Why and How to Measure the Association between Choice Options

Abstract

Prominent theories of decision making, such as {\it proportional difference model}, {\it priority heuristics}, {\it decision field theory} and {\it regret theory} assume that people do not evaluate options independently of each other. Instead, these theories predict that people compare the options' outcomes with each other. Therefore the theories' predictions strongly depend on the association between outcomes. In the present work, we examine how the association between options can be best described. For options with two outcomes the standard correlation measure between option's outcomes does not provide a meaningful interpretation. Therefore, we propose the standardized covariance between options A and B, denoted as $\sigma^*_{AB}$. We describe the properties and interpretation of this measurement and show its similarities and differences with the correlation measurement. Finally, we show how the predictions of different models of decision making vary depending on the value of the standardized covariance.


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