Does quiggin's and chew logarithmic function satisfy the properties in my question, earlier. If so would want to avoid it. See page 59 and 60 in
See page 59 and 60 of Quiggin's, rank dependent utility' GENERALIZED EXPECTED UTILITY THEORY
THE RANK-DEPENDENT MODEL' 1993. SEe http://link.springer.com/search?query=quiggin+generalized&facet-content-type=%22Book%22
t appears to be strictly increasing and onto; but is logarithmic and apparently has f(p) +f(1-p)=1 for all; strictly increasing and uniformly continuous sur-jective(bijective?) [0,1] to [0,1] with f(0.5)=0.5 f(1)=1, and f(0)=0;Is it bijective and uniformly continuous?; and is '1-f(p),' display the same properties except being uniformly and decreasing (by the same amount) as f(p) increases. I would Presume so.
On an interval. Which further points would need to be specified ie F(F(0.25)=0.25, and F(0.33)=0.33 to render it linear; ie the parameter Y being 1; F(x)=x, as the only possible other continuous function.
al
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