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Upper Distribution Independence

Upper Distribution Independence. Michael H. Birnbaum California State University, Fullerton. UDI is Violated CPT. CPT violates UDI but EU and RAM satisfy it. TAX violates UDI in the opposite direction as CPT.

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Upper Distribution Independence

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  1. Upper Distribution Independence Michael H. Birnbaum California State University, Fullerton

  2. UDI is Violated CPT • CPT violates UDI but EU and RAM satisfy it. • TAX violates UDI in the opposite direction as CPT.

  3. The upper branch consequence, z’, has different probabilities in the two choices.

  4. Upper Distribution Independence (3-UDI)

  5. Example Test

  6. Generic Configural Model where CPT, RAM, and TAX disagree on

  7. Generic Configural Model The generic model includes RDU, CPT, EU, RAM, TAX, GDU, as special cases.

  8. Violation of 3-UDI A violation will occur if S’fR’ and

  9. 2 Types of Violations: S’R2’: R’S2’:

  10. EU allows no violations • In EU, the weights are equal to the probabilities; therefore

  11. RAM Weights

  12. RAM allows no Violations • RAM model with any parameters satisfies 3-UDI.

  13. Cumulative Prospect Theory/ RDU

  14. CPT implies violations • If W(P) = P, CPT reduces to EU. • From previous data, we can calculate where to expect violations and predict which type of violation should be observed.

  15. CPT implies S’R2’ Violations • When g = 1, CPT reduces to EU. • Given the inverse-S weighting function, the fitted CPT model implies S’R2’ pattern. • If g > 1, S-Shaped, but the model can handle the opposite pattern. • A series of tests can be devised to provide overlapping combinations of parameters.

  16. TAX Model Each term has the same denominator; however, unlike the case of LDI, here the middle branch can gain more weight than it gives up.

  17. Special TAX: R’S2’ Violations • Special TAX model violates 3-UDI. • Here the ratio depends on p.

  18. Summary of Predictions • RAM, & EU satisfy 3-UDI • CPT violates 3-UDI: S’R2’ • TAX violates 3-UDI: R’S2’ • Here CPT is the most flexible model, RAM defends the null hypothesis, TAX makes opposite prediction from that of CPT.

  19. Results n = 1075 R’S2’

  20. Results: n = 503 R’R2’ (CPT predictedS’R2’ )

  21. Summary: Observed Violations fit TAX, not CPT • RAM and EU are refuted in this case by systematic violations. • TAX model, fit to previous data correctly predicted the modal choices. • Violations opposite those implied by CPT with its inverse-S W(P) function. • Fitted CPT was correct when it agreed with TAX, wrong otherwise.

  22. To Rescue CPT: • CPT can handle the result of any single test, by choosing suitable parameters. • For CPT to handle these data, let g > 1; i.e., an S-shaped W(P) function, contrary to previous inverse- S.

  23. Adds to the case against CPT/RDU/RSDU • Violations of 3-UDI favor TAX over RAM and are opposite predictions of CPT.

  24. Preview of Next Program • The next programs reviews tests of Restricted Branch Independence (RBI). • It turns out the violations of 3-RBI are opposite the predictions of CPT with inverse-S function. • They refute EU but are consistent with RAM and TAX.

  25. For More Information: mbirnbaum@fullerton.edu http://psych.fullerton.edu/mbirnbaum/ Download recent papers from this site. Follow links to “brief vita” and then to “in press” for recent papers.

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