Condorcet methods
123-408: Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results A single-member district or constituency is an electoral district represented by
246-501: A 'cycle'. This situation emerges when, once all votes have been tallied, the preferences of voters with respect to some candidates form a circle in which every candidate is beaten by at least one other candidate ( Intransitivity ). For example, if there are three candidates, Candidate Rock, Candidate Scissors, and Candidate Paper , there will be no Condorcet winner if voters prefer Candidate Rock over Candidate Scissors and Scissors over Paper, but also Candidate Paper over Rock. Depending on
369-400: A 68% majority of 1st choices among the remaining candidates and won as the majority's 1st choice. As noted above, sometimes an election has no Condorcet winner because there is no candidate who is preferred by voters to all other candidates. When this occurs the situation is known as a 'Condorcet cycle', 'majority rule cycle', 'circular ambiguity', 'circular tie', 'Condorcet paradox', or simply
492-602: A broader nationalist message. His election accelerated the Republican Party's shift towards right-wing populism and resulted in decreasing influence among its conservative factions. After the 2016 elections , Republicans maintained their majority in the Senate , the House , and governorships , and wielded newly acquired executive power with Trump's election. The Republican Party controlled 69 of 99 state legislative chambers in 2017,
615-542: A candidate because they are endorsed by a particular political party or because they are in favor of who would become or remain the leader of the government, more than their feelings for or against the actual candidate standing. Sometimes voters are in favor of a political party but do not like specific candidates. For example, voters in Canada re-elected the Alberta government in 1989 but, because of dissatisfaction with its leadership,
738-534: A contest between candidates A, B and C using the preferential-vote form of Condorcet method, a head-to-head race is conducted between each pair of candidates. A and B, B and C, and C and A. If one candidate is preferred over all others, they are the Condorcet Winner and winner of the election. Because of the possibility of the Condorcet paradox , it is possible, but unlikely, that a Condorcet winner may not exist in
861-544: A large majority of the Democratic Party's upper and middle-class support. McKinley defeated Bryan and returned the presidency to Republican control until the 1912 presidential election . The 1896 realignment cemented the Republicans as the party of big businesses while president Theodore Roosevelt added more small business support by his embrace of trust busting . He handpicked his successor William Howard Taft in
984-418: A number of Republicans and conservative thought leaders questioning whether Trump should continue as the party's main figurehead and leader. Despite this, Trump easily won the nomination to be the party's candidate again in the 2024 presidential election . Trump achieved a decisive victory against Democratic nominee Kamala Harris , winning every swing state and the popular vote, while the Republicans held
1107-504: A plurality or majority of voters, depending on the electoral system, support a particular candidate or party so strongly that the candidate's election is practically guaranteed in advance of the vote. This means votes for other candidates effectively make no difference to the result. This results in feelings of disenfranchisement, as well as increased nonparticipation , by both supporters of the dominant candidate (who can confidently abstain from voting because their preferred candidate's victory
1230-530: A reduction of the national debt and federal budget deficit through decreased government spending . The Tea Party movement was also described as a popular constitutional movement composed of a mixture of libertarian , right-wing populist , and conservative activism. The Tea Party movement's electoral success began with Scott Brown 's upset win in the January Senate special election in Massachusetts ;
1353-532: A result of a kind of tie known as a majority rule cycle , described by Condorcet's paradox . The manner in which a winner is then chosen varies from one Condorcet method to another. Some Condorcet methods involve the basic procedure described below, coupled with a Condorcet completion method, which is used to find a winner when there is no Condorcet winner. Other Condorcet methods involve an entirely different system of counting, but are classified as Condorcet methods, or Condorcet consistent, because they will still elect
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#17330860632301476-612: A single officeholder. It contrasts with a multi-member district , which is represented by multiple officeholders. In some countries, such as Australia and India , members of the lower house of parliament are elected from single-member districts, while members of the upper house are elected from multi-member districts. In some other countries, such as Singapore , members of parliament can be elected from either single-member or multi-member districts. The United States Constitution , ratified in 1789, states: "The House of Representatives shall be composed of Members chosen every second Year by
1599-523: A specific election. This is sometimes called a Condorcet cycle or just cycle and can be thought of as Rock beating Scissors, Scissors beating Paper, and Paper beating Rock . Various Condorcet methods differ in how they resolve such a cycle. (Most elections do not have cycles. See Condorcet paradox#Likelihood of the paradox for estimates.) If there is no cycle, all Condorcet methods elect the same candidate and are operationally equivalent. For most Condorcet methods, those counts usually suffice to determine
1722-462: A stronger connection between the representative and constituents and increases accountability and is a check on incompetence and corruption. In countries that have multi-member constituencies, it is argued that the constituency link is lost. For example, in Israel the whole country is a single constituency and representatives are selected by party-lists. On the other hand, today most voters tend to vote for
1845-520: A treaty annexing Hawaii before Cleveland could be inaugurated. Most Republicans supported the proposed annexation, but Cleveland opposed it. In the 1896 presidential election , Republican William McKinley 's platform supported the gold standard and high tariffs, having been the creator and namesake for the McKinley Tariff of 1890. Though having been divided on the issue prior to that year's National Convention , McKinley decided to heavily favor
