There Are Statistical . . . An Important and . . . The Problem That We . . . The Resulting . . . Is It Legitimate Statistics Let Us Prepare to . . . or Is It Sexism: Zipf Law Case of Inclusive Strategy Why Discrimination Case of Discriminatory . . . So Which of the Two . . . Is Not Rational Home Page Martha Osegueda Escobar 1 , Vladik Kreinovich 1 , Title Page and Thach N. Nguyen 2 ◭◭ ◮◮ 1 Department of Computer Science, University of Texas at El Paso, USA ◭ ◮ mcoseguedaescobar@miners.utep.edu, vladik@utep.edu 2 Banking University of Ho Chi Minh City, 56 Hoang Dieu 2 Page 1 of 29 Quan Thu Duc, Thu Duc, Ho Ch´ ı Minh City Go Back Vietnam,Thachnn@buh.edu.vn Full Screen Close Quit
There Are Statistical . . . An Important and . . . 1. There Are Statistical Differences The Problem That We . . . • People of different gender and/or ethnicity have differ- The Resulting . . . ent success rates in different disciplines. Let Us Prepare to . . . Zipf Law • For example, there are many highly successful female Case of Inclusive Strategy computer scientists. Case of Discriminatory . . . • However, in the US, in the US, So Which of the Two . . . – the percentage of female computer science students Home Page who get a PhD is lower Title Page – then the percentage of male students. ◭◭ ◮◮ • In some other disciplines and in other countries, the ◭ ◮ difference is reverse. Page 2 of 29 • Similarly with ethnicity; for example, Go Back – the corresponding percentage is higher among Asian-American students Full Screen – than among white students. Close Quit
There Are Statistical . . . An Important and . . . 2. An Important and Difficult Challenge The Problem That We . . . • The percentage of successful females varies from coun- The Resulting . . . try to country. Let Us Prepare to . . . Zipf Law • This is true even for countries with similar ethnicity. Case of Inclusive Strategy • This shows that the reasons for the statistical differ- Case of Discriminatory . . . ences are not biological. So Which of the Two . . . Home Page • We thus need to learn from the success of other coun- tries and other disciplines. Title Page • We need to make sure that everyone has an equal ◭◭ ◮◮ chance to succeed. ◭ ◮ • This idea may sound straightforward. Page 3 of 29 • However, in reality, how to do it is an important and Go Back difficult challenge, way beyond the scope of this paper. Full Screen Close Quit
There Are Statistical . . . An Important and . . . 3. The Problem That We Deal With in This Talk The Problem That We . . . • In this ta;l, we deal with a more mundane problem: The Resulting . . . what is the best strategy in the current situation? Let Us Prepare to . . . Zipf Law • The situation is very simple and straightforward. Case of Inclusive Strategy • We want to graduate a certain number of PhDs. Case of Discriminatory . . . • We have limited resources. So Which of the Two . . . Home Page • So, at first glance, it seems that a rational strategy is: Title Page – to concentrate on undergraduate students for ◭◭ ◮◮ whom the probability of success is higher, ◭ ◮ – i.e., on male students, Page 4 of 29 – and ignore the female students, since for them, the probability of success is lower. Go Back Full Screen Close Quit
There Are Statistical . . . An Important and . . . 4. The Problem (cont-d) The Problem That We . . . • This argument has nothing to do with prejudice against The Resulting . . . females: Let Us Prepare to . . . Zipf Law – if in a few years, the situation reverses, and the Case of Inclusive Strategy probability of a female student succeeding becomes Case of Discriminatory . . . higher than for male ones, So Which of the Two . . . – a person following this rational will start concen- Home Page trating on promising female students only and ig- nore male students completely. Title Page ◭◭ ◮◮ • A similar argument can be applied to hiring. ◭ ◮ • Female applicants tend to have a higher probability of retiring early because of their family obligations. Page 5 of 29 • So should we stop hiring them? Go Back • Should we just ignore resumes coming from female ap- Full Screen plicants and only hire males? Close Quit
