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The Theil index is a statistic primarily used to measure economic inequality and other economic phenomena, though it has also been used to measure racial segregation. The Theil index T T is the same as redundancy in information theory which is the maximum possible entropy of the data minus the observed entropy. It is a special case of the generalized entropy index . It can be viewed as a measure of redundancy, lack of diversity, isolation, segregation, inequality, non-randomness, and compressibility. It was proposed by a Dutch econometrician Henri Theil (1924–2000) at the Erasmus University Rotterdam .

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79-470: Henri Theil himself said (1967): "The (Theil) index can be interpreted as the expected information content of the indirect message which transforms the population shares as prior probabilities into the income shares as posterior probabilities." Amartya Sen noted, "But the fact remains that the Theil index is an arbitrary formula, and the average of the logarithms of the reciprocals of income shares weighted by income

158-556: A fellow of Trinity College, Cambridge . Between 1960 and 1961, Sen was a visiting professor at Massachusetts Institute of Technology in the United States, where he got to know Paul Samuelson , Robert Solow , Franco Modigliani , and Norbert Wiener . He was also a visiting professor at the University of California, Berkeley (1964–1965) and Cornell University (1978–1984). He taught as Professor of Economics between 1963 and 1971 at

237-405: A normative measure by imposing a coefficient ε {\displaystyle \varepsilon } to weight incomes. Greater weight can be placed on changes in a given portion of the income distribution by choosing ε {\displaystyle \varepsilon } , the level of "inequality aversion", appropriately. The Atkinson index becomes more sensitive to changes at

316-446: A book called The Idea of Justice . Based on his previous work in welfare economics and social choice theory, but also on his philosophical thoughts, Sen presented his own theory of justice that he meant to be an alternative to the influential modern theories of justice of John Rawls or John Harsanyi . In opposition to Rawls but also earlier justice theoreticians Immanuel Kant , Jean-Jacques Rousseau or David Hume , and inspired by

395-404: A country is due to within-group inequality, and the remaining quarter to between-group differences." If the population is divided into m {\displaystyle m} subgroups and then Theil's T index is For example, inequality within the United States is the average inequality within each state, weighted by state income, plus the inequality between states. The decomposition of

474-553: A daughter Indrani, who is a journalist in New York, and a son Kabir, a hip hop artist, MC, and music teacher at Shady Hill School . Eva died of cancer in 1985. In 1991, Sen married Emma Georgina Rothschild , who serves as the Jeremy and Jane Knowles Professor of History at Harvard University. The Sens have a house in Cambridge , Massachusetts , which is the base from which they teach during

553-496: A democratic norm in the world – where India was the first non-Western country to go for democracy – that we lose that reputation on the grounds of action that have been taken". He regarded the detention of Kashmiri political leaders as "a classical colonial excuse" to prevent backlash against the Indian government's decision and called for a democratic solution that would involve Kashmiri people. Sen has spent much of his later life as

632-479: A developing country, the Dobb-Sen strategy relied on maximising investible surpluses, maintaining constant real wages and using the entire increase in labour productivity, due to technological change, to raise the rate of accumulation. In other words, workers were expected to demand no improvement in their standard of living despite having become more productive. Sen's papers in the late 1960s and early 1970s helped develop

711-530: A functioning democracy". In addition to his important work on the causes of famines, Sen's work in the field of development economics has had considerable influence in the formulation of the " Human Development Report ", published by the United Nations Development Programme . This annual publication that ranks countries on a variety of economic and social indicators owes much to the contributions by Sen among other social choice theorists in

790-468: A political writer and activist. He has been outspoken about Narendra Modi's leadership in India. In an interview with The New York Times , he claimed that Modi's fearmongering among the Indian people was anti-democratic. "The big thing that we know from John Stuart Mill is that democracy is government by discussion, and, if you make discussion fearful, you are not going to get a democracy, no matter how you count

869-630: A professor of economics and fellow of Nuffield College , and then from 1980 the Drummond Professor of Political Economy and a fellow of All Souls College, Oxford . In 1985, Sen co-founded the Eva Colorni Trust at the former London Guildhall University in memory of his deceased wife. In 1987, Sen joined Harvard as the Thomas W. Lamont University Professor of Economics. In 1998 he was appointed as Master of Trinity College, Cambridge , becoming

