Condorcet methods
75-464: 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 The D'Hondt method , also called the Jefferson method or the greatest divisors method ,
150-462: A p , {\displaystyle \delta ^{*}=\min _{\mathbf {s} \in {\mathcal {S}}}\max _{p}a_{p},} where s = { s 1 , … , s P } {\displaystyle \mathbf {s} =\{s_{1},\dots ,s_{P}\}} is a seat allocation from the set of all allowed seat allocations S {\displaystyle {\mathcal {S}}} . Thanks to this, as shown by Juraj Medzihorsky,
225-501: 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
300-400: 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
375-534: 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
450-469: A fellowship at the Institute for Healthcare Improvement . Pagel was appointed as director of UCL's Clinical Operational Research Unit (CORU) in 2017. Her research uses approaches from mathematical modelling, operational research and data sciences to help people within the health service make better decisions. She focuses on mortality and morbidity outcomes following cardiac surgery in children and adults in
525-442: A more equal seats-to-votes ratio for different sized parties. The axiomatic properties of the D'Hondt method were studied and they proved that the D'Hondt method is a consistent and monotone method that reduces political fragmentation by encouraging coalitions. A method is consistent if it treats parties that received tied votes equally. Monotonicity means that the number of seats provided to any state or party will not decrease if
600-458: A number so that there is no need to examine the remainders. Any number in one range of quotas will accomplish this, with the highest number in the range always being the same as the lowest number used by the D'Hondt method to award a seat (if it is used rather than the Jefferson method), and the lowest number in the range being the smallest number larger than the next number which would award a seat in
675-544: A party wins one-third of the votes then it should gain about one-third of the seats. In general, exact proportionality is not possible because these divisions produce fractional numbers of seats. As a result, several methods, of which the D'Hondt method is one, have been devised which ensure that the parties' seat allocations, which are of whole numbers, are as proportional as possible. Although all of these methods approximate proportionality, they do so by minimizing different kinds of disproportionality. The D'Hondt method minimizes
750-532: 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
825-523: 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
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#1732848669893900-427: 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
975-483: Is active in school and university outreach , encouraging participation in mathematics and science subjects. Her work in developing the children's heart surgery website formed the basis of a national guide for researchers on how to involve the public and was separately featured in a Health Foundation guide on engagement. She also contributed to the Sense about Science guide "Making Sense of Statistics". In 2023, she
1050-407: 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
1125-494: 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
1200-429: Is an apportionment method for allocating seats in parliaments among federal states , or in proportional representation among political parties. It belongs to the class of highest-averages methods . Compared to ideal proportional representation, the D'Hondt method reduces somewhat the political fragmentation for smaller electoral district sizes, where it favors larger political parties over small parties. The method
1275-411: 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;
1350-412: 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
1425-401: 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
1500-513: 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
1575-427: Is necessary to divide these numbers by a common divisor, producing quotients whose sum is equal to the number of entities to be allocated. The system can be used both for distributing seats in a legislature among states pursuant to populations or among parties pursuant to an election result. The tasks are mathematically equivalent, putting states in the place of parties and population in place of votes. In some countries,
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#17328486698931650-440: 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
1725-471: Is shown in the table below. The Jefferson and the D'Hondt methods are equivalent. They always give the same results, but the methods of presenting the calculation are different. The method was first described in 1792 by Statesman and future US President Thomas Jefferson , in a letter to George Washington regarding the apportionment of seats in the United States House of Representatives pursuant to
1800-510: 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
1875-404: 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
1950-480: The First United States Census : For representatives there can be no such common ratio, or divisor which ... will divide them exactly without a remainder or fraction. I answer then ... that representatives [must be divided] as nearly as the nearest ratio will admit; and the fractions must be neglected. Washington had exercised his first veto power on a bill that introduced a new plan for dividing seats in
2025-475: 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
2100-540: 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
2175-460: 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
2250-546: 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
2325-639: The D'Hondt calculations. Applied to the above example of party lists, this range extends as integers from 20,001 to 25,000. More precisely, any number n for which 20,000 < n ≤ 25,000 can be used. 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] )
D'Hondt method - Misplaced Pages Continue
2400-819: The D'Hondt method splits the votes into exactly proportionally represented ones and residual ones. The overall fraction of residual votes is π ∗ = 1 − 1 δ ∗ . {\displaystyle \pi ^{*}=1-{\frac {1}{\delta ^{*}}}.} The residuals of party p are r p = v p − ( 1 − π ∗ ) s p , r p ∈ [ 0 , v p ] , ∑ p r p = π ∗ . {\displaystyle r_{p}=v_{p}-(1-\pi ^{*})s_{p},\;r_{p}\in [0,v_{p}],\sum _{p}\,r_{p}=\pi ^{*}.} For illustration, continue with
