, where polling booths contain a tray with ballots for each party running in the elections; the ballots are marked with the letter(s) assigned to that party. Voters are given an envelope into which they put the ballot of the party they wish to vote for, before placing the envelope in the ballot box. The same system is also implemented in Latvia.

Machine voting
Machine voting uses voting machines, which may be manual (e.g. lever machines) or electronic.

Online voting
Some countries allow people to vote online. Estonia was one of the first countries to use online voting: it was first used in their 2005 local elections.

Postal voting
Many countries allow postal voting, where voters are sent a ballot and return it by post.

Open ballot
In contrast to a secret ballot, an open ballot takes place in public and is commonly done by a show of hands. An example is the Landsgemeinde system in Switzerland, which is still in use in the cantons of Appenzell Innerrhoden, Glarus, Grisons, and Schwyz.

Other methods
In Gambia, voting is carried out using marbles. The method was introduced in 1965 to deal with illiteracy. Polling stations contain metal drums painted in party colours and emblems with candidates' photos attached to them. Voters are given a marble to place in the drum of their chosen candidate; when dropped into the drum, a bell sounds to register the vote. To avoid confusion, bicycles are banned near polling booths on election day. If the marble is left on top of the drum rather than placed in it, the vote is deemed invalid.

A similar system used in social clubs sees voters given a white ball to indicate support and a black ball to indicate opposition. This led to the coining of the term blackballing.

In person
Some votes are carried out in person if all the people eligible to vote are present. This could be by a show of hands or keypad polling.

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Hyperplane

In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension. Like a plane in space, a hyperplane is a flat hypersurface, a subspace whose dimension is one less than that of the ambient space. Two lower-dimensional examples of hyperplanes are one-dimensional lines in a plane and zero-dimensional points on a line.

Most commonly, the ambient space is $n$-dimensional Euclidean space, in which case the hyperplanes are the $(n − 1)$-dimensional flats, each of which separates the space into two half spaces. A reflection across a hyperplane is a kind of motion (geometric transformation preserving distance between points), and the group of all motions is generated by the reflections. A convex polytope is the intersection of half-spaces.

In non-Euclidean geometry, the ambient space might be the $n$-dimensional sphere or hyperbolic space, or more generally a pseudo-Riemannian space form, and the hyperplanes are the hypersurfaces consisting of all geodesics through a point which are perpendicular to a specific normal geodesic.

In other kinds of ambient spaces, some properties from Euclidean space are no longer relevant. For example, in affine space, there is no concept of distance, so there are no reflections or motions. In a non-orientable space such as elliptic space or projective space, there is no concept of half-planes. In greatest generality, the notion of hyperplane is meaningful in any mathematical space in which the concept of the dimension of a subspace is defined.

The difference in dimension between a subspace and its ambient space is known as its codimension. A hyperplane has codimension $1$.

Technical description
In geometry, a hyperplane of an n-dimensional space V is a subspace of dimension n − 1, or equivalently, of codimension 1 in V. The space V may be a Euclidean space or more generally an affine space, or a vector space or a projective space, and the notion of hyperplane varies correspondingly since the definition of subspace differs in these settings; in all cases however, any hyperplane can be given in coordinates as the solution of a single (due to the "codimension 1" constraint) algebraic equation of degree 1.

If V is a vector space, one distinguishes "vector hyperplanes" (which are linear subspaces, and therefore must pass through the origin) and "affine hyperplanes" (which need not pass through the origin; they can be obtained by translation of a vector hyperplane). A hyperplane in a Euclidean space separates that space into two half spaces, and defines a reflection that fixes the hyperplane and interchanges those two half spaces.

Special types of hyperplanes
Several specific types of hyperplanes are defined with properties that are well suited for particular purposes. Some of these specializations are described here.