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948-580: A second BA in economics in 1955 with a first class, topping the list as well. At this time, he was elected President of the Cambridge Majlis . While Sen was officially a PhD student at Cambridge (though he had finished his research in 1955–56), he was offered the position of First-Professor and First-Head of the Economics Department of the newly created Jadavpur University in Calcutta . Appointed to

1027-399: Is a measure of the redundancy of income (or other measure of wealth) in some individuals. Redundancy in some individuals implies scarcity in others. A high Theil index indicates the total income is not distributed evenly among individuals in the same way an uncompressed text file does not have a similar number of byte locations assigned to the available unique byte characters. According to

1106-458: Is an atheist . In an interview, he noted: In some ways people had got used to the idea that India was spiritual and religion-oriented. That gave a leg up to the religious interpretation of India, despite the fact that Sanskrit had a larger atheistic literature than exists in any other classical language . Madhava Acharya , the remarkable 14th century philosopher, wrote this rather great book called Sarvadarshansamgraha , which discussed all

1185-603: Is an Indian economist and philosopher. Sen has taught and worked in England and the United States since 1972. In 1998, Sen received the Nobel Memorial Prize in Economic Sciences for his contributions to welfare economics . He has also made major scholarly contributions to social choice theory , economic and social justice , economic theories of famines , decision theory , development economics , public health , and

1264-545: Is available here Archived 20 December 2016 at the Wayback Machine Atkinson index The Atkinson index (also known as the Atkinson measure or Atkinson inequality measure ) is a measure of income inequality developed by British economist Anthony Barnes Atkinson . The measure is useful in determining which end of the distribution contributed most to the observed inequality. The index can be turned into

1343-504: Is defined in reference to a corresponding social welfare function, where mean income multiplied by one minus the Atkinson index gives the welfare equivalent equally distributed income . Thus the Atkinson index gives the share of current income which could be sacrificed, without reducing social welfare, if perfect inequality were instated. For ε = 0 {\displaystyle \varepsilon =0} , (no aversion to inequality),

1422-440: Is distributed) is from the highest possible entropy ( S max = ln ⁡ ( N ) {\displaystyle S_{\text{max}}=\ln \left({N}\right)} , which represents income being maximally distributed amongst individuals in the population– a distribution analogous to the [most likely] outcome of an infinite number of random coin tosses: an equal distribution of heads and tails). Therefore,

1501-472: Is equal to the ratio of a particular individual's income to the total income of the entire population. This gives the observed entropy S Theil {\displaystyle S_{\text{Theil}}} of a population to be: The Theil index T T {\displaystyle T_{T}} measures how far the observed entropy ( S Theil {\displaystyle S_{\text{Theil}}} , which represents how randomly income

1580-403: Is further away from the complete equality. Formulating the index to represent negative entropy instead of entropy allows it to be a measure of inequality rather than equality. The Theil index can be transformed into an Atkinson index , which has a range between 0 and 1 (0% and 100%), where 0 indicates perfect equality and 1 (100%) indicates maximum inequality. (See Generalized entropy index for

1659-504: Is known to be one of the greatest Indian economists in the field of international trade and currently teaches at Columbia University ). This is a period considered to be a Golden Period in the history of the DSE. In 1971, he joined the London School of Economics as a professor of economics, and taught there until 1977. From 1977 to 1988, he taught at the University of Oxford , where he was first

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1738-479: Is more intuitive to many people since it is based on the Lorenz curve . However, it is not easily decomposable like the Theil. In addition to multitude of economic applications, the Theil index has been applied to assess performance of irrigation systems and distribution of software metrics . Amartya Sen Amartya Kumar Sen ( Bengali pronunciation: [ˈɔmortːo ˈʃen] ; born 3 November 1933)

1817-399: Is not a measure that is exactly overflowing with intuitive sense." For a population of N "agents" each with characteristic x , the situation may be represented by the list x i ( i  = 1,..., N ) where x i is the characteristic of agent i . For example, if the characteristic is income, then x i is the income of agent i . The Theil T index is defined as and