1968-427: A voter's choice within any given pair can be determined from the ranking. Some elections may not yield a Condorcet winner because voter preferences may be cyclic—that is, it is possible that every candidate has an opponent that defeats them in a two-candidate contest. The possibility of such cyclic preferences is known as the Condorcet paradox . However, a smallest group of candidates that beat all candidates not in
2091-547: A winner at the end of election day. Voter suppression in the South gave Republican-controlled returning officers enough of a reason to declare that fraud, intimidation and violence had soiled the states' results. They proceeded to throw out enough Democratic votes for Republican Rutherford B. Hayes to be declared the winner. Democrats refused to accept the results and the Electoral Commission made up of members of Congress
2214-407: Is also a Condorcet method, even though the voters do not vote by expressing their orders of preference. There are multiple rounds of voting, and in each round the vote is between two of the alternatives. The loser (by majority rule) of a pairing is eliminated, and the winner of a pairing survives to be paired in a later round against another alternative. Eventually, only one alternative remains, and it
2337-494: Is also referred to collectively as Condorcet's method. A voting system that always elects the Condorcet winner when there is one is described by electoral scientists as a system that satisfies the Condorcet criterion. Additionally, a voting system can be considered to have Condorcet consistency, or be Condorcet consistent, if it elects any Condorcet winner. In certain circumstances, an election has no Condorcet winner. This occurs as
2460-411: Is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner , is formally called the Condorcet winner or Pairwise Majority Rule Winner (PMRW). The head-to-head elections need not be done separately;
2583-412: Is an election between four candidates: A, B, C, and D. The first matrix below records the preferences expressed on a single ballot paper, in which the voter's preferences are (B, C, A, D); that is, the voter ranked B first, C second, A third, and D fourth. In the matrix a '1' indicates that the runner is preferred over the 'opponent', while a '0' indicates that the runner is defeated. Using a matrix like
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#17330860632302706-401: Is holding an election on the location of its capital . The population is concentrated around four major cities. All voters want the capital to be as close to them as possible. The options are: The preferences of each region's voters are: To find the Condorcet winner every candidate must be matched against every other candidate in a series of imaginary one-on-one contests. In each pairing
2829-513: Is known as ambiguity resolution, cycle resolution method, or Condorcet completion method . Circular ambiguities arise as a result of the voting paradox —the result of an election can be intransitive (forming a cycle) even though all individual voters expressed a transitive preference. In a Condorcet election it is impossible for the preferences of a single voter to be cyclical, because a voter must rank all candidates in order, from top-choice to bottom-choice, and can only rank each candidate once, but
2952-438: Is nearly assured) as well as supporters of other candidates (who know their preferred candidate is essentially guaranteed to lose). Single-member districts enable gerrymandering, the practice of manipulating district boundaries to favor one political party. Whereas proportional multi-member districts ensure that political parties are represented roughly in proportion to the share of the vote they receive, in single-member districts
3075-440: Is no preference between candidates that were left unranked. Some Condorcet elections permit write-in candidates . The count is conducted by pitting every candidate against every other candidate in a series of hypothetical one-on-one contests. The winner of each pairing is the candidate preferred by a majority of voters. Unless they tie, there is always a majority when there are only two choices. The candidate preferred by each voter
3198-510: Is taken to be the one in the pair that the voter ranks (or rates) higher on their ballot paper. For example, if Alice is paired against Bob it is necessary to count both the number of voters who have ranked Alice higher than Bob, and the number who have ranked Bob higher than Alice. If Alice is preferred by more voters then she is the winner of that pairing. When all possible pairings of candidates have been considered, if one candidate beats every other candidate in these contests then they are declared
3321-404: Is the winner. This is analogous to a single-winner or round-robin tournament; the total number of pairings is one less than the number of alternatives. Since a Condorcet winner will win by majority rule in each of its pairings, it will never be eliminated by Robert's Rules. But this method cannot reveal a voting paradox in which there is no Condorcet winner and a majority prefer an early loser over
3444-475: The 1980 United States presidential election . The Reagan presidency , lasting from 1981 to 1989, constituted what is known as " the Reagan Revolution ". It was seen as a fundamental shift from the stagflation of the 1970s, with the introduction of Reagan's economic policies intended to cut taxes, prioritize government deregulation and shift funding from the domestic sphere into the military to check
3567-490: The 2014 United States House of Representatives elections , the Republican Party won 51.2% of the popular vote but 56.7% of the seats. Supporters view this effect as beneficial, claiming that two-party systems are more stable, and that the minority opposition does not have undue power to break a coalition. First-past-the-post minimizes the influence of third parties and thus arguably keeps out forms of opposition outside of
3690-847: The 2018 Wisconsin State Assembly election , for example, the Republican Party won 45% of the popular vote but 64% of the seats, due in part to gerrymandering). Contrary to conventional wisdom, a 2023 study found that single-member district systems do not have more geographically representative parliaments than systems with multi-member districts. Condorcet method Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results A Condorcet method ( English: / k ɒ n d ɔːr ˈ s eɪ / ; French: [kɔ̃dɔʁsɛ] )
3813-466: The 2022 elections confident and with analysts predicting a red wave , but it ultimately underperformed expectations, with voters in swing states and competitive districts joining Democrats in rejecting candidates who had been endorsed by Trump or who had denied the results of the 2020 election. The party won control of the House with a narrow majority, but lost the Senate and several state legislative majorities and governorships. The results led to
