# Why and How to Measure the Association between Choice Options

- Sandra Andraszewicz,
*University of Basel, Basel, Switzerland*
- Jörg Rieskamp,
*University of Basel, Basel, Switzerland*

## 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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