1896-417: Is the fraction of the population with income k and W = Nμ is the total income, then ∑ k = 0 W f k = 1 {\displaystyle \sum _{k=0}^{W}f_{k}=1} and the Theil index is: where μ {\displaystyle \mu } is again the mean income: Note that in this case income k is an integer and k=1 represents

1975-430: Is violated: T [ x ∪ x ] ≠ T [ x ] {\displaystyle T[x\cup x]\neq T[x]} and does not qualify as a measure of inequality. The Theil index measures an entropic "distance" the population is away from the egalitarian state of everyone having the same income. The numerical result is in terms of negative entropy so that a higher number indicates more order that

2054-585: The Delhi School of Economics (where he completed his magnum opus , Collective Choice and Social Welfare , in 1969). During this time Sen was also a frequent visitor to various other premiere Indian economic schools and centres of excellence, such as Jawaharlal Nehru University , the Indian Statistical Institute , the Centre for Development Studies , Gokhale Institute of Politics and Economics , and

2133-911: The Indian Economic Association (1989) and the American Economic Association (1994). He has also served as president of the Development Studies Association and the Human Development and Capability Association . He serves as the honorary director of the Academic Advisory Committee of the Center for Human and Economic Development Studies at Peking University in China. Sen has been called "the Conscience of

2212-523: The World Bank , "The best-known entropy measures are Theil’s T ( T T {\displaystyle T_{T}} ) and Theil’s L ( T L {\displaystyle T_{L}} ), both of which allow one to decompose inequality into the part that is due to inequality within areas (e.g. urban, rural) and the part that is due to differences between areas (e.g. the rural-urban income gap). Typically at least three-quarters of inequality in

2291-634: The 2020 Peace Prize of the German Book Trade for his pioneering scholarship addressing issues of global justice and combating social inequality in education and healthcare. Amartya Sen was born on 3 November 1933 in a Bengali family in Santiniketan , Bengal, British India. The first Asian to win a Nobel Prize, the polymath and writer Rabindranath Tagore , gave Amartya Sen his name ( Bengali : অমর্ত্য , romanized :  ômorto , lit.   ' immortal or heavenly ' ). Sen's family

2370-404: The Atkinson index will tend to be one or very close to one for very large ε {\displaystyle \varepsilon } . The Atkinson index then varies between 0 and 1 and is a measure of the amount of social utility to be gained by complete redistribution of a given income distribution, for a given ε {\displaystyle \varepsilon } parameter. Under

2449-549: The Centre for Studies in Social Sciences. He was a companion of distinguished economists like Manmohan Singh (ex-Prime Minister of India and a veteran economist responsible for liberalising the Indian economy), K. N. Raj (advisor to various prime ministers and a veteran economist who was the founder of the Centre for Development Studies, Trivandrum, which is one of India's premier think tanks and schools), and Jagdish Bhagwati (who

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2528-415: The Theil L index is defined as where μ {\displaystyle \mu } is the mean income: Theil-L is an income-distribution's dis-entropy per person, measured with respect to maximum entropy (...which is achieved with complete equality). (In an alternative interpretation of it, Theil-L is the natural-logarithm of the geometric-mean of the ratio: (mean income)/(income i), over all

2607-458: The Theil index is the difference between the theoretical maximum entropy (which would be reached if the incomes of every individual were equal) minus the observed entropy: When x {\displaystyle x} is in units of population/species, S Theil {\displaystyle S_{\text{Theil}}} is a measure of biodiversity and is called the Shannon index . If

2686-405: The Theil index is used with x=population/species, it is a measure of inequality of population among a set of species, or "bio-isolation" as opposed to "wealth isolation". The Theil index measures what is called redundancy in information theory. It is the left over "information space" that was not utilized to convey information, which reduces the effectiveness of the price signal . The Theil index

2765-413: The Theil index which identifies the share attributable to the between-region component becomes a helpful tool for the positive analysis of regional inequality as it suggests the relative importance of spatial dimension of inequality. Both Theil's T and Theil's L are decomposable. The difference between them is based on the part of the outcomes distribution that each is used for. Indexes of inequality in