Affine hyperplanes
An affine hyperplane is an affine subspace of codimension 1 in an affine space. In Cartesian coordinates, such a hyperplane can be described with a single linear equation of the following form (where at least one of the $$a_i$$s is non-zero and $$b$$ is an arbitrary constant):

 * $$a_1x_1 + a_2x_2 + \cdots + a_nx_n = b.\ $$

In the case of a real affine space, in other words when the coordinates are real numbers, this affine space separates the space into two half-spaces, which are the connected components of the complement of the hyperplane, and are given by the inequalities

 * $$a_1x_1 + a_2x_2 + \cdots + a_nx_n < b\ $$

and

 * $$a_1x_1 + a_2x_2 + \cdots + a_nx_n > b.\ $$

As an example, a point is a hyperplane in 1-dimensional space, a line is a hyperplane in 2-dimensional space, and a plane is a hyperplane in 3-dimensional space. A line in 3-dimensional space is not a hyperplane, and does not separate the space into two parts (the complement of such a line is connected).

Any hyperplane of a Euclidean space has exactly two unit normal vectors: $$\pm\hat{n}$$. In particular, if we consider $$\mathbb{R}^{n+1}$$ equipped with the conventional inner product (dot product), then one can define the affine subspace with normal vector $$\hat{n}$$ and origin translation $$\tilde{b} \in \mathbb{R}^{n+1}$$ as the set of all $$x \in \mathbb{R}^{n+1}$$ such that $$\hat{n} \cdot (x-\tilde{b})=0$$.

Affine hyperplanes are used to define decision boundaries in many machine learning algorithms such as linear-combination (oblique) decision trees, and perceptrons.

Vector hyperplanes
In a vector space, a vector hyperplane is a subspace of codimension 1, only possibly shifted from the origin by a vector, in which case it is referred to as a flat. Such a hyperplane is the solution of a single linear equation.

Projective hyperplanes
Projective hyperplanes, are used in projective geometry. A projective subspace is a set of points with the property that for any two points of the set, all the points on the line determined by the two points are contained in the set. Projective geometry can be viewed as affine geometry with vanishing points (points at infinity) added. An affine hyperplane together with the associated points at infinity forms a projective hyperplane. One special case of a projective hyperplane is the infinite or ideal hyperplane, which is defined with the set of all points at infinity.

In projective space, a hyperplane does not divide the space into two parts; rather, it takes two hyperplanes to separate points and divide up the space. The reason for this is that the space essentially "wraps around" so that both sides of a lone hyperplane are connected to each other.

Applications
In convex geometry, two disjoint convex sets in n-dimensional Euclidean space are separated by a hyperplane, a result called the hyperplane separation theorem.

In machine learning, hyperplanes are a key tool to create support vector machines for such tasks as computer vision and natural language processing.

The datapoint and its predicted value via a linear model is a hyperplane.

Dihedral angles
The dihedral angle between two non-parallel hyperplanes of a Euclidean space is the angle between the corresponding normal vectors. The product of the transformations in the two hyperplanes is a rotation whose axis is the subspace of codimension 2 obtained by intersecting the hyperplanes, and whose angle is twice the angle between the hyperplanes.

Support hyperplanes
A hyperplane H is called a "support" hyperplane of the polyhedron P if P is contained in one of the two closed half-spaces bounded by H and $$H\cap P \neq \varnothing$$. The intersection of P and H is defined to be a "face" of the polyhedron. The theory of polyhedra and the dimension of the faces are analyzed by looking at these intersections involving hyperplanes.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Hyperplane


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Tourist attraction

A tourist attraction is a place of interest that tourists visit, typically for its inherent or an exhibited natural or cultural value, historical significance, natural or built beauty, offering leisure and amusement.

Types
Places of natural beauty such as beaches, tropical island resorts, national parks, mountains, deserts and forests, are examples of traditional tourist attractions which people may visit. Cultural tourist attractions can include historical places, sites of significant historic event, monuments, ancient temples, zoos, aquaria, museums and art galleries, botanical gardens, buildings and structures (such as forts, castles, libraries, former prisons, skyscrapers, bridges), theme parks and carnivals, living history museums, public art (sculptures, statues, murals), ethnic enclave communities, historic trains and cultural events. Factory tours, industrial heritage, creative art and crafts workshops are the object of cultural niches like industrial tourism and creative tourism. Many tourist attractions are also landmarks. But sports events such as a soccer game, Formula 1 race or sailing regatta can also attract tourists.