There Are Statistical . . . An Important and . . . 5. The Resulting Discriminatory Strategy Strat- The Problem That We . . . egy May Sound Rational, But Is It Moral? The Resulting . . . • The usual argument against the above hypothetical Let Us Prepare to . . . strategy is that: Zipf Law Case of Inclusive Strategy – while it may sound rational, Case of Discriminatory . . . – it goes against the basic moral principles. So Which of the Two . . . • Everyone should get a chance to succeed. Home Page • We should judge every person based on his/her indi- Title Page viduality, not based on their gender, race, ethnicity. ◭◭ ◮◮ • This is an explanation many people give. ◭ ◮ • In this talk, we show that discriminatory strategies are Page 6 of 29 not just immoral, they are actually not rational . Go Back Full Screen Close Quit
There Are Statistical . . . An Important and . . . 6. Let Us Start Analyzing the Problem The Problem That We . . . • Without losing generality, let us consider the problem The Resulting . . . of hiring. Let Us Prepare to . . . Zipf Law • The same argument can be used for selecting the most Case of Inclusive Strategy promising students to “groom” them for PhD. Case of Discriminatory . . . • For simplicity, let us assume that the candidates belong So Which of the Two . . . to two possible groups. Home Page • We have a group for which the probability of success p Title Page is higher. ◭◭ ◮◮ • For simplicity, we will call this group majority , ◭ ◮ • We say “for simplicity”, since, e.g., Asian-Americans Page 7 of 29 are not a majority. Go Back • We also have a group for which the probability of suc- cess p ′ is somewhat lower: p ′ < p . Full Screen • For simplicity, we will call this group minority . Close Quit
There Are Statistical . . . An Important and . . . 7. We Will Compare Two Strategies The Problem That We . . . • Let us consider two possible strategies: The Resulting . . . Let Us Prepare to . . . – a discriminatory strategy, when we ignore all mi- Zipf Law nority applicants, and Case of Inclusive Strategy – an inclusive strategy, when we consider all appli- Case of Discriminatory . . . cants. So Which of the Two . . . • We analyze these strategies from a purely economic Home Page viewpoint: which one brings more benefit to the com- Title Page pany. ◭◭ ◮◮ • From this viewpoint, each of these two strategies has its gains and its losses. ◭ ◮ • In the discriminatory strategy: Page 8 of 29 – we save some money on analyzing minority appli- Go Back cants, Full Screen – but we miss potential gains that we could have if Close we hired good female employees. Quit
There Are Statistical . . . An Important and . . . 8. We Will Compare Two Strategies (cont-d) The Problem That We . . . • In the inclusive strategy: The Resulting . . . Let Us Prepare to . . . – we lose some money on checking the applications Zipf Law of all minority applicants, Case of Inclusive Strategy – but we may gain by hiring good female employees. Case of Discriminatory . . . • If we combine these gains and losses, which of the two So Which of the Two . . . strategies will turn out to be the most beneficial? Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 9 of 29 Go Back Full Screen Close Quit
There Are Statistical . . . An Important and . . . 9. Let Us Prepare to Evaluate Gains and Losses The Problem That We . . . • The cost of analyzing an application is approximately The Resulting . . . the same for all candidates. Let Us Prepare to . . . Zipf Law • Let us denote this cost by a . Case of Inclusive Strategy • There is also a cost of training a person and supporting Case of Discriminatory . . . this person through the probation period. So Which of the Two . . . Home Page • Let us denote this cost by t . Title Page • What can be drastically different is the gain. ◭◭ ◮◮ ◭ ◮ Page 10 of 29 Go Back Full Screen Close Quit
There Are Statistical . . . An Important and . . . 10. Zipf Law The Problem That We . . . • Like many other things, potential gains are distributed The Resulting . . . according the Zipf law . Let Us Prepare to . . . Zipf Law • If we denote the lifetime gain from hiring the best pos- Case of Inclusive Strategy sible candidate by G , then: Case of Discriminatory . . . – the gain from hiring the 2nd best candidate is G 2 , So Which of the Two . . . Home Page – the gain from hiring the 3rd best candidate is G 3 , Title Page – and, in general, the gain from hiring the i -th best ◭◭ ◮◮ candidate is G i . ◭ ◮ Page 11 of 29 Go Back Full Screen Close Quit
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