Ole Peters (2019). Comment on D. Bernoulli (1738). RESEARCHERS.ONE, https://www.researchers.one/article/2019-05-1.

July 25, 2019 11:49 am

Corrected a typo in Eq.15 and Table 2, spotted by a twitter user

https://twitter.com/princeChar/status/1154386484545445888

Square bracket before p_i should be after p_i or before the sum, or omitted.

Many thanks!

July 27, 2019 5:09 am

The comment by Fitzsimmons, if I understand correctly, amounts to pointing out that Bernoulli's decision theory (BDT) is equivalent to expected utility theory (EUT) for linear utility.

This is correct and discussed in the manuscript, e.g. on p.7:

*"Only a linear utility function guarantees the equality fmB = fmU. In other words, Bernoulli’s decision theory, which is often wrongly presented as equivalent to EUT, is really only equivalent to EUT under the assumption of linear utility. But that is equivalent to Huygens’s decision theory that we encountered in Sec. 2, and that was deemed an unrealistic model of human behavior."*

Linear utility is equivalent to what I call Huygens's decision theory (HDT) here, namely to the maximization of expected dollar wealth (without a utility function). This leads to the following situation: Bernoulli's decision theory is only equivalent to expect utility theory in the special case where neither Bernoulli's decision theory, nor expected utility theory has any effect, namely where both are equivalent to Huygens's decision theory, which had been found to be inadequate, and whose inadequacy had motivated the development of BDT and EUT.

July 30, 2019 1:45 pm

The point of my comment was that for a general (concave increasing) utility function, the criteria of EUT is close to that of D. Bernoulli, and coincident after a correction factor (the probability of losing) is inserted. My last sentence, in which I remark on the (trivial) special case of linear utitlity, was beside the point.

A remark on the possibility of reconciling BDT and EUT.