2844-414: The ability of the people to have a voice in government and to be able to scrutinise the authorities. Economic facilities concern both the resources within the market and the market mechanism itself. Any focus on income and wealth in the country would serve to increase the economic facilities for the people. Social opportunities deal with the establishments that provide benefits like healthcare or education for

2923-562: The academic year. They also have a home in Cambridge, England, where Sen is a Fellow of Trinity College, Cambridge, and Rothschild is a Fellow of Magdalene College . He usually spends his winter holidays at his home in Shantiniketan in West Bengal , India, where he used to go on long bike rides until recently. Asked how he relaxes, he replies: "I read a lot and like arguing with people." Sen

3002-902: The anti-gay Section 377 of the Indian Penal Code . Sen has served as Honorary Chairman of Oxfam, the UK based international development charity, and is now its Honorary Advisor. Sen is also a member of the Berggruen Institute 's 21st Century Council. Sen is an Honorary Fellow of St Edmund's College, Cambridge . He is also one of the 25 leading figures on the Information and Democracy Commission launched by Reporters Without Borders . A 56-minute documentary named Amartya Sen: A Life Re-examined directed by Suman Ghosh details his life and work. A documentary about Amartya Sen, titled The Argumentative Indian (the title of one of Sen's own books ),

3081-402: The area of economic measurement of poverty and inequality. Sen's revolutionary contribution to development economics and social indicators is the concept of " capability " developed in his article "Equality of What?". He argues that governments should be measured against the concrete capabilities of their citizens. This is because top-down development will always trump human rights as long as

3160-624: The books he was most interested in was Kenneth Arrow 's Social Choice and Individual Values . In Cambridge, there were major debates between supporters of Keynesian economics , and the neo-classical economists who were sceptical of Keynes. Because of a lack of enthusiasm for social choice theory in both Trinity and Cambridge, Sen chose a different subject for his PhD thesis, which was on " The Choice of Techniques " in 1959. The work had been completed earlier, except for advice from his adjunct supervisor in India, A. K. Dasgupta , given to Sen while teaching and revising his work at Jadavpur, under

3239-562: The chancellor post of Nalanda University , stating that the Government of India was not keen on him continuing in the post. In August 2019, during the clampdown and curfew in Kashmir for more than two weeks after the Indian revocation of Jammu and Kashmir's special status , Sen criticised the government and said "As an Indian, I am not proud of the fact that India, after having done so much to achieve

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3318-442: The common restriction that ε {\displaystyle \varepsilon } is nonnegative. The Atkinson ε {\displaystyle \varepsilon } parameter is often called the "inequality aversion parameter", since it regulates the sensitivity of the implied social welfare losses from inequality to income inequality as measured by some corresponding generalised entropy index. The Atkinson index

3397-540: The concept of Asian values , meaningless and disingenuous. Before Sen's work, these had been viewed as only the ends of development; luxuries afforded to countries that focus on increasing income. However, Sen argued that the increase in real freedoms should be both the ends and the means of development. He elaborates upon this by illustrating the closely interconnected natures of the five main freedoms as he believes that expansion of one of those freedoms can lead to expansion in another one as well. In this regard, he discussed

3476-529: The correlation between social opportunities of education and health and how both of these complement economic and political freedoms as a healthy and well-educated person is better suited to make informed economic decisions and be involved in fruitful political demonstrations, etc. A comparison is also drawn between China and India to illustrate this interdependence of freedoms. Sen noted that both countries had been working towards developing their economies—China since 1979 and India since 1991. In 2009, Sen published

3555-420: The definition of terms remains in doubt (is a "right" something that must be provided or something that simply cannot be taken away?). For instance, in the United States citizens have a right to vote. To Sen, this concept is fairly empty. In order for citizens to have a capacity to vote, they first must have "functionings". These "functionings" can range from the very broad, such as the availability of education, to

3634-661: The expense of development. Rather than create an entirely new theory for ethical development in Asia, Sen sought to reform the current development model. Sen has been married three times. His first wife was Nabaneeta Dev Sen , an Indian writer and scholar, with whom he had two daughters: Antara , a journalist and publisher, and Nandana , a Bollywood actress. Their marriage broke up shortly after they moved to London in 1971. In 1978 Sen married Eva Colorni , an Italian economist, daughter of Eugenio Colorni and Ursula Hirschmann and niece of Albert O. Hirschman . The couple had two children,