Tourists' expectations when visiting a particular place are related to several features of the chosen destination: culture, architecture, gastronomy, infrastructure, landscape, events, shopping, etc. These features attract people to the destination and contribute to the overall experience of the trip. The ultimate primary purpose of attractions is to attract the customer's attention so that they can come to a specific location and explore the various attractions on vacation. In the travel and tourism industry, attractions therefore play a particularly important role as this attracts tourists from all over the world.

Tourist attractions are also created to capitalize on legends such as a supposed UFO crash site near Roswell, New Mexico and the alleged Loch Ness monster sightings in Scotland. Ethnic communities may become tourist attractions, such as Chinatowns in the United States and the black British neighborhood of Brixton in London, England. Tourists also look for special local culinary experiences such as street kitchens in Asian metropolises or the coffeehouse culture in Central Europe. In particular, cultural property and the individual places of the UNESCO World Heritage Site have developed into tourist attractions. If too many tourists frequent individual places, this can lead to environmental pollution and resistance from the local population, such as in Barcelona or Venice. With regard to this whole subject, there are already lists of destinations that are not recommended to tourists.

There are innumerable lists and reviews of tourist attractions. Visitor statistics, cultural significance, beauty or age are used and these always reflect the author's personal assessments. Sometimes it is particularly emphasized that this particular tourist attraction has not yet been in the focus of the international tourism industry. Some of the sights are internationally known or target the national or local market. Some attractions are reserved for the local population or are rarely advertised because the main traffic routes and main airports are too far away.

In the United States, owners and marketers of attractions advertise tourist attractions on billboards along the sides of highways and roadways, especially in remote areas. Tourist attractions often distribute free promotional brochures to be displayed in rest areas, information centers, fast food restaurants, and motel rooms or lobbies.

While some tourist attractions provide visitors a memorable experience for a reasonable admission charge or even for free, others may be of low quality and overprice their goods and services (such as admission, food, and souvenirs) in order to profit excessively from tourists. Such places are commonly known as tourist traps. Within cities, rides on boats and sightseeing buses are sometimes popular.

Novelty attractions
Novelty attractions are oddities such as the "biggest ball of twine" in Cawker City, Kansas, the Corn Palace in Mitchell, South Dakota, or Carhenge in Alliance, Nebraska, where old cars serve in the place of stones in a replica of Stonehenge. Novelty attractions are not limited to the American Midwest, but are part of Midwestern culture.

Tourist destination
A tourist destination is a city, town, or other area that is significantly dependent on revenues from tourism, or "a country, state, region, city, or town which is marketed or markets itself as a place for tourists to visit". It may contain one or more tourist attractions and possibly some "tourist traps". Fátima town, for example, is a popular tourist destination in Portugal. Siem Reap town is a popular tourist destination in Cambodia, mainly owing to its proximity to the Angkor temples. The Loire valley, the third tourist destination in France, is a good example of a region marketed and branded as a place for tourists to visit, mainly known for its Châteaux of the Loire valley.

A tropical island resort is an island or archipelago that depends on tourism as its source of revenue. The Bahamas in the Caribbean, Bali in Indonesia, Phuket in Thailand, Hawaii in the United States, Fiji in the Pacific, and Santorini and Ibiza in the Mediterranean are examples of popular island resorts.

France, the United States, and Spain were the three most popular international destinations in 2017. The total number of international travelers arriving in those countries was about 234 million, contributing 8.9%, 7.7%, and 14.9%, respectively, to the total GDP of those countries.

Although some years back, Africa was lean on tourism, the continent is currently regarded as the second fastest growing tourism region with over 67 million tourists visits to Africa in 2018. Ethiopia, with a growth rate of 48.6% in 2018, is at the top of the list of African tourist centers. Other tourist locations in Africa include Cape Town, South Africa, Giza Necropolis, Egypt, The Maasai Mara National Reserve, Kenya, Victoria Falls, Zimbabwe and Zambia.

From the tourism industry supply perspective, a destination is usually defined by a geo-political boundary, and destination marketing is most commonly funded by governments. From the traveler perspective, a destination might be perceived quite differently.