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3936-534: The Coinage Act of 1873 , as a solution to the depressed American economy in the aftermath of that year's panic . Ahead of the 1880 presidential election , both James G. Blaine and opponent John Sherman failed to win the Republican nomination; each then backed James A. Garfield for president. Garfield won the 1880 presidential election, but was assassinated early in his term . His death helped create support for
4059-619: The Court of International Trade by the time he left office, shifting the court system to the right . Other notable achievements during his presidency included the passing of the Tax Cuts and Jobs Act in 2017; the creation of the U.S. Space Force , the first new independent military service since 1947; and the brokering of the Abraham Accords , a series of normalization agreements between Israel and various Arab states . The second half of his term
4182-534: The Iraq War . In the 2008 presidential election , Arizona Republican senator John McCain was defeated by Illinois Democratic senator Barack Obama . The Republicans experienced electoral success in the 2010 elections . The 2010 elections coincided with the ascendancy of the Tea Party movement , an anti-Obama protest movement of fiscal conservatives . Members of the movement called for lower taxes , and for
4305-635: The Kansas–Nebraska Act , which repealed the Missouri Compromise and opened the Kansas and Nebraska Territories to slavery and future admission as slave states. They denounced the expansion of slavery as a great evil, but did not call for complete abolition , including in the Southern states. While opposition to the expansion of slavery was the most consequential founding principle of the party, like
4428-475: The Marquis de Condorcet , who championed such systems. However, Ramon Llull devised the earliest known Condorcet method in 1299. It was equivalent to Copeland's method in cases with no pairwise ties. Condorcet methods may use preferential ranked , rated vote ballots, or explicit votes between all pairs of candidates. Most Condorcet methods employ a single round of preferential voting, in which each voter ranks
4551-523: The Pendleton Civil Service Reform Act , which was passed in 1883; the bill was signed into law by Republican president Chester A. Arthur , who succeeded Garfield. In 1884, Blaine won the Republican presidential nomination, but lost the general election to Democrat Grover Cleveland . Cleveland was the first Democrat to be elected president since James Buchanan. Dissident Republicans, known as Mugwumps , had defected from Blaine due to
4674-461: The Pew Research Center found that social conservatives and free market advocates remained the other two main groups within the party's coalition of support, with all three being roughly equal in number. However, libertarians and libertarian-leaning conservatives increasingly found fault with what they saw as Republicans' restricting of vital civil liberties while corporate welfare and
4797-563: The Second New Deal , saying it represented class warfare and socialism . Roosevelt was easily re-elected president in 1936 ; however, as his second term began, the economy declined , strikes soared, and he failed to take control of the Supreme Court and purge the Southern conservatives from the Democratic Party. Republicans made a major comeback in the 1938 House elections . Southern conservatives joined with most Republicans to form
4920-799: The Soviet Union by utilizing deterrence theory . During a visit to then- West Berlin in June 1987, he addressed Soviet leader Mikhail Gorbachev during a speech at the Berlin Wall , demanding that he " Tear down this wall! ". The remark was later seen as influential in the fall of the wall in 1989, and was retroactively seen as a defining achievement. The Soviet Union was dissolved in 1991 . Following Reagan's presidency, Republican presidential candidates frequently claimed to share Reagan's views and aimed to portray themselves and their policies as heirs to his legacy. Reagan's vice president, George H. W. Bush , won
5043-546: The Thirteenth Amendment to the U.S. Constitution —which banned slavery, except as punishment for a crime—was ratified in 1865. Following the assassination of Lincoln , Johnson ascended to the presidency. Johnson was vitriolic in his criticisms of the Radical Republicans during a national tour ahead of the 1866 elections . Anti-Johnson Republicans won a two-thirds majority in both chambers of Congress following
Single-member district - Misplaced Pages Continue
5166-597: The Uniform Congressional District Act ( 2 U.S. Code §2c ), under the justification that they served as bulwarks against southern Democrats diluting the electoral power of African Americans by using strategically drawn at-large multi-member districts. For instance, Southern Democrats could create a single statewide multi-member district elected by plurality vote, all but guaranteeing the white majority would elect only Democrats. It has been argued by proponents of single-member constituencies that it encourages
5289-619: The World Trade Organization . Bush lost his re-election bid in 1992 . While there is debate about whether Perot's candidacy cost Bush re-election, Charlie Cook asserted that Perot's messaging carried weight with Republican and conservative voters. In the 1994 elections , the Republican Party, led by House minority whip Newt Gingrich , who campaigned on the " Contract with America ", won majorities in both chambers of Congress, gained 12 governorships, and regained control of 20 state legislatures . The Republican Party won control of
5412-504: The conservative coalition , which dominated domestic issues in Congress until 1964. By the time of World War II , both parties split on foreign policy issues, with the anti-war isolationists dominant in the Republican Party and the interventionists dominant in the Democratic Party. Roosevelt won a third term in 1940 and a fourth in 1944 . Conservatives abolished most of the New Deal during
5535-589: The large-scale corruption present in the Grant administration , with the emerging Stalwart faction defending Grant and the spoils system , and the Half-Breeds advocating reform of the civil service . Republicans who opposed Grant branched off to form the Liberal Republican Party , nominating Horace Greeley in the 1872 presidential election . The Democratic Party attempted to capitalize on this divide in
5658-515: The 1908 election , but they became enemies as the party split down the middle. Taft defeated Roosevelt for the 1912 nomination . Roosevelt ran on the ticket of his new Progressive Party . He called for social reforms , many of which were later championed by New Deal Democrats in the 1930s. He lost and when most of his supporters returned to the GOP, they found they did not agree with the new conservative economic thinking , leading to an ideological shift to
5781-540: The Condorcet winner if there is one. Not all single winner, ranked voting systems are Condorcet methods. For example, instant-runoff voting and the Borda count are not Condorcet methods. In a Condorcet election the voter ranks the list of candidates in order of preference. If a ranked ballot is used, the voter gives a "1" to their first preference, a "2" to their second preference, and so on. Some Condorcet methods allow voters to rank more than one candidate equally so that
