Numerical analysis of a time allocation model accounting for choice overload

Abstract

The cost of time has been suggested as a factor associated with the choice overload problem. This term refers to the discomfort or paralysis experienced by individuals when facing a choice within a large set of alternatives, as it has been evidenced in experiments by behavioural and social psychologists. We introduce a rational model of time allocation to analyse how increasing the number of options of a given product may change consumer's allocation of time and in turn affect her welfare. Under some standard assumptions, the numerical analysis of the model reproduces two key experimental findings, namely choice paralysis – i.e. the choice problem is abandoned if the number of options is too large – and choice dissatisfaction – that is, the apparent paradox that increasing the number of considered options beyond certain limit, in turn choosing better, eventually diminishes welfare. The model analysis provides specific threshold values for the occurrence of both phenomena.

Keywords:

• time use
• allocation of time
• choice overload
• paradox of choice
• optimization
• consumer behaviour

2010 AMS Subject Classifications:

• 65K99
• 91B42
• 91E99

Acknowledgments

JMR was partially supported by Ministerio de Ciencia e Innovación (Spain) under Grant MTM2009-12672.

Notes

1. Input data were obtained from the first entry listed by a popular internet search engine for the search term ‘organized trips to Europe’, namely www.affordabletours.com. Travel data on this website were filtered by ‘tour destination to Europe’, dates ‘June 2013’ and length ‘14 days or more’. A total number of 319 results were obtained (September 2012).

2. The final version of the code was programmed in R, which allows for an easy integration of resampling methods (G), random number generation (τ) and numerical optimization (BFGS is a built-in method). The final outcome was generated on an Intel Core i7, 2.80 GHz PC, under Ubuntu 10.10. Both the code and the original data on prices are available from the corresponding author upon request.

3. Best deals in the three cases #1, #2 and #3 are as follows. Case #1: N*=56 and G(56)=1730.99$ after investing T_s=65.31 h searching, spending T_w=75 h working and enjoying herself the remaining time. Case #2: N*=38 and G(38)=1774.12$ for T_s=66.96 h and T_w=75 h. Case #3: N*=7 and G(7)=2089.79$ for T_s=16.87 h and T_w=149.15 h.

4. Best deals in the cases #4 and #5 are as follows. Case #4: N*=319 and G(319)=1629.00$ after investing T_s=26.05 h searching, spending T_w=66.45 h working and enjoying herself the remaining time. Case #5: N*=84 and G(84)=1693.06$ for T_s=229.20 h and T_w=69.65 h.