Choosing between options that differ in benefits and required effort. Varying reward and effort independently helps distinguish reduced reward sensitivity from increased effort cost.[ref]
Distinct effects of apathy and dopamine on effort-based decision-making in Parkinson's disease by Campbell Le Heron and others. 2018, reward and physical-effort choice
Consider a logistic choice rule with and fixed noise scale. At one positive offer , changes satisfying leave utility and acceptance probability unchanged. One offer therefore cannot identify reward gain and effort cost separately.
For example, and both give at . Their predictions differ at other offers. Independently varying reward and effort can identify the two coefficients within this model when the design has rank two and choice data are informative. If noise scale is also unknown, its tradeoff with the coefficients requires additional constraints.
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