Ben Wright considered three methods of concatenating people (Teams, Packs and Chains, RMT 9:2 432-433). Mallows (1991) proposed another concatenation: majority vote. Wright discovered that adding a low ability person to a Team (required to make unanimous decisions) lowers the success rate of the Team. Mallows discovered that, with majority decisions, even adding a competent person lowers the success rate of a competent group!
If two people of similar abilities Bn and Bm respond to an item of difficulty D independently, but are required to agree on their answer, then the combined Team ability, T, is
T = (Bn - Di) + (Bm-Di) = 2(B-D)
where B is the average of Bn and Bm.
Add a third person of similar ability and permit majority decision making. Then the Majority ability, M, under Rasch model conditions is
= (exp(3(B-D)) + 3exp(2(B-D)))/(1 + 3exp(B-D))
1.5(B-D) <= M < 2(B-D)=T when B>=D
which accords with Mallows' pessimism.
In contrast, however, adding a third incompetent person to two other incompetents and allowing a majority vote increases their probability of success!
1.5(B-D) > M > 2(B-D)=T when B<D
Is this why democracy succeeds?
Mallows C (1991) Should you sign up that third author? Chance p. 7.
Majority rule. Wright BD, Mallows C. Rasch Measurement Transactions, 1995, 9:3 p.443
|Rasch Measurement Transactions (free, online)||Rasch Measurement research papers (free, online)||Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch||Applying the Rasch Model 3rd. Ed., Bond & Fox||Best Test Design, Wright & Stone|
|Rating Scale Analysis, Wright & Masters||Introduction to Rasch Measurement, E. Smith & R. Smith||Introduction to Many-Facet Rasch Measurement, Thomas Eckes||Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.||Statistical Analyses for Language Testers, Rita Green|
|Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar||Journal of Applied Measurement||Rasch models for measurement, David Andrich||Constructing Measures, Mark Wilson||Rasch Analysis in the Human Sciences, Boone, Stave, Yale|
|in Spanish:||Análisis de Rasch para todos, Agustín Tristán||Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez|
|Forum||Rasch Measurement Forum to discuss any Rasch-related topic|
Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement
Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.
|Coming Rasch-related Events|
|March 21, 2019, Thur.||13th annual meeting of the UK Rasch user group, Cambridge, UK, http://www.cambridgeassessment.org.uk/events/uk-rasch-user-group-2019|
|April 4 - 8, 2019, Thur.-Mon.||NCME annual meeting, Toronto, Canada,https://ncme.connectedcommunity.org/meetings/annual|
|April 5 - 9, 2019, Fri.-Tue.||AERA annual meeting, Toronto, Canada,www.aera.net/Events-Meetings/Annual-Meeting|
|April 12, 2019, Fri.||On-line course: Understanding Rasch Measurement Theory - Master's Level (G. Masters), https://www.acer.org/au/professional-learning/postgraduate/rasch|
|July 2-5, 2019, Tue.-Fri.||2019 International Measurement Confederation (IMEKO) Joint Symposium, St. Petersburg, Russia,https://imeko19-spb.org|
|July 11-12 & 15-19, 2019, Thu.-Fri.||A Course in Rasch Measurement Theory (D.Andrich), University of Western Australia, Perth, Australia, flyer - http://www.education.uwa.edu.au/ppl/courses|
|Aug 5 - 10, 2019, Mon.-Sat.||6th International Summer School "Applied Psychometrics in Psychology and Education", Institute of Education at HSE University Moscow, Russia.https://ioe.hse.ru/en/announcements/248134963.html|
|Aug. 9 - Sept. 6, 2019, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Aug. 14 - 16, 2019. Wed.-Fri.||An Introduction to Rasch Measurement: Theory and Applications (workshop led by Richard M. Smith) https://www.hkr.se/pmhealth2019rs|
|August 25-30, 2019, Sun.-Fri.||Pacific Rim Objective Measurement Society (PROMS) 2019, Surabaya, Indonesia https://proms.promsociety.org/2019/|
|Oct. 11 - Nov. 8, 2019, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Nov. 3 - Nov. 4, 2019, Sun.-Mon.||International Outcome Measurement Conference, Chicago, IL,http://jampress.org/iomc2019.htm|
|Jan. 24 - Feb. 21, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|May 22 - June 19, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 26 - July 24, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|Aug. 7 - Sept. 4, 2020, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Oct. 9 - Nov. 6, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 25 - July 23, 2021, Fri.-Fri.|
The URL of this page is www.rasch.org/rmt/rmt93c.htm