Economic impact and protection
Tourism generates substantial economic benefits for both host countries and tourists' home countries. Especially in developing countries, one of the primary motivations for a region to promote itself as a tourism destination is the expected economic benefit. According to the World Tourism Organization, 698 million people travelled to a foreign country in 2000, spending more than US$478 billion. International tourism receipts combined with passenger transport currently total more than US$575 billion – making tourism the world's number one export earner.

Tourist attractions can:
 * contribute to government revenues; direct contributions are generated by taxes on incomes from tourism employment and tourism businesses, and by direct levies on tourists, such as departure taxes
 * provide employment
 * support conservation of habitats, species and historic sites
 * stimulate infrastructure investment
 * contribute to local economies
 * provide foreign currency earnings

In the event of war, many tourist attractions are a special goal in order to cause lasting damage to the enemy or to finance the war. International attempts are therefore made to protect and preserve these economic and cultural foundations of a community, city or country. There is intensive cooperation between the United Nations, UNESCO and Blue Shield International on the protection of cultural goods and UNESCO World Heritage Sites. However, cooperation between organizations and state authorities is not enough to prevent destruction, robbery and looting. The founding president of Blue Shield International Karl von Habsburg summed it up with the words: “Without the local community and without the local participants, that would be completely impossible”.

title: Tourist attraction


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Counting sort

In computer science, counting sort is an algorithm for sorting a collection of objects according to keys that are small positive integers; that is, it is an integer sorting algorithm. It operates by counting the number of objects that possess distinct key values, and applying prefix sum on those counts to determine the positions of each key value in the output sequence. Its running time is linear in the number of items and the difference between the maximum key value and the minimum key value, so it is only suitable for direct use in situations where the variation in keys is not significantly greater than the number of items. It is often used as a subroutine in radix sort, another sorting algorithm, which can handle larger keys more efficiently.

Counting sort is not a comparison sort; it uses key values as indexes into an array and the $Ω(n log n)$ lower bound for comparison sorting will not apply. Bucket sort may be used in lieu of counting sort, and entails a similar time analysis. However, compared to counting sort, bucket sort requires linked lists, dynamic arrays, or a large amount of pre-allocated memory to hold the sets of items within each bucket, whereas counting sort stores a single number (the count of items) per bucket.

Input and output assumptions
In the most general case, the input to counting sort consists of a collection of $n$ items, each of which has a non-negative integer key whose maximum value is at most $k$. In some descriptions of counting sort, the input to be sorted is assumed to be more simply a sequence of integers itself, but this simplification does not accommodate many applications of counting sort. For instance, when used as a subroutine in radix sort, the keys for each call to counting sort are individual digits of larger item keys; it would not suffice to return only a sorted list of the key digits, separated from the items.

In applications such as in radix sort, a bound on the maximum key value $k$ will be known in advance, and can be assumed to be part of the input to the algorithm. However, if the value of $k$ is not already known then it may be computed, as a first step, by an additional loop over the data to determine the maximum key value.

The output is an array of the elements ordered by their keys. Because of its application to radix sorting, counting sort must be a stable sort; that is, if two elements share the same key, their relative order in the output array and their relative order in the input array should match.

Pseudocode
In pseudocode, the algorithm may be expressed as:

function CountingSort(input, k) count ← array of k + 1 zeros output ← array of same length as input for i = 0 to length(input) - 1 do j = key(input[i]) count[j] = count[j] + 1 for i = 1 to k do count[i] = count[i] + count[i - 1] for i = length(input) - 1 down to 0 do j = key(input[i]) count[j] = count[j] - 1 output[count[j]] = input[i] return output

Here  is the input array to be sorted,   returns the numeric key of each item in the input array,   is an auxiliary array used first to store the numbers of items with each key, and then (after the second loop) to store the positions where items with each key should be placed, is the maximum value of the non-negative key values and  is the sorted output array.

