Theory and Decision

, Volume 76, Issue 1, pp 1–7 | Cite as

Common consequence effects in pricing and choice

Article

Abstract

This paper presents an experimental study of common consequence effects in binary choice, willingness-to-pay (WTP) elicitation, and willingness-to-accept (WTA) elicitation. We find strong evidence in favor of the fanning out hypothesis (Machina, Econometrica 50:277–323, 1982) for both WTP and WTA. In contrast, the choice data do not show a clear pattern of violations in the absence of certainty effects. Our results underline the relevance of differences between pricing and choice tasks, and their implications for models of decision making under risk.

Keywords

Common consequence effects Fanning out WTP WTA Cancelation 

1 Introduction

Common consequence effects—including the famous paradox of Allais (1953)—are the most prominent experimental design for observing violations of expected utility theory (Machina 1987; Birnbaum 2004). A common consequence effect (CCE) occurs if the preference between two lotteries changes if the same probability mass is shifted from one common outcome to a different common outcome in both lotteries. Numerous empirical studies reported this type of violation of expected utility, providing a motivation for the development of alternative theories like cumulative prospect theory, rank-dependent utility or the TAX model.1 Given their theoretical importance and long tradition in empirical research on decision making under risk, it is surprising that almost all empirical studies have analyzed CCEs employing pairwise choice data. Work on CCEs with pricing data is virtually absent in the decision making literature. From an empirical perspective, however, pricing behavior is relevant in many market transactions, with agents stating buying and selling prices. If CCEs did (not) occur for pricing behavior, their economic relevance would be reinforced (challenged).

In principle, pricing and choice data should reveal the same preference ordering. Many empirical observations show that this is not the case in practice. The most prominent example of such response mode effects is the preference reversal phenomenon (Lichtenstein and Slovic 1971). The preference between two alternatives elicited by a straight choice is the opposite of the preference elicited by minimal selling prices. In addition, for different pricing methods response mode effects can be observed, for instance the widely studied disparity between willingness-to-pay (WTP) and willingness-to-accept (WTA) (Knetsch and Sinden 1984). Given these response mode effects, we may expect that the incidence of CCEs also varies between choice task and pricing tasks, and between different pricing methods.2

The present paper studies the incidence of CCEs under direct pairwise choice, WTP elicitation (maximal buying price), and WTA elicitation (minimal selling price). We consider eight different pairs of choice situations involving common consequence probability shifts, and distinguish between two empirical patterns: the fanning out hypothesis and the fanning in hypothesis (discussed below). For the elicitation of WTP and WTA we employ incentive-compatible second-price auctions. The experimental design is presented in the next section. The following section presents the theoretical framework and the experimental results. The last section concludes.

2 Experimental design

The experiment was conducted at the University of York (EXEC) with 24 students subjects. The experiment involved 30 lottery pairs, 12 of which are analyzed in the present paper, shown in Table 1. All lotteries involved the four consequences 0, 10, 30, and 40 with different probabilities, as given in the table. Note that some consequences could have zero probabilities, but that there were no degenerate lotteries. Thus, we exclude certainty effects. The lotteries were visually presented as segmented circles on the computer screen (see Appendix). Subjects had to attend five separate sessions. At the end of the last session, one question for each subject was randomly chosen and played out for real. The average payment to the subjects was 34.17, with 80 being the highest and 0 being the lowest payment.
Table 1

The lottery pairs

No.

Safe lottery

Risky lottery

 

0

10

30

40

0

10

30

40

1

0.00

0.60

0.10

0.30

0.02

0.60

0.00

0.38

2

0.30

0.60

0.10

0.00

0.32

0.60

0.00

0.08

3

0.00

0.50

0.50

0.00

0.35

0.00

0.50

0.15

4

0.50

0.50

0.00

0.00

0.85

0.00

0.00

0.15

5

0.00

0.20

0.30

0.50

0.20

0.00

0.00

0.80

6

0.50

0.20

0.30

0.00

0.70

0.00

0.00

0.30

7

0.00

0.20

0.70

0.10

0.20

0.00

0.40

0.40

8

0.00

0.00

0.50

0.50

0.10

0.00

0.00

0.90

9

0.50

0.00

0.50

0.00

0.60

0.00

0.00

0.40

10

0.00

0.00

0.75

0.25

0.00

0.10

0.25

0.65

11

0.00

0.25

0.50

0.25

0.00

0.35

0.00

0.65

12

0.25

0.25

0.50

0.00

0.25

0.35

0.00

0.40

Entries are probabilities

In the five sessions, subjects had to perform altogether eight tasks three of which will be analyzed in the present paper: (1) report a preference for each pairwise choice question (CHOICE task); (2) report their willingness-to-pay (i.e., the maximal buying price) for each lottery (WTP task); and (3) report their willingness-to-accept (i.e., the minimal selling price) for each lottery (WTA task). For all tasks we used incentive-compatible elicitation mechanisms.