5904-460: The Condorcet winner. As noted above, if there is no Condorcet winner a further method must be used to find the winner of the election, and this mechanism varies from one Condorcet consistent method to another. In any Condorcet method that passes Independence of Smith-dominated alternatives , it can sometimes help to identify the Smith set from the head-to-head matchups, and eliminate all candidates not in
6027-546: The Copeland winner has the highest possible Copeland score. They can also be found by conducting a series of pairwise comparisons, using the procedure given in Robert's Rules of Order described above. For N candidates, this requires N − 1 pairwise hypothetical elections. For example, with 5 candidates there are 4 pairwise comparisons to be made, since after each comparison, a candidate is eliminated, and after 4 eliminations, only one of
6150-529: The Democrats, whom they saw as the party of bloated, secular, and liberal government. This period saw the rise of "pro-government conservatives"—a core part of the Bush's base—a considerable group of the Republicans who advocated for increased government spending and greater regulations covering both the economy and people's personal lives, as well as for an activist and interventionist foreign policy. Survey groups such as
6273-556: The GOP and he proved unable to shift the party to a more moderate position. Historians cite the 1964 presidential election and its respective National Convention as a significant shift, which saw the conservative wing, helmed by Arizona senator Barry Goldwater , battle liberal New York governor Nelson Rockefeller and his eponymous Rockefeller Republican faction for the nomination. With Goldwater poised to win, Rockefeller, urged to mobilize his liberal faction, retorted, "You're looking at it, buddy. I'm all that's left." Following
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#17330860632306396-406: The GOP by co-nominating Greeley under their party banner. Greeley's positions proved inconsistent with the Liberal Republican Party that nominated him, with Greeley supporting high tariffs despite the party's opposition. Grant was easily re-elected. The 1876 presidential election saw a contentious conclusion as both parties claimed victory despite three southern states not officially declaring
6519-579: The GOP cooperated with Truman's Cold War foreign policy, funded the Marshall Plan and supported NATO , despite the continued isolationism of the Old Right. Eisenhower had defeated conservative leader senator Robert A. Taft for the 1952 Republican presidential nomination , but conservatives dominated the domestic policies of the Eisenhower administration . Voters liked Eisenhower much more than they liked
6642-520: The House and retook control of the Senate, thus delivering a Republican trifecta . Trump significantly improved his vote share among almost all demographics nationwide, particularly among Hispanic voters, in a working class coalition described as the most racially diverse for a Republican presidential candidate in decades. As of 2024, the GOP holds a majority in the U.S. House of Representatives . It also holds 27 state governorships , 28 state legislatures , and 23 state government trifectas . Six of
6765-499: The House of Representatives for the first time in 40 years , and won a majority of U.S. House seats in the South for the first time since Reconstruction. However, most voters had not heard of the Contract and the Republican victory was attributed to traditional mid-term anti-incumbent voting and Republicans becoming the majority party in the South for the first time since Reconstruction, winning many former Southern Democrats . Gingrich
6888-587: The People of the several States...Representatives...shall be apportioned among the several States which may be included within this Union, according to their respective Numbers." In other words, the Constitution specifies that each state will be apportioned a number of representatives in the House of Representatives proportional to its population. It does not, however, specify how those representatives should be apportioned. In
7011-522: The Republican House's legislative agenda if he were to serve as speaker. Illinois representative Dennis Hastert was promoted to speaker in Livingston's place, serving in that position until 2007. Republican George W. Bush won the 2000 and 2004 presidential elections . He campaigned as a " compassionate conservative " in 2000, wanting to better appeal to immigrants and minority voters. The goal
7134-421: The Republican Party lost seven seats in the House , but still retained control of that chamber. However, Republicans were unable to gain control of the Senate , continuing their minority status with a net loss of two seats. In the aftermath of the loss, some prominent Republicans spoke out against their own party. A 2012 election post-mortem by the Republican Party concluded that the party needed to do more on
7257-618: The Republican Party had greatly shifted towards illiberalism following the election of Trump, and research conducted by the V-Dem Institute concluded that the party was more similar to Europe's most right-wing parties such as Law and Justice in Poland or Fidesz in Hungary. In 2022 and 2023, Supreme Court justices appointed by Trump proved decisive in landmark decisions on gun rights , abortion , and affirmative action . The party went into
7380-401: The Republican Party's first National Convention in 1856 , the party adopted a national platform emphasizing opposition to the expansion of slavery into the free territories. Although Republican nominee John C. Frémont lost that year's presidential election to Democrat James Buchanan , Buchanan managed to win only four of the fourteen northern states. Despite the loss of the presidency and
7503-855: The Republican banner. Since 2009, the party has faced significant factionalism within its own ranks and has shifted towards right-wing populism . In the 21st century, the Republican Party receives its strongest support from rural voters , evangelical Christians , men , senior citizens , and voters without college degrees . On economic issues, the party has maintained a pro-business attitude since its inception. It supports low taxes and deregulation while opposing socialism , labor unions and single-payer healthcare . The populist faction supports economic protectionism , including tariffs . On social issues, it advocates for restricting abortion , discouraging and often prohibiting recreational drug use , promoting gun ownership and easing gun restrictions , and opposing transgender rights . In foreign policy,
