Abstract
This study uses the television show Cash Cab as a natural experiment to investigate gender differences in decision making under uncertainty. As expected, men are much more likely to accept the end-of-game gamble than are women, but men and women appear to weigh performance variables differently when relying on subjective probabilities. At best men base their risky decisions on general aspects of their previous “good” play (not all of which is relevant at the time the decision is made) and at worst fail to condition their risky decisions on any of the relevant information available to them. In sharp contrast, women appear to consider all of the information available to them, including previous “poor” play as well as their most recent confident “good” play, which, by design, is likely the most relevant information to consider.
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Notes
The initial value was set at $25 for the first two production seasons, and double rides did not occur. After that, the initial value was set at $50, with an initial value of $100 for Double Rides. In our sample, from season three on, 13.5 percent of rides have been Double Rides.
Empirically, 71 percent of the completed rides that accept the gamble answer the VBQ correctly, whereas this same group answered 85 percent of its previous questions correctly.
Babies were not included in the number of contestants, but children who could participate were included (and occasionally children provided correct answers). One ride included 5 contestants, with three of the five being children. We classified this as a ride of 4 contestants.
The confidence judgment was recorded by each author prior to hearing whether the answer was correct, and their independent assessment of confidence matched on over 93 percent of all questions.
In each of these games, the probabilities are either obvious or fairly straightforward to calculate. Even in Deal, No Deal, in which there are 26 briefcases to keep track of, the show provides the contestant a visual aid to understand what options remain.
Because of our interest in gender differences, we limit the sample to three types of rides: all-female rides (\(n = 73\)), half-female rides (\(n = 119\)) being either one female and one male or two females and two males, and all-male rides (\(n = 108\)). We remove 79 three-person, multi-sex rides from the analysis in order to better focus on the three gender groups for which we have large enough sample sizes for regression analysis. Future research might investigate how three-person rides make the VBQ decision and how having more men or more women matters in group decision making (Ertac and Gurdal 2012; Ronay and Kim 2006).
Because of the limitations of LPM estimation, a data appendix containing all regression results under logit regression are available upon request. The results from the logit regressions are qualitatively unchanged from the LPM results reported throughout the paper.
None of the estimated coefficients change significantly when the distance of the ride is included in the model, and the estimated coefficient on distance is statistically insignificant in all specifications. Therefore, none of the regression models include the distance of the ride.
The general consensus in the literature is that groups are more risk-loving than individuals, and our results for Cash Cab support that on the whole. Intuitively, however, the behavior on Cash Cab could have gone the other way as the contestants are friends, and more risk-loving friends could acquiesce to their risk-averse friends. Unfortunately, the data do not allow us to isolate these two confounding effects.
We do not know which multi-rider games include family units, for which total winnings is likely the better measure affecting decisions, or friendships, for which per-share winnings is likely the better measure. Bliss et al. (2012) argue that, even though per-share measures of winnings are what should matter theoretically, Cash Cab contestants make decisions based on total winnings. Our results are quantitatively unchanged if we include total winnings or winnings per contestant. Following Bliss et al. (2012), therefore, all of the results reported in the paper include total winnings.
Only twelve observations have winnings in excess of $1,950 when the VBQ is offered, and only three of these accepted the gamble. However, the ride with the greatest winnings ($3,100) accepted the VBQ gamble (and went on to answer it correctly).
The empirical model includes the number of questions rather than the percent of questions, because of the shortness of the game. Over 70 percent of all rides encounter between seven to eleven questions. Thus, one question is roughly ten percent for most rides. Moreover, the idea that good or bad play may later enter into the VBQ decision in such a short game would seem to be an additive, not percentage, effect. The model also does not control for the number of questions asked. In model (2) of Table (3), and again in model (4), the number of total questions asked is a linear combination of the number of questions answered correctly and the number of strikes. In the other models, the variables are highly co-linear. The number of questions was never statistically significant when it was included in any of the models, so this variable is omitted from Tables 2 and 3. A data appendix of results is available upon request that includes performance variables as percentages and that includes the number of questions asked of each set of contestants.
Measuring the variables from question 9 on is less useful as most rides do not receive more than 9 questions.
Although the measures of accuracy and confidence in Tables 2 and 3 are correlated, multicolinearity does not appear to be a problem in any of the regressions as none of the variables are associated with a variance inflation factor above 3. If models (2) and (3) are combined into one, the variance inflation factors exceed 7 for most of the response variables. In this case, the response accuracy variables remain statistically insignificant, while the confidence variables keep their sign but are slightly less statistically significant.
While Table 4 might appear to suggest that all-female rides perform less well than all-male rides, this is not actually the case. Whereas all-female groups are asked 8 % fewer questions than all-male groups, the all-female rides are also 2.3 city blocks shorter than all-male rides, which corresponds to being about ten percent shorter. Similarly, although Table 4 shows that, on average, all-female rides earn less money at the completion of their ride (i.e., before the VBQ) than all-male groups, this difference too can be attributed to the additional 0.94 questions answered correctly by all-male groups (which is typically a question worth $200) as well as to the extra frequency with which longer distance rides are presented with the opportunity to answer a Red Light Challenge.
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Acknowledgments
We thank Sarah Cattano, Line Producer for Lion Television, for discussing production aspects of Cash Cab. The paper benefited from comments offered by the Editor and two anonymous referees. All remaining errors are our own.
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Kelley, M.R., Lemke, R.J. Gender differences when subjective probabilities affect risky decisions: an analysis from the television game show Cash Cab . Theory Decis 78, 153–170 (2015). https://doi.org/10.1007/s11238-013-9389-9
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DOI: https://doi.org/10.1007/s11238-013-9389-9