3713-565: The first Asian head of an Oxbridge college. In January 2004, Sen returned to Harvard. In May 2007, he was appointed chairman of Nalanda Mentor Group to plan the establishment of Nalanda University . The university was intended to be a revival of Nalanda mahavihara , an ancient educational centre. He chaired the Social Sciences jury for the Infosys Prize from 2009 to 2011, and the Humanities jury from 2012 to 2018. On 19 July 2012, Sen

3792-466: The generalized entropy (GE) family are more sensitive to differences in income shares among the poor or among the rich depending on a parameter that defines the GE index. The smaller the parameter value for GE, the more sensitive it is to differences at the bottom of the distribution. The decomposability is a property of the Theil index which the more popular Gini coefficient does not offer. The Gini coefficient

3871-556: The importance of public discussion (understanding democracy in the sense of John Stuart Mill ) and a focus on people's capabilities (an approach that he had co-developed), including the notion of universal human rights, in evaluating various states with regard to justice. Sen began his career both as a teacher and a research scholar in the Department of Economics, Jadavpur University as a professor of economics in 1956. He spent two years in that position. From 1957 to 1963, Sen served as

3950-475: The incomes. The related Atkinson(1) is just 1 minus the geometric-mean of (income i)/(mean income), over the income distribution.) Because a transfer between a larger income & a smaller one will change the smaller income's ratio more than it changes the larger income's ratio, the transfer-principle is satisfied by this index. Equivalently, if the situation is characterized by a discrete distribution function f k ( k  = 0,..., W ) where f k

4029-496: The lower end of the income distribution as ε {\displaystyle \varepsilon } increases. Conversely, as the level of inequality aversion falls (that is, as ε {\displaystyle \varepsilon } approaches 0) the Atkinson becomes less sensitive to changes in the lower end of the distribution. The Atkinson index is for no value of ε {\displaystyle \varepsilon } highly sensitive to top incomes because of

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4108-432: The marginal social welfare from income is invariant to income, i.e. marginal increases in income produce as much social welfare whether they go to a poor or rich individual. In this case, the welfare equivalent equally distributed income is equal to mean income, and the Atkinson index is zero. For ε = + ∞ {\displaystyle \varepsilon =+\infty } (infinite aversion to inequality)

4187-404: The marginal social welfare of income of the poorest individual is infinitely larger than any even slightly richer individual, and the Atkinson social welfare function is equal to the smallest income in the sample. In this case, the Atkinson index is equal to mean income minus the smallest income, divided by mean income. As in large typical income distributions incomes of zero or near zero are common,

4266-484: The measures of well-being of countries. Sen is currently the Thomas W. Lamont University Professor , and Professor of Economics and Philosophy at Harvard University . He previously served as Master of Trinity College at the University of Cambridge . In 1999, he received India's highest civilian honour, Bharat Ratna , for his contribution to welfare economics. The German Publishers and Booksellers Association awarded him

4345-428: The mortality impact of unequal rights between the genders in the developing world, particularly Asia. Other studies, including one by Emily Oster , had argued that this is an overestimation, though Oster has since then recanted her conclusions. In 1999, Sen further advanced and redefined the capability approach in his book Development as Freedom . Sen argued that development should be viewed as an effort to advance

4424-441: The philosophical works of Adam Smith and Mary Wollstonecraft , Sen developed a theory that is both comparative and realisations-oriented (instead of being transcendental and institutional). However, he still regards institutions and processes as being equally important. As an alternative to Rawls's veil of ignorance , Sen chose the thought experiment of an impartial spectator as the basis of his theory of justice. He also stressed

4503-445: The populace, allowing individuals to live better lives. Transparency guarantees allow individuals to interact with some degree of trust and knowledge of the interaction. Protective security is the system of social safety nets that prevent a group affected by poverty being subjected to terrible misery. Development encompassing non-economic areas, Sen argues, renders the notion of a dichotomy between "freedom" and "development," as implied by

4582-412: The position at age 22, he is still the youngest chairman to have headed the Department of Economics. He served in that position, starting the new Economics Department, from 1956 to 1958. Meanwhile, Sen was elected to a Prize Fellowship at Trinity College, which gave him four years to study any subject; he made the decision to study philosophy . Sen explained: "The broadening of my studies into philosophy