2475-821: The House of Representatives that would have increased the number of seats for northern states. Ten days after the veto, Congress passed a new method of apportionment, now known as Jefferson's Method. It was used to achieve the proportional distribution of seats in the House of Representatives among the states until 1842. It was also invented independently in 1878 in Europe, by Belgian mathematician Victor D'Hondt , who wrote in his publication Système pratique et raisonné de représentation proportionnelle , published in Brussels in 1882: To allocate discrete entities proportionally among several numbers, it
2550-518: The Jefferson system is known by the names of local politicians or experts who introduced them locally. For example, it is known in Israel as the Bader–Ofer system . Jefferson's method uses a quota (called a divisor), as in the largest remainder method . The divisor is chosen as necessary so that the resulting quotients, disregarding any fractional remainders , sum to the required total; in other words, pick
2625-583: The National Congenital Heart Disease Audit since 2013 to publish hospital survival rates, and the associated software, developed by Pagel, has been purchased by all UK hospitals performing children's heart surgery. She then led a multidisciplinary project working with the Children's Heart Federation, Sense about Science and Sir David Spiegelhalter to build a website on survival after children's heart surgery, launched in 2016. Pagel
2700-635: 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
2775-858: The UCL Clinical Operational Research Unit applying mathematics to problems in health care. In 2016, Pagel was awarded a Harkness Fellowship in Health Care Policy and Practice by the Commonwealth Fund , through which Pagel spent 2016–2017 in the USA researching (a) the priorities of Republican and Democrat politicians for the goals of national health policy working with the Milbank Memorial Fund and (b) how clinical decision support systems can be better implemented within intensive care settings. During that year, she also completed
2850-680: The UK Operational Research Society . She was appointed as Vice President of the UK Operational Research Society for a three-year period from January 2022 to December 2024 and delivered the prestigious annual Blackett Lecture in December 2022. In 2023 she was named as the Mathematics Section President for the annual British Science Festival. Presidents are considered leaders in their fields. She
2925-565: The UK Government during the COVID-19 pandemic . As part of her work for Independent SAGE, she is regularly quoted in several newspapers, writes for national newspapers and appeared on national and international broadcast media (e.g. ITV News , Sky News , Channel 4 News , and BBC Newsnight , India NDTV ) and various podcasts discussing the UK's response to the pandemic. In 2019, Pagel
3000-553: The UK, leading and contributing to several large national projects; understanding the course of a child's stay in paediatric intensive care; mathematical methods to support service delivery within hospitals. In her role since 2020 at UCL's CHIMERA centre (Collaborative Healthcare Innovation through Mathematics, EngineeRing and AI), Pagel co-leads a multidisciplinary team which analyses anonymised data from intensive care patients at University College Hospital and Great Ormond Street Hospital . Using tools including machine learning ,
3075-420: The above example of four parties. The advantage ratios of the four parties are 1.2 for A, 1.1 for B, 1 for C, and 0 for D. The reciprocal of the largest advantage ratio is 1/1.15 = 0.87 = 1 − π . The residuals as shares of the total vote are 0% for A, 2.2% for B, 2.2% for C, and 8.7% for party D. Their sum is 13%, i.e., 1 − 0.87 = 0.13 . The decomposition of the votes into represented and residual ones
D'Hondt method - Misplaced Pages Continue
3150-604: The advantage ratio is a p = s p v p , {\displaystyle a_{p}={\frac {s_{p}}{v_{p}}},} where The largest advantage ratio, δ = max p a p , {\displaystyle \delta =\max _{p}a_{p},} captures how over-represented is the most over-represented party. The D'Hondt method assigns seats so that this ratio attains its smallest possible value, δ ∗ = min s ∈ S max p
3225-411: 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
3300-452: The calculation. Each party's vote is divided by 1, 2, 3, or 4 in consecutive columns, then the 8 highest values resulting are selected. The quantity of highest values in each row is the number of seats won. For comparison, the "True proportion" column shows the exact fractional numbers of seats due, calculated in proportion to the number of votes received. (For example, 100,000/230,000 × 8 = 3.48) The slight favouring of
3375-601: 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
3450-533: The centre aims to improve understanding of the physiology of patients during illness and recovery, in order to improve their care. Pagel was instrumental in developing a statistical model to take into account the complexity of individual children with congenital heart disease , when considering a hospital's survival rate. This led to the Partial Risk Adjustment in Surgery (PRAiS) model, which has been used by
3525-496: 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
3600-424: 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
3675-468: The corresponding party gets a seat. Note that in Round 1, the quotient shown in the table, as derived from the formula, is precisely the number of votes returned in the ballot. While in this example, parties B, C, and D formed a coalition against Party A. You can see that Party A received 3 seats instead of 4 due to the coalition having 30,000 more votes than Party A. The chart below shows an easy way to perform
3750-423: The electoral district is divided, first by 1, then by 2, then 3, up to the total number of seats to be allocated for the district/constituency. Say there are p parties and s seats. Then a grid of numbers can be created, with p rows and s columns, where the entry in the i th row and j th column is the number of votes won by the i th party, divided by j . The s winning entries are the s highest numbers in