In summary, the algorithm loops over the items in the first loop, computing a histogram of the number of times each key occurs within the  collection. After that in the second loop, it performs a prefix sum computation on  in order to determine, for each key, the position range where the items having that key should be placed; i.e. items of key $$i$$ should be placed starting in position. Finally, in the third loop, it loops over the items of  again, but in reverse order, moving each item into its sorted position in the   array.

The relative order of items with equal keys is preserved here; i.e., this is a stable sort.

Complexity analysis
Because the algorithm uses only simple  loops, without recursion or subroutine calls, it is straightforward to analyze. The initialization of the count array, and the second for loop which performs a prefix sum on the count array, each iterate at most $k + 1$ times and therefore take $O(k)$ time. The other two for loops, and the initialization of the output array, each take $O(n)$ time. Therefore, the time for the whole algorithm is the sum of the times for these steps, $O(n + k)$.

Because it uses arrays of length $k + 1$ and $n$, the total space usage of the algorithm is also $O(n + k)$. For problem instances in which the maximum key value is significantly smaller than the number of items, counting sort can be highly space-efficient, as the only storage it uses other than its input and output arrays is the Count array which uses space $O(k)$.

Variant algorithms
If each item to be sorted is itself an integer, and used as key as well, then the second and third loops of counting sort can be combined; in the second loop, instead of computing the position where items with key  should be placed in the output, simply append   copies of the number   to the output.

This algorithm may also be used to eliminate duplicate keys, by replacing the  array with a bit vector that stores a   for a key that is present in the input and a   for a key that is not present. If additionally the items are the integer keys themselves, both second and third loops can be omitted entirely and the bit vector will itself serve as output, representing the values as offsets of the non- entries, added to the range's lowest value. Thus the keys are sorted and the duplicates are eliminated in this variant just by being placed into the bit array.

For data in which the maximum key size is significantly smaller than the number of data items, counting sort may be parallelized by splitting the input into subarrays of approximately equal size, processing each subarray in parallel to generate a separate count array for each subarray, and then merging the count arrays. When used as part of a parallel radix sort algorithm, the key size (base of the radix representation) should be chosen to match the size of the split subarrays. The simplicity of the counting sort algorithm and its use of the easily parallelizable prefix sum primitive also make it usable in more fine-grained parallel algorithms.

As described, counting sort is not an in-place algorithm; even disregarding the count array, it needs separate input and output arrays. It is possible to modify the algorithm so that it places the items into sorted order within the same array that was given to it as the input, using only the count array as auxiliary storage; however, the modified in-place version of counting sort is not stable.

History
Although radix sorting itself dates back far longer, counting sort, and its application to radix sorting, were both invented by Harold H. Seward in 1954.

title: Counting sort


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Chris Elliott

Christopher Nash Elliott (born May 31, 1960) is an American actor, comedian and writer known for his surreal sense of humor. He appeared in comedic sketches on Late Night with David Letterman (1982–1988), created and starred in the comedy series Get a Life (1990–1992) on Fox, and wrote and starred in the film Cabin Boy (1994). His writing has won four consecutive Primetime Emmy Awards. His other television appearances include recurring roles on Everybody Loves Raymond (2003–2005) and How I Met Your Mother (2009–2014), and starring roles as Chris Monsanto in Adult Swim's Eagleheart (2011–2014) and Roland Schitt in Schitt's Creek (2015–2020). He also appeared in the films Manhunter (1986), Nutty Professor II: The Klumps (2000), Osmosis Jones (2001) and The Rewrite (2014).

Early life
Elliott was born in New York City, and is the youngest of five children of Lee (née Peppers), a model and TV director, and Bob Elliott, who was part of the successful comedy team Bob and Ray. He grew up on the Upper East Side. He attended the National Theater Institute at the Eugene O'Neill Theater Center for a semester.