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#17330860632307626-497: The Republicans lost five seats, though whether it was due to poor messaging or Clinton's popularity providing a coattail effect is debated. Gingrich was ousted from party power due to the performance, ultimately deciding to resign from Congress altogether. For a short time afterward, it appeared Louisiana representative Bob Livingston would become his successor; Livingston, however, stepped down from consideration and resigned from Congress after damaging reports of affairs threatened
7749-494: The Republicans struck a deal with Clinton on the Balanced Budget Act of 1997 , which included tax cuts, the Republican House majority had difficulty convening on a new agenda ahead of the 1998 elections . During the ongoing impeachment of Bill Clinton in 1998, Gingrich decided to make Clinton's misconduct the party message heading into the elections, believing it would add to their majority. The strategy proved mistaken and
7872-635: The Schulze method, use the information contained in the sum matrix to choose a winner. Cells marked '—' in the matrices above have a numerical value of '0', but a dash is used since candidates are never preferred to themselves. The first matrix, that represents a single ballot, is inversely symmetric: (runner, opponent) is ¬(opponent, runner). Or (runner, opponent) + (opponent, runner) = 1. The sum matrix has this property: (runner, opponent) + (opponent, runner) = N for N voters, if all runners were fully ranked by each voter. [REDACTED] Suppose that Tennessee
7995-495: The Senate on June 6, 2001, when Vermont Republican senator Jim Jeffords switched his party affiliation to Democrat. The Republicans regained the Senate majority in the 2002 elections , helped by Bush's surge in popularity following the September 11 attacks , and Republican majorities in the House and Senate were held until the Democrats regained control of both chambers in the 2006 elections , largely due to increasing opposition to
8118-464: The Senate voted to acquit him. Trump lost the 2020 presidential election to Democrat Joe Biden . He refused to concede the race, claiming widespread electoral fraud and attempting to overturn the results . On January 6, 2021, the United States Capitol was attacked by Trump supporters following a rally at which Trump spoke. After the attack, the House impeached Trump for a second time on
8241-408: The Senate. Over the course of his presidency, Trump appointed three justices to the Supreme Court : Neil Gorsuch , Brett Kavanaugh , and Amy Coney Barrett . It was the most Supreme Court appointments for any president in a single term since Richard Nixon . Trump appointed 260 judges in total, creating overall Republican-appointed majorities on every branch of the federal judiciary except for
8364-592: The Whig Party it replaced, Republicans also called for economic and social modernization . At the first public meeting of the anti-Nebraska movement on March 20, 1854, at the Little White Schoolhouse in Ripon, Wisconsin , the name "Republican" was proposed as the name of the party. The name was partly chosen to pay homage to Thomas Jefferson 's Democratic-Republican Party . The first official party convention
8487-411: The basis for defining preference and determined that Memphis voters preferred Chattanooga as a second choice rather than as a third choice, Chattanooga would be the Condorcet winner even though finishing in last place in a first-past-the-post election. An alternative way of thinking about this example if a Smith-efficient Condorcet method that passes ISDA is used to determine the winner is that 58% of
8610-601: The candidates from most (marked as number 1) to least preferred (marked with a higher number). A voter's ranking is often called their order of preference. Votes can be tallied in many ways to find a winner. All Condorcet methods will elect the Condorcet winner if there is one. If there is no Condorcet winner different Condorcet-compliant methods may elect different winners in the case of a cycle—Condorcet methods differ on which other criteria they satisfy. The procedure given in Robert's Rules of Order for voting on motions and amendments
8733-579: The charge of incitement of insurrection , making him the only federal officeholder to be impeached twice. Trump left office on January 20, 2021. His impeachment trial continued into the early weeks of the Biden presidency , and he was acquitted on February 13, 2021 . Since the 2020 election, election denial has become increasingly mainstream in the party, with the majority of 2022 Republican candidates being election deniers. The party also made efforts to restrict voting based on false claims of fraud. By 2020,
8856-496: The complete order of finish (i.e. who won, who came in 2nd place, etc.). They always suffice to determine whether there is a Condorcet winner. Additional information may be needed in the event of ties. Ties can be pairings that have no majority, or they can be majorities that are the same size. Such ties will be rare when there are many voters. Some Condorcet methods may have other kinds of ties. For example, with Copeland's method , it would not be rare for two or more candidates to win
8979-424: The context in which elections are held, circular ambiguities may or may not be common, but there is no known case of a governmental election with ranked-choice voting in which a circular ambiguity is evident from the record of ranked ballots. Nonetheless a cycle is always possible, and so every Condorcet method should be capable of determining a winner when this contingency occurs. A mechanism for resolving an ambiguity
9102-612: The corruption which had plagued his political career. Republican Benjamin Harrison defeated Cleveland in the 1888 election . During his presidency, Harrison signed the Dependent and Disability Pension Act , which established pensions for all veterans of the Union who had served for more than 90 days and were unable to perform manual labor. Following his loss to Cleveland in the 1892 presidential election , Harrison unsuccessfully attempted to pass
9225-544: The decade produced an unprecedented prosperity until the Wall Street Crash of 1929 heralded the Great Depression. The New Deal coalition forged by Democratic president Franklin D. Roosevelt controlled American politics for most of the next three decades, excluding the presidency of Republican Dwight D. Eisenhower in the 1950s. After Roosevelt took office in 1933, New Deal legislation sailed through Congress and
9348-400: The dominant rival party. Critics of two-party systems believe that two-party systems offer less choice to voters, create an exaggerated emphasis on issues that dominate more marginal seats, and does not completely remove the possibility of a balanced chamber (or hung parliament ), which can also give undue power to independents and lead to more, not less, stability. A safe seat is one in which