For pairwise choice questions, the subjects would simply play out the preferred lottery. For the WTP and WTA tasks, standard second-price auctions were employed. In the case of WTP, subjects had to submit a bid for each lottery. If a WTP question was selected for the reward, the subject received an endowment \(y,\) where \(y\) is the highest amount in the corresponding lottery. Moreover, if the subject submitted the highest bid for this lottery then she would pay the second highest bid and then play out the lottery (receiving whatever outcome resulted). If the subject did not submit the highest bid, she kept her endowment and did not play lottery. For WTA subjects were asked to assume that they owned the lottery and had to make an offer to dispose of it. Assume that a WTA question was selected for real pay. If the subject did not submit the lowest offer then the subject played out the corresponding lottery. However, if she did submit the lowest offer, she received the second lowest offer as reward, not playing out the lottery.

3 Theoretical predictions and experimental results

The stimuli in Table 1 involve altogether eight CCEs which are listed in the first two columns of Table 2. As an example, let us consider CCE No. 1, consisting of lottery pairs 1 and 2. Table 1 shows that each pair consists of a relatively safe and a relatively risky lottery. Pair 2 can be constructed from pair 1 by shifting a probability mass of .30 from the common outcome 40 to the common outcome 0 in both lotteries. According to expected utility, this manipulation must not change the preference between the risk and the safe lottery. That is, an expected utility maximizing agent will choose either the safe lottery in both pairs, or the risky lottery in both pairs.
Table 2

Results

No.

Pairs

CHOICE

WTP

WTA

Predicted

  

EU

FO

FI

EU

FO

FI

EU

FO

FI

CPT

TAX

1

1&2

54.2

37.5

8.3

41.7

50.0

8.3

50.0

29.2

20.8

FO

FO

2

3&4

50.0

16.7

33.3

58.4

33.3

8.3

54.2

33.3

12.5

FO

FO

3

5&6

79.2

4.2

16.6

45.8

33.4

20.8

75.0

16.7

8.3

FO

FO

4

5&7

91.6

4.2

4.2

37.5

41.7

20.8

75.0

16.7

8.3

EU

EU

5

8&9

75.0

20.8

4.2

45.8

45.8

8.3

58.3

25.0

16.7

FO

FO

6

10&11

54.2

33.3

12.5

54.2

37.5

8.3

41.7

41.7

16.6

FO

EU

7

11&12

54.2

20.8

25.0

54.2

29.2

16.6

37.5

33.3

29.2

EU

FO

8

10&12

54.2

29.2

16.6

33.3

50.0

16.7

54.2

37.5

8.3

FO

FO

All

 

64.1

20.8

15.1

46.4

40.1

13.5

55.7

29.2

15.1

  

Entries are percentages. Italics indicate modal pattern, and bold print indicates modal CCE pattern

EU Consistent with expected utility, FO fanning out, FI fanning in, CPT cumulative prospect theory

There are two possible patterns of violating expected utility in CCE situations, termed fanning out (FO) and fanning in (FI) according to Machina (1982). Fanning out holds if the degree of risk aversion is increasing with the attractiveness of lotteries. Note that the lotteries in pair 1 are more attractive than the lotteries in pair 2 according to the criterion of first-order stochastic dominance. Thus, in the example CCE no.1, a violation of expected utility in the direction of fanning out occurs if a subject chooses the safe lottery in pair 1, and the risky lottery in pair 2. Similarly, fanning in holds if the degree of risk aversion is decreasing with the attractiveness of lotteries. In the example, fanning in implies a safe choice in pair 2 and a risky choice in pair 1.

