Investigating the empirical validity of salience theory while controlling for display format effects

Experiment 1:
Using a within-subjects design, we examine (i) whether the salience-predicted correlation effect found by DKK in their experiment on relative skewness prevails when controlling for event-splitting and (ii) whether the choice pattern obtained by Frydman and Mormann (2018) in their experiment on varying levels of correlation within an Allais-type choice setting prevails when employing the same display format but presenting lotteries as uncorrelated.

Experiment 2:
Using a within-subjects design, we examine whether subjects switch preferences due to salience-predicted correlation effects within an experimental framework that does not require changes in the display format to illustrate a modified correlation structure. Choice problems involve two lotteries that share the same expected value, where one lottery is denoted as the risky and one is denoted as the safe lottery. We present each choice problem under two different correlation structures, both in a gain and a loss setting. Additionally, we present subjects’ all problems once more within an event-splitting frame, where event-splitting effects are supposed to oppose a salience-predicted correlation effect.

2021-07-05

2021-07-06

Experiment 1:
Replication of DKK’s (2020) experiment on relative skewness:
(i) Salience-predicted shifts in preferences over a left-skewed and a right-skewed lottery when changing the correlation while simultaneously controlling for a potential event-splitting effect. (ii) shifts in preferences over a left-skewed and a right-skewed lottery when maintaining event-splitting but keeping the correlation constant.

Replication of Frydman and Mormann’s (2018) experiment on varying levels of correlation in an Allais-type choice setting:
Proportion of Allais-type preferences under Panel A, B, and C, with lotteries presented as uncorrelated by means of two distinct pie charts.

Experiment 2:
(i) Proportion of risky lottery choices under both employed correlation structures, both in a gain and a loss setting. (ii) Proportion of risky lottery choices under both employed correlation structures presented within a frame where event-splitting contravenes a salience-predicted correlation effect, again both in a gain and a loss setting.

Experiment 2:
Preferences exhibited by the majority of subjects under the two employed correlation structures.

Experiment 2:
Within the two correlation structures in our experimental framework, salience theory predicts any decision maker to once choose the risky lottery and once choose the safe lottery due to its linear value function. Examining the choice behavior of the majority of subjects permits a direct inference on the actually required value function instead of the linear one. In the gain setting, salience theory would require a concave value function if a majority of subjects prefer the safe lottery even though correlation favors the risky lottery. In the loss setting, salience theory would require a convex value function if a majority of subjects prefer the risky lottery even though correlation favors the safe lottery.

Experiment 1:
Each subject makes 22 binary choices, of which 18 choices relate to the replication of the experiment of DKK on relative skewness. We present subjects DKK's original 12 choice problems, which are based on 6 pairs of left- and right-skewed lotteries, once under negative and once under positive correlation. Additionally, we present subjects 6 problems, which involve the same pairs of left- and right-skewed lotteries under the negative correlation but a similar form of event-splitting as in the case of the positive correlation.
The remaining 4 choice problems relate to the replication of the experiment of Frydman and Mormann (2018), which involves varying levels of correlation in an Allais-type choice setting. We present subjects the same choice problems based on Panels A, B, C, and D. Yet, each employed pair of lotteries is framed as uncorrelated, with two distinct pie charts that contain the same sort of event-splitting, i.e., the same display format as originally employed by Frydman and Mormann (2018).

Experiment 2:
Each subject makes 24 binary choices. Each choice problem is based on an experimental framework involving two lotteries with the same expected value, and one second-order stochastically dominates the other. We construct three different setups of lottery pairs, presented to subjects under two correlation structures, both in a gain and a loss setting, equaling 12 problems in total. Additionally, we present subjects all 12 problems in an event-splitting format, where event-splitting effects are supposed to contravene a salience-predicted correlation effect. Whenever the salience mechanism favors the risky lottery, the event of disbursement of its downside payoff is split into two subevents. Whenever the salience mechanism favors the safe lottery, the event of disbursement of the risky lottery's upside payoff is split into two subevents.

Experiment 1:
Incentivization is guaranteed by the random-lottery procedure. After the experiment, one of the 22 choice problems is randomly assigned to each subject. The respective lottery a subject has chosen in this choice problem is then played for real money. Payoffs are denoted in the experimental currency Taler (4 Taler = 1 EUR).

Experiment 2:
The experimental framework involves three equally likely states of the world. There are two available lotteries, each disbursing three different payoffs, one in each state. The lotteries read as LR=(x1, 1/3; x4, 1/3; x5, 1/3) and LS=(x2; 1/3; x3; 1/3; x5; 1/3) with x1>x2>x3>x4>x5=0 and x1+x4=x2+x3 as well as x3+x4>=x1. Thus, both lotteries have the same expected value, and the risky lottery LR is a mean preserving spread of the safe lottery LS, i.e., LS second-order stochastically dominates LR.
There exist six possible correlation structures between LR and LS of which we employ the correlation structure that – according to salience theory – favors LR the most and the one that favors LS the most. Which lottery is favored by a salience-predicted correlation effect under each correlation structure reverses in the loss setting.
Incentivization is guaranteed by the random-lottery procedure. Due to the existence of choice problems that contain losses, subjects are told in advance that they receive 17 euros for participation. Potential gains (losses) would then be added (subtracted). After the experiment, one of the 24 choice problems is randomly assigned to each subject. The respective lottery a subject has chosen in this choice problem is then played for real money. Payoffs are denoted in the experimental currency Taler (4 Taler = 1 EUR).

Using a random generator (computer)

Individual

No

Experiment 1:
130 individuals.

Experiment 2:
130 individuals (no subject takes part in both experiments).

Experiment 1: Replication of DKK: 1560 paired choices (780 paired choices per treatment) Replication of Frydman and Mormann (2018): 390 paired choices (130 paired choices per treatment) Experiment 2: 1560 paired choices (390 paired choices per treatment: (i) display format with three equally likely states in a gain setting. (ii) display format with three equally likely states in a loss setting. (iii) event-splitting display format in a gain setting. (iv) event-splitting display format in a loss setting.)

Experiment 1:
It is a within treatment, 130 individuals.
Experiment 2:
It is a within treatment, 130 individuals.