9471-574: The early years of the United States, a form of multi-member districts called plural districts were the norm. In contrast with modern proportional multi-member districts (which had not yet been invented), plural districts were elected at-large in plurality votes. By 1842, single-member House districts had become the norm, with twenty-two states using single-member districts and only six using at-large multi-member districts. On 14 December 1967, single-member House districts were mandated by law pursuant to
9594-518: The economy moved sharply upward from its nadir in early 1933. The 1934 elections left the GOP with only 25 senators against 71 Democrats. The House likewise had overwhelming Democratic majorities. The Republican Party factionalized into a majority Old Right , based predominantly in the Midwest , and a liberal wing based in the Northeast that supported much of the New Deal. The Old Right sharply attacked
9717-417: The elections, which helped lead the way toward his impeachment and near ouster from office in 1868, the same year Ulysses S. Grant was elected as the next Republican president . Grant was a Radical Republican, which created some division within the party. Massachusetts senator Charles Sumner and Illinois senator Lyman Trumbull opposed most of his Reconstructionist policies. Others took issue with
9840-400: The entire district is represented by a single politician, even if a sizeable minority (or even a majority, in the case of plurality voting) of the electorate votes for candidates from other parties. This enables political parties to rig elections in their favor by drawing districts in such a way that more districts are won by their party than their proportion of the overall vote would dictate (in
9963-474: The eventual winner (though it will always elect someone in the Smith set ). A considerable portion of the literature on social choice theory is about the properties of this method since it is widely used and is used by important organizations (legislatures, councils, committees, etc.). It is not practical for use in public elections, however, since its multiple rounds of voting would be very expensive for voters, for candidates, and for governments to administer. In
10086-470: The following sum matrix: When the sum matrix is found, the contest between each pair of candidates is considered. The number of votes for runner over opponent (runner, opponent) is compared with the number of votes for opponent over runner (opponent, runner) to find the Condorcet winner. In the sum matrix above, A is the Condorcet winner because A beats every other candidate. When there is no Condorcet winner Condorcet completion methods, such as Ranked Pairs and
10209-511: The gold standard over free silver in his campaign messaging, but promised to continue bimetallism to ward off continued skepticism over the gold standard, which had lingered since the Panic of 1893 . Democrat William Jennings Bryan proved to be a devoted adherent to the free silver movement, which cost Bryan the support of Democratic institutions such as Tammany Hall , the New York World and
10332-450: The group, known as the Smith set , always exists. The Smith set is guaranteed to have the Condorcet winner in it should one exist. Many Condorcet methods elect a candidate who is in the Smith set absent a Condorcet winner, and is thus said to be "Smith-efficient". Condorcet voting methods are named for the 18th-century French mathematician and philosopher Marie Jean Antoine Nicolas Caritat,
10455-479: The lack of a majority in the U.S. Congress , Republicans were able to orchestrate a Republican speaker of the House of Representatives , which went to Nathaniel P. Banks . Historian James M. McPherson writes regarding Banks' speakership that "if any one moment marked the birth of the Republican party, this was it." The Republicans were eager for the 1860 elections . Former Illinois U.S. representative Abraham Lincoln spent several years building support within
10578-631: The leadership of Lincoln and a Republican Congress, the Republican Party led the fight to defeat the Confederate States in the American Civil War , thereby preserving the Union and abolishing slavery . After the war, the party largely dominated national politics until the Great Depression in the 1930s, when it lost its congressional majorities and the Democrats' New Deal programs proved popular. Dwight D. Eisenhower 's election in 1952
10701-419: The most it had held in history. The Party also held 33 governorships, the most it had held since 1922. The party had total control of government in 25 states; it had not held total control of this many states since 1952. The opposing Democratic Party held full control of only five states in 2017. In the 2018 elections , Republicans lost control of the House of Representatives, but strengthened their hold on
10824-467: The national debt hiked considerably under Bush's tenure. In contrast, some social conservatives expressed dissatisfaction with the party's support for economic policies that conflicted with their moral values. The Republican Party lost its Senate majority in 2001 when the Senate became split evenly; nevertheless, the Republicans maintained control of the Senate due to the tie-breaking vote of Bush's vice president, Dick Cheney . Democrats gained control of
10947-406: The national level to attract votes from minorities and young voters. In March 2013, Republican National Committee chairman Reince Priebus issued a report on the party's electoral failures in 2012, calling on Republicans to reinvent themselves and officially endorse immigration reform. He proposed 219 reforms, including a $ 10 million marketing campaign to reach women, minorities, and gay people;
11070-422: The nine current U.S. Supreme Court justices were appointed by Republican presidents. Its most recent presidential nominee is Donald Trump , who served as the 45th president of the United States and was the party's candidate again in the 2024 presidential election . There have been 19 Republican presidents, the most from any one political party. The Republican Party's founding members chose its name as homage to
11193-425: The one above, one can find the overall results of an election. Each ballot can be transformed into this style of matrix, and then added to all other ballot matrices using matrix addition . The sum of all ballots in an election is called the sum matrix. Suppose that in the imaginary election there are two other voters. Their preferences are (D, A, C, B) and (A, C, B, D). Added to the first voter, these ballots would give
11316-419: The original 5 candidates will remain. To confirm that a Condorcet winner exists in a given election, first do the Robert's Rules of Order procedure, declare the final remaining candidate the procedure's winner, and then do at most an additional N − 2 pairwise comparisons between the procedure's winner and any candidates they have not been compared against yet (including all previously eliminated candidates). If