Previous empirical research revealed that violations of expected utility for choice data are systematic since the FO pattern was much more frequently observed than the FI pattern. However, this evidence relies mostly on CCEs that involve a certainty effect, i.e., one alternative is a certain outcome (as in the Allais paradox; Schmidt 1998). In the absence of certainty effects, some studies observed, in contrast, more FI than FO patterns (Conlisk 1989; Prelec 1990). Non-expected utility models like Kahneman and Tversky (1979) Prospect Theory or Birnbaum and McIntosh (1996) TAX model have been proposed to account for violations of expected utility as revealed in CCEs. From a theoretical point of view, however, FO is not necessarily the dominant pattern under prospect theory (Wu and Gonzalez 1998). As the last column of Table 2 shows, we have selected our stimuli such that the most prominent parameterizations of cumulative prospect theory (Tversky and Kahneman 1992) and the TAX model imply either FO or consistency with expected utility for all our CCEs.

Columns 3–5 of Table 2 present the results of our experiment. For all three elicitation methods and all eight CCEs, the table reports the percentage of subjects behaving consistent with expected utility (EU), consistent with FO, or consistent with FI. For the pairwise choice data, FO is observed more frequently (20.8 % compared to 15.1 %), but this difference is insignificant according to the test of Conlisk (1989). Indeed, in half of the pairs FO is observed more frequently, and in the other half FI is observed more frequently. Note also that the behavior of 64 % of all subjects was consistent with EU in the choice elicitation. These results are consistent with previous studies: there no clear evidence of FO in choice if certainty effects are not involved (Conlisk 1989; Prelec 1990).

Comparing choice and pricing data, the last row of Table 2 reveals two observations. On the one hand, the consistency with expected utility is reduced under pricing. According to the test of Conlisk, for both WTP and WTA consistency with expected utility is significantly lower than for choice at the 1 %-level (D \(= -\)4.11) and 5 %-level (D \(= -\)1.87), respectively. Moreover, for each of the eight CCEs fanning out is more frequently observed than fanning in. This is true for both WTP and WTA. In total, the difference between the frequency of FO and FI amounts to 26.6 % points for WTP and 14.1 % points for WTA (both differences are significant at the 1 %-level). Also for pricing, however, the modal pattern is that of consistency with expected utility.

4 Discussion and conclusions

Our results show that violations of expected utility in the context of CCEs are more pronounced for pricing than for choice data. There are significant common consequence effects in pricing even in the absence of certainty effects, and predominantly in the form of fanning out. Nevertheless, for all three elicitation modes, expected utility is the model pattern observed.

On the one hand, the current findings thus support the view that extreme settings, like the Allais paradox certainty effects, play an important role in violations of expected utility. On the other hand, it also shows that pricing is more prone to violations. In particular, willingness-to-pay elicitation seems most affected by common consequence effects. The violations are clearly systematic for both pricing tasks, with fanning out more prevalent than fanning in for each pair.

The different prevalence of violations in pricing and choice is unfortunate from a theoretical point of view, because prominent alternatives to expected utility, like rank-dependent utility or TAX, do not make differential predictions for pricing and choice. Two potential mechanisms for such choice-pricing differences that have been studied in the literature include the cancelation operation in (original) prospect theory (Kahneman and Tversky 1979; Bonini et al. 2004), and shifts in reference points across elicitation methods (Bleichrodt 2007; Trautmann et al. 2011).3 With the editing operation of cancelation, the decision maker cancels common outcomes before choosing between two lotteries. For pricing decisions each lottery is evaluated in isolation, and the operation of cancelation cannot be applied. Common outcomes will, therefore, have a stronger impact for pricing than for binary choice. With shifting reference points, different elicitation methods will induce the decision maker to assume different reference points, leading to preference reversals.

Common consequence effects provide a challenge to expected utility theory. Non-expected utility theories have been developed that successfully account for these effects. Choice versus pricing differences in common consequence effects are potentially more problematic. Established alternatives to expected utility do not predict such reversals, and more context-dependent modeling is needed to provide explanation of the pattern. The challenge to such modeling will be to include context, while maintaining predictability across settings.

Footnotes

  1. 1.

    Bleichrodt et al. (2008); Wakker (2010) and Zank (2010) provide detailed discussions of the properties of these models.

  2. 2.

    These response mode effects occur within the context of description-based decisions, in contrast to experience-based decisions. See Barron and Erev (2003) and Erev et al. (2010) for a detailed discussion of preference shifts between these two decision contexts. All analyses in this study consider description-based decisions.

  3. 3.

    A related idea is in Blavatskyy and Köhler (2009), suggesting a procedural model of lottery pricing.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Kiel Institute for the World EconomyUniversity of KielKielGermany
  2. 2.CentER, Department of EconomicsTilburg UniversityTilburgThe Netherlands

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