3825-474: 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
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#17328486698933900-470: 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
3975-450: 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,
4050-472: The house size increases. After all the votes have been tallied, successive quotients are calculated for each party. The party with the largest quotient wins one seat, and its quotient is recalculated. This is repeated until the required number of seats is filled. The formula for the quotient is quot = V s + 1 {\displaystyle {\text{quot}}={\frac {V}{s+1}}} where: The total votes cast for each party in
4125-477: The largest seats-to-votes ratio among all parties. This ratio is also known as the advantage ratio. In contrast, the average seats-to-votes ratio is optimized by the Webster/Sainte-Laguë method . For party p ∈ { 1 , … , P } {\displaystyle p\in \{1,\dots ,P\}} , where P {\displaystyle P} is the overall number of parties,
4200-468: The largest party over the smallest is apparent. A worked-through example for non-experts relating to the 2019 elections in the UK for the European Parliament written by Christina Pagel for UK in a Changing Europe is available. A more mathematically detailed example has been written by British mathematician Professor Helen Wilson . The D'Hondt method approximates proportionality by minimizing
4275-489: The largest seats-to-votes ratio. Empirical studies based on other, more popular concepts of disproportionality show that the D'Hondt method is one of the least proportional among the proportional representation methods. The D'Hondt favours large parties and coalitions over small parties due to strategic voting . In comparison, the Sainte-Laguë method reduces the disproportional bias towards large parties and it generally has
4350-425: 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
4425-419: 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
4500-519: The paradox of voting means that it is still possible for a circular ambiguity in voter tallies to emerge. Christina Pagel Christina Pagel ( / ˈ p ɑː ɡ ə l / PAH -gəl ) is a German-British mathematician and professor of operational research at University College London (UCL) within UCL's Clinical Operational Research Unit (CORU), which applies operational research, data analysis and mathematical modelling to topics in healthcare. She
4575-426: 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
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#17328486698934650-469: 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
4725-426: 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
4800-482: 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
4875-420: 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
4950-448: 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
5025-617: The whole grid; each party is given as many seats as there are winning entries in its row. Alternatively, the procedure can be reversed by starting with a house apportionment that assigns "too many seats" to every party, then removing legislators one at a time from the most-overrepresented party. In this example, 230,000 voters decide the disposition of 8 seats among 4 parties. Since 8 seats are to be allocated, each party's total votes are divided by 1, then by 2, 3, and 4 (and then, if necessary, by 5, 6, 7, and so on). The 8 highest entries (in bold text) range from 100,000 down to 25,000 . For each,
5100-529: 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
5175-523: 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
5250-777: Was Director of UCL CORU from 2017 to 2022 and is currently Vice President of the UK Operational Research Society . She also co-leads, alongside Rebecca Shipley , UCL's CHIMERA research hub which analyses data from critically ill hospital patients. Pagel graduated with a BA in mathematics from The Queen's College, Oxford in 1996. She also holds an MSc in Mathematical Physics from King's College London , and MAs in Classical Civilisation, Medieval History and an MSc in Applied Statistics with Medical Applications from Birkbeck College , University of London. In 2002 Pagel
5325-557: Was awarded a PhD in Space Physics on Turbulence in the interplanetary magnetic field from Imperial College London . Pagel's early career was spent in Boston , Massachusetts, studying the scattering of electrons in interplanetary space using data from the ACE spacecraft at Boston University with Professor Nancy Crooker . In 2005 she left physics, returning to London to take up a position with
5400-600: Was awarded the Lyn Thomas Impact Medal from the Operational Research Society , along with her colleagues Sonya Crowe and Martin Utley. The award was made for their work related to congenital heart disease and recognised the "significant impact on the lives of children with congenital heart disease, as well on their families and the growing population of adults with the condition". In September 2021, Pagel
5475-477: Was first described in 1792 by American Secretary of State and later President of the United States Thomas Jefferson . It was re-invented independently in 1878 by Belgian mathematician Victor D'Hondt , which is the reason for its two different names. Proportional representation systems aim to allocate seats to parties approximately in proportion to the number of votes received. For example, if
5550-565: Was one of two recipients (alongside Devi Sridhar ) of a special recognition award from The BMJ , and in October 2021 she won a HealthWatch UK award, both for her work in public engagement in science during the COVID-19 pandemic. She was a Turing Fellow of the Alan Turing Institute by special appointment from 2021 to 2022. In November 2021, she was awarded the "Companion of OR" prize by
5625-470: Was the Mathematics Section President for the annual British Science Festival. Pagel uses tools from her research to design and analyse political data from public polls, particularly in the context of Brexit and health policy, and she is known as a regular podcast contributor on both themes. In May 2020, Pagel joined the Independent SAGE committee, whose aim is to offer independent advice to
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