Lack of accurate intuition is often cited as a scientific challenge, especially when interpreting probabilistic and statistical research. A popular technique for developing statistical intuition involves imagining a game of chance with well-defined financial outcomes. In 1956 Kelly used this technique to propose an intuitive interpretation of relative entropy 1%DIFDELCMD < ]%%% . He considered a growth-optimizing investor in a game with mutually exclusive outcomes (a "horse race") and showed that the rate of return expected by such an investor is equal to the relative entropy which measures disagreement between the investor's believed probabilities and the official odds. Effectively, Kelly showed that a growth-optimizing investor would expect on average to convert 1 bit of additional information into a 100\% return on investment. Notwithstanding the mathematics, this interpretation has been vigorously criticized by Samuelson as dangerous on the grounds that most people are not growth-optimizing 2,3%DIFDELCMD < ]%%% . Here we show that a deeper connection between information and expected returns is in fact true. Relative to the Kelly information benchmark, variation in people's risk aversion does indeed cause a drop in expected returns. However, the amount of the drop is also information-driven: it is proportional to the absolute difference between the relative entropy and its celebrated generalization -- the R\'enyi divergence 4 . Given the widespread use of the R\'enyi divergence in science and engineering, and because financial returns are much easier to imagine, we expect our intuition to be useful in a broad range of fields. Financial intuition might also be useful in its own right as an instrument for raising financial support and accelerating the adoption of sound scientific developments .
 %DIFDELCMD < ]%%% %DIFDELCMD < ]%%% Disagreement is an essential element of science and life in general. Currently, the amount of disagreement between two probability distributions is quantified by highly abstract entropic measures such as the R\'enyi divergence . Despite their widespread use in science and engineering, such quantities lack numerical intuition and their axiomatic definitions contain no practical insight as to how the disagreement can be resolved. An economic approach addresses both of these problems by transforming disagreements into tangible investment opportunities. The R\'enyi divergence appears connected to the optimized performance of such investments. Optimization around individual opinions provides a social mechanism by which funds flow naturally to support a more accurate view. Such social mechanisms can help to resolve difficult disagreements (e.g., financial arguments concerning the global climate) .
D
Lack of accurate intuition is often cited as a scientific challenge, especially when interpreting probabilistic and statistical research. A popular technique for developing statistical intuition involves imagining a game of chance with well-defined financial outcomes. In 1956 Kelly used this technique to propose an intuitive interpretation of relative entropy
D
1
D
. He considered a growth-optimizing investor in a game with mutually exclusive outcomes (a "horse race") and showed that the rate of return expected by such an investor is equal to the relative entropy which measures disagreement between the investor's believed probabilities and the official odds. Effectively, Kelly showed that a growth-optimizing investor would expect on average to convert 1 bit of additional information into a 100\% return on investment. Notwithstanding the mathematics, this interpretation has been vigorously criticized by Samuelson as dangerous on the grounds that most people are not growth-optimizing
D
2,3
R
. Here we show that a deeper connection between information and expected returns is in fact true. Relative to the Kelly information benchmark, variation in people's risk aversion does indeed cause a drop in expected returns. However,
Disagreement is an essential element of science and life in general. Currently,
R
the drop is also information-driven: it is proportional to the absolute difference between the relative entropy and its celebrated generalization -- the
disagreement between two probability distributions is quantified by highly abstract entropic measures such as the
D
4
R
. Given the widespread use of the R\'enyi divergence
. Despite their widespread use
R
and because financial returns are much easier to imagine, we expect our intuition to be useful in a broad range of fields. Financial intuition might also be useful in its own right as an instrument for raising financial support and accelerating the adoption of sound scientific developments
such quantities lack numerical intuition and their axiomatic definitions contain no practical insight as to how the disagreement can be resolved. An economic approach addresses both of these problems by transforming disagreements into tangible investment opportunities. The R\'enyi divergence appears connected to the optimized performance of such investments. Optimization around individual opinions provides a social mechanism by which funds flow naturally to support a more accurate view. Such social mechanisms can help to resolve difficult disagreements (e.g., financial arguments concerning the global climate)