Career
Elliott was hired as a production assistant on Late Night with David Letterman, and was with the show from its very beginning in February 1982. Over the first year of the show, he was seen on camera irregularly and usually in small sketch roles. In the spring of 1983, Elliott became a writer on the show and his on-camera appearances became more frequent. He became known in the mid-to-late 1980s for playing an assortment of recurring quirky, oddball characters on Late Night. His characters on the show included:

 * "The Conspiracy Guy": During staged audience "question and answer" sessions with Dave, Elliott would approach the microphone and begin accusing Letterman of various plots and schemes, after which "security" would wrestle Elliott to the ground and drag him out of the studio while Elliott yelled threats to Dave.
 * "The Panicky Guy": Elliott would pretend to be an audience member, who panics and runs from the studio at the slightest threat of danger (similar to doomed characters in disaster movies). Once in the hallway he would be run over and crushed by an advancing floor waxer, with his hands raised in terror. In one variation, he played a German Panicky Guy in Lederhosen, who was run over by a hand dolly full of cheese wheels.
 * "The Guy Under the Seats": a short character-comedy bit followed by Elliott as himself (living under the seats, that is) who eventually becomes angry at Letterman and threatens him with some metaphorically articulated comeuppance in the future and always closing with the line "But until that day, I'm gonna be right here, making your life...a living hell."
 * "The Fugitive Guy": a parody of the TV series The Fugitive
 * "The Laid Back Guy": When the studio changed his name on the West Coast to Pierce, Chris portrayed the laid back guy based on his observations of the differences between the West and East Coast. Laid back guy only appeared during West Coast interviews, and stayed around to make sure that Dave "kept things cool."
 * "The Regulator Guy": a parody of The Terminator films. The Regulator Guy spoke with a vaguely Germanic accent and claimed to be "from the future". The Regulator Guy segments were usually pre-taped and presented by Letterman as the trailer for an upcoming television series. The font used for the title was similar to the font used for the then-popular American television series The Equalizer. Chris in fact appeared on an episode of The Equalizer playing a peeping Tom mildly assaulted by the Equalizer. In the Regulator Guy's only live, on-stage appearance, Elliott, carried by wires, "flew" over the audience via jet pack onto the Late Night set. The "jet pack" prop appeared to malfunction, which the Regulator Guy then blamed for ruining his dramatic appearance.
 * "Skylark": an obnoxious, generic, Las Vegas lounge lizard with similar flamboyant features and characteristics as Rip Taylor (including throwing confetti). Skylark debuted when Late Night went to Las Vegas for a week of shows.
 * "Marlon Brando": a recurring parody of Brando, whom Elliott portrays as a slovenly and semi-deranged version of the famous actor.
 * "Chris Elliott Jr.": a spoof of talk-show host Morton Downey Jr.
 * "Johnny Graham": a cabaret musician who hosted the Johnny Graham Piano Request Show in the style of John Wallowitch.

During one Late Night special focused on short films, Elliott was the star of a short about himself entitled "A Television Miracle", in which he alluded that he was actually an animatronic being that was created for the TV show. The "miracle" was the behind-the-scenes work needed to bring his character to life and others.

As his career on Late Night blossomed, Elliott also took small movie roles, often as a supporting actor in non-comedies such as Michael Mann's Manhunter and James Cameron's The Abyss. He also has a small supporting role in an episode of Miami Vice.

In 1986, Elliott co-wrote and starred in the Cinemax special FDR: A One Man Show, a spoof comedy about the life and times of the president. Elliott looked and sounded nothing like the man; he portrayed events from Roosevelt's life that never happened, such as a Japanese bombing of the White House, and his crossing the Potomac in a rowboat. By the end of the show, he had performed Gallagher's shtick of smashing watermelons and other soft fruits on stage.

Elliott left Late Night in early 1990, though he would return as a guest interview subject many times on Late Night and Letterman's subsequent talk show The Late Show with David Letterman.

In 1990, Elliott created and starred in his own sitcom, which was called Get a Life, about a 30-year-old paperboy named Chris Peterson who lived at home with his parents. Elliott's real-life father, Bob Elliott, appeared in the show as Chris's father. The January 1999 issue of TV Guide called the "Zoo Animals on Wheels" episode the 19th funniest TV moment of all time.

In 1993, Elliott teamed up with producer Brad Hall and directed a series of critically acclaimed short films that Elliott showed when appearing on Late Show with David Letterman. That year he also appeared as a news cameraman in the Harold Ramis film Groundhog Day.