4661-463: The profession" and "the Mother Teresa of Economics" for his work on famine, human development theory , welfare economics , the underlying mechanisms of poverty, gender inequality , and political liberalism . However, he denies the comparison to Mother Teresa, saying that he has never tried to follow a lifestyle of dedicated self-sacrifice. Amartya Sen also added his voice to the campaign against

4740-546: The real freedoms that individuals enjoy, rather than simply focusing on metrics such as GDP or income-per-capita. Sen was inspired by violent acts he had witnessed as a child leading up to the Partition of India in 1947. On one morning, a Muslim daily labourer named Kader Mia stumbled through the rear gate of Sen's family home, bleeding from a knife wound in his back. Because of his extreme poverty, he had come to Sen's primarily Hindu neighbourhood searching for work; his choices were

4819-587: The religious schools of thought within the Hindu structure. The first chapter is "Atheism"—a very strong presentation of the argument in favor of atheism and materialism. Sen has received over 90 honorary degrees from universities around the world. In 2019, London School of Economics announced the creation of the Amartya Sen Chair in Inequality Studies. A list of Persian translations of Amartya Sen's work

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4898-523: The same education policies that Japan did in the late 19th century. However, he conceded that there is a tradeoff between democracy and progress in Asia because democracy is a near reality in India and not in China. In a 1999 article in The Atlantic , Sen recommended for India a middle path between the "hard-knocks" development policy that creates wealth at the expense of civil liberties, and radical progressivism that only seeks to protect civil liberties at

4977-632: The school stressed cultural diversity, and embraced cultural influences from the rest of the world. In 1951, he went to Presidency College, Calcutta , where he earned a BA in economics with First in the First Class, with a minor in Mathematics, as a graduating student of the University of Calcutta . While at Presidency, Sen was diagnosed with oral cancer, and given a 15 per cent chance of living five years. With radiation treatment, he survived, and in 1953 he moved to Trinity College, Cambridge , where he earned

5056-399: The smallest increment of income possible (e.g., cents). if the situation is characterized by a continuous distribution function f ( k ) (supported from 0 to infinity) where f ( k )  dk is the fraction of the population with income k to k  +  dk , then the Theil index is: where the mean is: Theil indices for some common continuous probability distributions are given in

5135-580: The starvation of his family or the risk of death in coming to the neighbourhood. The price of Kader Mia's economic unfreedom was his death. Kader Mia need not have come to a hostile area in search of income in those troubled times if his family could have managed without it. This experience led Sen to begin thinking about economic unfreedom from a young age. In Development as Freedom , Sen outlined five specific types of freedoms: political freedoms, economic facilities, social opportunities, transparency guarantees, and protective security. Political freedoms refer to

5214-524: The supervision of the "brilliant but vigorously intolerant" post-Keynesian Joan Robinson . Quentin Skinner notes that Sen was a member of the secret society Cambridge Apostles during his time at Cambridge. During 1960–61, Amartya Sen visited the Massachusetts Institute of Technology , on leave from Trinity College. Sen's work on 'Choice of Techniques' complemented that of Maurice Dobb . In

5293-417: The table below: If everyone has the same income, then T T equals 0. If one person has all the income, then T T gives the result ln ⁡ N {\displaystyle \ln N} , which is maximum inequality. Dividing T T by ln ⁡ N {\displaystyle \ln N} can normalize the equation to range from 0 to 1, but then the independence axiom

5372-551: The theory of social choice , which first came to prominence in the work by the American economist Kenneth Arrow . Arrow had most famously shown that when voters have three or more distinct alternatives (options), any ranked order voting system will in at least some situations inevitably conflict with what many assume to be basic democratic norms. Sen's contribution to the literature was to show under what conditions Arrow's impossibility theorem applied, as well as to extend and enrich

5451-647: The theory of social choice, informed by his interests in history of economic thought and philosophy. In 1981, Sen published Poverty and Famines: An Essay on Entitlement and Deprivation (1981), a book in which he argued that famine occurs not only from a lack of food, but from inequalities built into mechanisms for distributing food. Sen also argued that the Bengal famine was caused by an urban economic boom that raised food prices , thereby causing millions of rural workers to starve to death when their wages did not keep up. In 1999 he wrote, "no famine has ever taken place ... in