11439-447: The paradox of voting means that it is still possible for a circular ambiguity in voter tallies to emerge. Republican Party (United States) The Republican Party , also known as the GOP ( Grand Old Party ), is one of the two major contemporary political parties in the United States . It emerged as the main political rival of the then-dominant Democratic Party in the 1850s, and
11562-539: The party establishment is interventionist, while the populist faction supports isolationism and in some cases non-interventionism . In 1854, the Republican Party was founded in the Northern United States by forces opposed to the expansion of slavery , ex- Whigs , and ex- Free Soilers . The Republican Party quickly became the principal opposition to the dominant Democratic Party and the briefly popular Know Nothing Party. The party grew out of opposition to
11685-615: The party, campaigning heavily for Frémont in 1856 and making a bid for the Senate in 1858 , losing to Democrat Stephen A. Douglas but gaining national attention from the Lincoln–Douglas debates it produced. At the 1860 Republican National Convention , Lincoln consolidated support among opponents of New York U.S. senator William H. Seward , a fierce abolitionist who some Republicans feared would be too radical for crucial states such as Pennsylvania and Indiana , as well as those who disapproved of his support for Irish immigrants. Lincoln
11808-676: The passage of the Civil Rights Act of 1964 and Voting Rights Act of 1965 , the southern states became more reliably Republican in presidential politics, while northeastern states became more reliably Democratic. The GOP went on to control the White House from 1969 to 1977 under 37th president Richard Nixon , and when he resigned in 1974 due to the Watergate scandal , Gerald Ford became the 38th president, serving until 1977. Ronald Reagan defeated incumbent Democratic President Jimmy Carter in
11931-425: The premier and leader of the governing party, Don Getty , lost his seat. It has been argued that single-member districts tend to promote two-party systems (with some regional parties). Called Duverger's law , this principle has also been empirically supported by the cube rule , which shows how the winning party in a first-past-the-post system is mathematically over-represented in the legislature. For example, in
12054-487: The presidency in a landslide in the 1988 election . However, his term was characterized by division within the Republican Party. Bush's vision of economic liberalization and international cooperation with foreign nations saw the negotiation and, during the presidency of Democrat Bill Clinton in the 1990s, the signing of the North American Free Trade Agreement (NAFTA) and the conceptual beginnings of
12177-426: The procedure's winner does not win all pairwise matchups, then no Condorcet winner exists in the election (and thus the Smith set has multiple candidates in it). Computing all pairwise comparisons requires ½ N ( N −1) pairwise comparisons for N candidates. For 10 candidates, this means 0.5*10*9=45 comparisons, which can make elections with many candidates hard to count the votes for. The family of Condorcet methods
12300-482: The right in the Republican Party. The Republicans returned to the presidency in the 1920s, winning on platforms of normalcy , business-oriented efficiency, and high tariffs. The national party platform avoided mention of prohibition, instead issuing a vague commitment to law and order . Warren G. Harding died in 1923 and Calvin Coolidge easily defeated the splintered opposition in 1924. The pro-business policies of
12423-469: The same number of pairings, when there is no Condorcet winner. A Condorcet method is a voting system that will always elect the Condorcet winner (if there is one); this is the candidate whom voters prefer to each other candidate, when compared to them one at a time. This candidate can be found (if they exist; see next paragraph) by checking if there is a candidate who beats all other candidates; this can be done by using Copeland's method and then checking if
12546-464: The seat had been held for decades by Democrat Ted Kennedy . In November, Republicans recaptured control of the House , increased their number of seats in the Senate , and gained a majority of governorships . The Tea Party would go on to strongly influence the Republican Party, in part due to the replacement of establishment Republicans with Tea Party-style Republicans. When Obama was re-elected president in 2012 , defeating Republican Mitt Romney ,
12669-426: The set before doing the procedure for that Condorcet method. Condorcet methods use pairwise counting. For each possible pair of candidates, one pairwise count indicates how many voters prefer one of the paired candidates over the other candidate, and another pairwise count indicates how many voters have the opposite preference. The counts for all possible pairs of candidates summarize all the pairwise preferences of all
12792-519: The setting of a shorter, more controlled primary season; and the creation of better data collection facilities. Following the 2014 elections , the Republican Party took control of the Senate by gaining nine seats. With 247 seats in the House and 54 seats in the Senate, the Republicans ultimately achieved their largest majority in the Congress since the 71st Congress in 1929. In the 2016 presidential election , Republican nominee Donald Trump defeated Democratic nominee Hillary Clinton . The result
12915-417: The two parties have dominated American politics since then. The Republican Party was founded in 1854 by anti-slavery activists who opposed the Kansas–Nebraska Act , which allowed for the potential extension of slavery to the western territories. The party supported classical liberalism and economic reform geared to industry, supporting investments in manufacturing, railroads, and banking. The party
13038-477: The values of republicanism promoted by Democratic-Republican Party, which its founder, Thomas Jefferson, called the "Republican Party". The idea for the name came from an editorial by the party's leading publicist, Horace Greeley, who called for "some simple name like 'Republican' [that] would more fitly designate those who had united to restore the Union to its true mission of champion and promulgator of Liberty rather than propagandist of slavery". The name reflects
13161-482: The voter might express two first preferences rather than just one. If a scored ballot is used, voters rate or score the candidates on a scale, for example as is used in Score voting , with a higher rating indicating a greater preference. When a voter does not give a full list of preferences, it is typically assumed that they prefer the candidates that they have ranked over all the candidates that were not ranked, and that there
13284-420: The voters, a mutual majority , ranked Memphis last (making Memphis the majority loser ) and Nashville, Chattanooga, and Knoxville above Memphis, ruling Memphis out. At that point, the voters who preferred Memphis as their 1st choice could only help to choose a winner among Nashville, Chattanooga, and Knoxville, and because they all preferred Nashville as their 1st choice among those three, Nashville would have had