Elliott became a cast member of Saturday Night Live in 1994. Also that year, Elliott starred in his first movie—entitled Cabin Boy—which also featured a short appearance by Elliott's old boss, David Letterman, and was produced by Tim Burton. He was nominated for a Razzie Award as Worst New Star.

In 2007, Elliott again began appearing on the Late Show with David Letterman with fellow former Letterman writer Gerard Mulligan. On average, these bits appeared once per month.

His other television credits include the chowder taster on Throwdown with Bobby Flay, airdate 9/2/09, and the voice of Dogbert on the short-run show Dilbert for UPN. He played a serial killer in the series Third Watch in the episodes "The Hunter, Hunted" and "Greatest Detectives in the World" from season six. He played the role of Peter in the last three seasons of Everybody Loves Raymond and a role in a semi-autobiographical sitcom pilot for CBS, entitled You've Reached the Elliotts, playing a man who tries to balance a modest show business career with his home life. From 2009 to 2014, Elliott played the estranged father of How I Met Your Mother character Lily Aldrin, whose relationship strengthened as the show progressed. As well as multiple appearances on The King of Queens, Elliott made guest appearances on Late Show, That '70s Show in the episode "2000 Light Years From Home", and According to Jim. From February 3, 2011 to January 16, 2014, Elliott starred in the Adult Swim series Eagleheart, produced by Conan O'Brien's production company, Conaco.

In 2015, he had a guest role on an episode of NBC's Law & Order: Special Victims Unit and began a starring role as Roland Schitt in Schitt's Creek. In 2016, he co-starred with Amy Sedaris on the Sony Crackle series Thanksgiving. Elliott was also in an Avocados from Mexico commercial in February 2018.

In 2021 he was cast in Maggie, an ABC sitcom pilot starring Rebecca Rittenhouse that was subsequently picked up by Hulu, and he voiced the character of Rocket in Marvel New Media/SiriusXM's radio drama podcast series Marvel's Wastelanders: Star-Lord, appearing alongside Timothy Busfield, Patrick Page, Vanessa Williams and Danny Glover.

Author
Elliott has written four books spoofing history or pseudo-history. Daddy's Boy: A Son's Shocking Account of Life with a Famous Father is a comedic fictionalized biography about growing up with his famous father, spoofing Christina Crawford's Mommie Dearest. The Shroud of the Thwacker is a historical novel about Elliott's investigation of a serial killer in 1882 New York City, spoofing London's infamous Jack the Ripper case. Into Hot Air tells the story of Chris climbing Mount Everest with a group of celebrities tagging along to underwrite the trek as he investigates his Uncle Percy's failed Everest expedition. And The Guy Under The Sheets is an "unauthorized autobiography" that tells a comedically fictional version of Elliott's life in which Elliott "reveals" that he is the son not of comedian Bob Elliott, but, rather, of playwright Sam Elliot and actress Bette Davis.

Personal life
Elliott has been married to Paula Niedert since 1986. Niedert worked as a talent coordinator on Late Night with David Letterman when they met. They have two daughters: Abby and Bridey. Abby was a cast member of Saturday Night Live from 2008 until 2012, making her the first SNL cast member to be the child of a previous cast member. His father Bob Elliott, of the popular comedy duo Bob & Ray, co-starred on an SNL Christmas episode in the 1978–1979 (fourth) season, making for three generations of Elliotts on SNL.

Primetime Emmy Awards

 * 1984 Outstanding Writing in a Variety, Comedy or Music Program for Late Night with David Letterman
 * 1985 Outstanding Writing in a Variety, Comedy or Music Program for Late Night with David Letterman
 * 1986 Outstanding Writing in a Variety, Comedy or Music Program for Late Night with David Letterman
 * 1987 Outstanding Writing in a Variety, Comedy or Music Program for Late Night with David Letterman

Canadian Screen Awards

 * 2016 Best Performance by an Actor in a Featured Supporting Role or Guest Role in a Comedic Series for Schitt's Creek

Screen Actors Guild Awards

 * 2020 Outstanding Performance by an Ensemble in a Comedy Series for Schitt's Creek

title: Chris Elliott