5530-419: The transformation.) The Theil index is derived from Shannon 's measure of information entropy S {\displaystyle S} , where entropy is a measure of randomness in a given set of information. In information theory, physics, and the Theil index, the general form of entropy is When looking at the distribution of income in a population, p i {\displaystyle p_{i}}

5609-483: The utilitarian ethical standard and some restrictive assumptions (a homogeneous population and constant elasticity of substitution utility), ε {\displaystyle \varepsilon } is equal to the income elasticity of marginal utility of income. The Atkinson index is defined as: where y i {\displaystyle y_{i}} is individual income ( i = 1, 2, ..., N ) and μ {\displaystyle \mu }

5688-596: The very specific, such as transportation to the polls . Only when such barriers are removed can the citizen truly be said to act out of personal choice. It is up to the individual society to make the list of minimum capabilities guaranteed by that society. For an example of the "capabilities approach" in practice, see Martha Nussbaum 's Women and Human Development . He wrote a controversial article in The New York Review of Books entitled "More Than 100 Million Women Are Missing" (see Missing women of Asia ), analysing

5767-481: The votes." He disagreed with Modi's ideology of Hindu nationalism, and advocated for a more integrated and diverse ideology that reflects the heterogeneity of India. Sen also wrote an article for The New York Times in 2013 documenting the reasons why India trailed behind China in economic development. He advocated for healthcare reform, because low-income people in India have to deal with exploitative and inadequate private healthcare. He recommended that India implement

5846-481: Was a close associate of Tagore. K. M. Sen served as the second Vice-Chancellor of Visva Bharati University from 1953 to 1954. Sen began his school education at St Gregory's School in Dhaka in 1940. In the fall of 1941, he was admitted to Patha Bhavana , Santiniketan, where he completed his school education. The school had many progressive features, such as distaste for examinations or competitive testing. In addition,

5925-664: Was from Wari and Manikganj , Dhaka , both in present-day Bangladesh . His father, Ashutosh Sen, was a Professor of Chemistry at Dhaka University , then the Development Commissioner in Delhi and then Chairman of the West Bengal Public Service Commission. Sen moved with his family to West Bengal in 1945. Sen's mother, Amita Sen, was the daughter of Kshiti Mohan Sen , the eminent Sanskritist and scholar of ancient and medieval India. Sen's maternal grandfather

6004-541: Was important for me not just because some of my main areas of interest in economics relate quite closely to philosophical disciplines (for example, social choice theory makes intense use of mathematical logic and also draws on moral philosophy , and so does the study of inequality and deprivation), but also because I found philosophical studies very rewarding on their own." His interest in philosophy, however, dates back to his college days at Presidency, where he read books on philosophy and debated philosophical themes. One of

6083-614: Was named the first chancellor of the proposed Nalanda University (NU). Sen was criticised as the project suffered due to inordinate delays, mismanagement, and lack of presence of faculty on ground. Finally teaching began in August 2014. On 20 February 2015, Sen withdrew his candidature for a second term. He has served as president of the Econometric Society (1984), the International Economic Association (1986–1989),

6162-758: Was released in 2017. A 2001 portrait of Sen by Annabel Cullen is in Trinity College's collection. A 2003 portrait of Sen hangs in the National Portrait Gallery in London. In 2011, he was present at the Rabindra Utsab ceremony at Bangabandhu International Conference Centre (BICC), Bangladesh . He unveiled the cover of Sruti Gitobitan, a Rabindrasangeet album comprising all the 2222 Tagore songs , brought out by Rezwana Chowdhury Bannya , principal of Shurer Dhara School of Music. Max Roser said that it

6241-551: Was the work of Sen that made him create Our World in Data . Sen was critical of Narendra Modi when he was announced as the prime ministerial candidate for the BJP . In April 2014, he said that Modi would not make a good prime minister. He conceded later in December 2014 that Modi did give people a sense of faith that things can happen. In February 2015, Sen opted out of seeking a second term for

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