13407-448: The voters. Pairwise counts are often displayed in a pairwise comparison matrix , or outranking matrix , such as those below. In these matrices , each row represents each candidate as a 'runner', while each column represents each candidate as an 'opponent'. The cells at the intersection of rows and columns each show the result of a particular pairwise comparison. Cells comparing a candidate to themselves are left blank. Imagine there
13530-467: The war, but they did not attempt to do away with Social Security or the agencies that regulated business. Historian George H. Nash argues: Unlike the "moderate", internationalist, largely eastern bloc of Republicans who accepted (or at least acquiesced in) some of the "Roosevelt Revolution" and the essential premises of President Harry S. Truman 's foreign policy, the Republican Right at heart
13653-529: The winner is the candidate preferred by a majority of voters. When results for every possible pairing have been found they are as follows: The results can also be shown in the form of a matrix: ↓ 2 Wins ↓ 1 Win As can be seen from both of the tables above, Nashville beats every other candidate. This means that Nashville is the Condorcet winner. Nashville will thus win an election held under any possible Condorcet method. While any Condorcet method will elect Nashville as
13776-523: The winner, if instead an election based on the same votes were held using first-past-the-post or instant-runoff voting , these systems would select Memphis and Knoxville respectively. This would occur despite the fact that most people would have preferred Nashville to either of those "winners". Condorcet methods make these preferences obvious rather than ignoring or discarding them. On the other hand, in this example Chattanooga also defeats Knoxville and Memphis when paired against those cities. If we changed
13899-553: Was a rare break between Democratic presidents and he presided over a period of increased economic prosperity after World War II . Following the 1960s era of civil rights legislation, enacted by Democrats, the South became more reliably Republican, and Richard Nixon carried 49 states in the 1972 election , with what he touted as his " silent majority ". The 1980 election of Ronald Reagan realigned national politics, bringing together advocates of free-market economics, social conservatives , and Cold War foreign policy hawks under
14022-539: Was a zealous radical. Gingrich's strategy of " constitutional hardball " resulted in increasing political polarization . The Republicans maintained their majority for the first time since 1928 despite Bob Dole losing handily to Clinton in the presidential election . However, Gingrich's national profile proved a detriment to the Republican Congress, which enjoyed majority approval among voters in spite of Gingrich's relative unpopularity. After Gingrich and
14145-415: Was counterrevolutionary. Anti-collectivist, anti-Communist , anti-New Deal, passionately committed to limited government , free market economics , and congressional (as opposed to executive) prerogatives, the G.O.P. conservatives were obliged from the start to wage a constant two-front war: against liberal Democrats from without and "me-too" Republicans from within. After 1945, the internationalist wing of
14268-506: Was elected president in the general election . This election result helped kickstart the American Civil War , which lasted from 1861 until 1865. The 1864 presidential election united War Democrats with the GOP in support of Lincoln and Tennessee Democratic senator Andrew Johnson , who ran for president and vice president on the National Union Party ticket; Lincoln was re-elected. Under Republican congressional leadership,
14391-576: Was established to decide who would be awarded the states' electors. After the Commission voted along party lines in Hayes' favor, Democrats threatened to delay the counting of electoral votes indefinitely so no president would be inaugurated on March 4. This resulted in the Compromise of 1877 and Hayes finally became president. Hayes doubled down on the gold standard , which had been signed into law by Grant with
14514-524: Was held on July 6, 1854, in Jackson, Michigan . The party emerged from the great political realignment of the mid-1850s, united in pro-capitalist stances with members often valuing Radicalism . The realignment was powerful because it forced voters to switch parties, as typified by the rise and fall of the Know Nothing Party , the rise of the Republican Party and the splits in the Democratic Party. At
14637-471: Was increasingly controversial, as he implemented a family separation policy for migrants , deployed federal law enforcement forces in response to racial protests and reacted slowly to the COVID-19 pandemic before clashing with health officials over testing and treatment. Trump was impeached by the House of Representatives in 2019 on charges of abuse of power and obstruction of Congress. On February 5, 2020,
14760-399: Was made speaker, and within the first 100 days of the Republican majority, every proposition featured in the Contract was passed, with the exception of term limits for members of Congress. One key to Gingrich's success in 1994 was nationalizing the election, which in turn led to his becoming a national figure during the 1996 House elections , with many Democratic leaders proclaiming Gingrich
14883-456: Was successful in the North, and by 1858, it had enlisted most former Whigs and former Free Soilers to form majorities in almost every northern state. White Southerners of the planter class became alarmed at the threat to the future of slavery in the United States. With the 1860 election of Abraham Lincoln , the first Republican president, the Southern states seceded from the United States. Under
15006-454: Was to prioritize drug rehabilitation programs and aid for prisoner reentry into society, a move intended to capitalize on President Clinton's tougher crime initiatives such as his administration's 1994 crime bill . The platform failed to gain much traction among members of the party during his presidency. The Republican Party remained fairly cohesive for much of the 2000s, as both strong economic libertarians and social conservatives opposed
15129-538: Was unexpected; polls leading up to the election showed Clinton leading the race. Trump's victory was fueled by narrow victories in three states— Michigan , Pennsylvania , and Wisconsin —that had been part of the Democratic blue wall for decades. It was attributed to strong support amongst working-class white voters, who felt dismissed and disrespected by the political establishment. Trump became popular with them by abandoning Republican establishment orthodoxy in favor of
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