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Theory and Decision

Erschienen in:

01.08.2014

Double or nothing?! Small groups making decisions under risk in “Quiz Taxi”

verfasst von: Klemens Keldenich, Marcus Klemm

Erschienen in: Theory and Decision | Ausgabe 2/2014

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Abstract

This paper investigates the behavior of contestants in the game show “Quiz Taxi” when faced with the decision whether to bet the winnings they have acquired on a final “double or nothing” question. The decision in this natural experiment is made by groups of two or three persons. This setup enables the decision-making process to be studied with regard to group and communication characteristics. The contestants show fairly risk averse behavior. There is also a significant heterogeneity in attitude to risk. In particular, all-female groups are much less likely to go for the risky option. Furthermore, decision-making behavior appears to vary across differently composed groups and prior performance. The study also documents the importance of discussions: The propensity to gamble increases with discussion length, and the correlation between communication content and the final choice is strong, indicating that time and subjective context are important features of decisions made under risk.

Vorheriger Artikel The generalized homogeneity assumption and the Condorcet jury theorem

Nächster Artikel Condorcet’s principle and the strong no-show paradoxes

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The game show “Quiz Taxi” is the German version of the English show “Cash Cab” which first aired in 2005. It was sold to over 25 countries and is still running in several of those, e.g., USA and Australia.

Since “Quiz Taxi” contestants know about the design of the decision problem and must have subjective probabilities for the possible outcomes, their decisions are made under risk, not under uncertainty. Therefore, the term “risk” is used in the following (see Knight 1921, for the seminal contribution about the difference between risk and uncertainty).

“Deal or No Deal” has become very popular among economists. See Blavatskyy and Pogrebna (2008, 2010), De Roos and Sarafidis (2010), and Gee (2007) for further investigations.

In the first season, the master question had not been introduced yet and the monetary rewards were lower. In the last season, a new wild card was introduced by which the group composition could change during the cab ride.

In the interview mentioned above, the host notes that the reasons for backing out of the cab are very diverse. He speculates that some people are afraid that they might make a fool of themselves, simply do not want to be on TV, or are just accompanied by the wrong persons. In two episodes, people who declined to play were shown. Their reasons for not participating were time constraints.

According to the producer, basically all cab rides recorded were aired, especially if the master question was reached. Therefore, an ex-post selection process can be ruled out.

Contestants can win back a previously used passersby-wild card by successfully solving an additional task when the cab stops at a red traffic light.

The age is estimated by appearance of the contestants if no direct information is revealed during the show. Three broad categories are used: below 30 years of age, 30–50 years of age, and above 50 years of age. Due to a very low number of observations in the last group, the latter two are combined for the empirical analysis.

Since the process of recording this data is subject to measurement error, all information obtained from the transcripts is cross-checked. Furthermore, controlling for the person who coded the data does not have any influence on the obtained estimation results.

We treat the group decision basically like the decision of an individual. While this abstracts from explicitly modeling the aggregation of the potentially different preferences of the group members, accounting for group characteristics and looking separately at groups that are initially undecided allows for an implicit description of how the groups might deal with diverging opinions.

A linear probability model (OLS) or a logit model deliver identical estimation results. The estimation results are available from the authors upon request.

The argument for setting the wealth level to zero is based on prospect theory (Kahneman and Tversky 1979) where individuals are assumed to evaluate gains and losses directly and not with regard to their overall wealth (see also Beetsma and Schotman 2001; Fullenkamp et al. 2003). With wealth set to zero, the critical probability is \(p_{i}^{*} = 0.5^{1-\gamma }\) with \(0 < \gamma < 1\).

The assumption of low wealth also serves the purpose of being able to estimate a \(\gamma \ge 1\) which is undefined in the case of zero wealth, but not likely given the observed decisions. For \(p_{i} = 0.75\), \(\gamma \) is estimated at approximately 5, but the maximum likelihood procedure does not yield completely stable results for high probabilities of success because expected utility maximization would imply choosing to play the master question in most cases which is incompatible with 67 % of groups not doing so.

The explanatory power of this regression is rather low (Pseudo \(R^{2}\) of 0.07). The predicted probability’s mean is 0.76 with a standard deviation of 0.12, a minimum of 0.36, and a maximum of 0.98.

Clearly, the comparability of all of these estimates is very limited because they are obtained from very different samples over very different monetary ranges using various methodologies. Therefore, the external validity of estimates of risk aversion parameters is questionable (Rabin 2000).

The statistical difference of the coefficients is tested by estimating fully interacted linear OLS and Heckman regressions. The linear models do not yield different results than the probit models, but facilitate the test of statistical significance of the interaction terms (Ai and Norton 2003). The significance level is at least 10 %, but 5 % or 1 % in most cases. When the sample is split into three groups, bold font indicates that at least one group’s coefficient is significantly different from the other two, but not necessarily that all coefficients are significantly different from each other.

In this sample split only, the Heckman models deliver a somewhat different result: The coefficient of the stake is more negative for female and mixed teams, but not in a statistically significant way (Table 3). Since the correlation between the risky choice and the stake can be confounded by the unobservable subjective probability of answering the master question correctly, this difference in estimation results suggests that the sex composition affects risk attitude as well as the perceived chances of success or a group’s enthusiasm.

Less than ten teams mention that they have seen the show before. Their views on the difficulty of the question are diverse. While the order in which the episodes were aired does not necessarily correspond to the order in which they were produced, the two should be almost identical. Seasons are arranged in pairs to avoid too small samples.

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Titel: Double or nothing?! Small groups making decisions under risk in “Quiz Taxi”
verfasst von: Klemens Keldenich
Marcus Klemm
Publikationsdatum: 01.08.2014
Verlag: Springer US
Erschienen in: Theory and Decision / Ausgabe 2/2014
Print ISSN: 0040-5833
Elektronische ISSN: 1573-7187
DOI: https://doi.org/10.1007/s11238-013-9398-8

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