Categorización de los procesos Niveles de detalle

In order to understand the experimental procedure, it is helpful to first understand the baseline case where all preference elicitations are consistent with each other. See figure 5.1 for an illustration of P-Bet and $-Bet CE elicitations in three di↵erent procedures: A) By inferring an SI point, B) through direct valuation, C) through

an MSoP Task.

A) Shows a typical observation of choice probabilities between P-Bet/$-Bet lotteries against di↵erent sure amounts. Following Mosteller and Nogee (1951), the lottery choice probability decreases in choices against higher sure amounts. While the lottery is always chosen over £0, at the SI point the lottery choice probability is 50% for some sure amount.

B) Displays a consistent di↵erence in CE values: the P-Bet is valued higher than the$-Bet. Valuations are possible along the lotteries’ ranges, with the$-Bet’s range being larger (not to scale in the figure). In addition, the di↵erence in CEs quantifies the di↵erence in attractiveness to the participant. The SI points from A) suggest CE di↵erences in choices that reflect a preference for the P-Bet and this di↵erence is also generated in the valuation procedure B).

C) Shows a hypothetical response of a DM who had chosen the lottery over a sure amount x and was prompted for an MSoP. If her preferences would be consistent across procedures, she would value the lottery in the MSoP task to equal the sure amount at the SI point. Then, her MSoP added to x would equal the SI point’s sure amount, withx+M SoP =SI. This CE di↵erence is a strength of preference in monetary terms, the MSoP value.

In the figure, she states MSoP values consistent with procedure A) for both lotteries. E.g., for the P-Bet her valuation reaches the SI point with xP+M SoP =

yP = SIP. If yP were consistently larger than her SIP, the DM’s MSoP values

would show a positive mismatch for the P-Bet. MSoP values are also consistent with procedure B) as the P-Bet is again valued higher than the$-Bet.

Participants thatonly state their MSoP between two lotteries without stat- ing the respective CEs, still respond to something logically similar to a valuation task. Instead of reporting two valuations of two options, they only report a sin- gle valuation di↵erence between the options. Therefore, any MSoP task is also a preference elicitation procedure. Figure 5.1 constructs an example where di↵erent procedures generate the same CE values.

But the preference reversal as well as the MSoP mismatch show that this is not always the case. Still, it is not clear where these inconsistencies stem from. The question remains if eliciting a CE value in one procedure might a↵ect the elicited CE value in another procedure. E.g., if a choice task (procedure A) is immediately followed by an MSoP task (procedure C). While the MSoP mismatch might stem from the valuation procedure alone, it is not possible to rule out its connection to a previous choice as a causal factor.

Figure 5.1: Three di↵erent methods to elicit P-Bet/$-Bet Certainty Equivalents (not to scale)

5.1.1.1 Preference Reversals

Chapter 4 already gives the qualitative prediction of an inconsistency between choices (procedure A) and valuations (procedure B). The BREUT valuation model predicts that a majority of valuations is higher than the SI point of a lottery.

5.1.1.2 Spill-Over E↵ects

The BREUT valuation model predicts that incorporating mental evidence from a choice phase into an MSoP valuation leads to a positive mismatch in the stated MSoP. Even if the MSoP valuation is not entirely based on the pre-existing mental evidence base, it is possible that it does cause a mismatch in an otherwise unbiased valuation. In the example of procedure C) in figure 5.1, this means that the DM will on average state a too high MSoP value that overshoots the SI point (xP +

M SoPM ismatch_=yM ismatch

P > SIP).

Furthermore, this positive mismatch in MSoP values will go into both direc- tions. If a participant finds a lottery less attractive than on average, a valuation based on this mental evidence base will be biased towards a lower than average value. This will be reflected in the MSoP, which now quantifies a downward adjustment of the sure amount. So if the DM now adjusts downwards too much, the MSoP value also shows a positive mismatch. In both cases, due to the spill-over of mental evidence from choice to MSoP process, adjustments result in too high MSoP values and overshoot the SI point. Butler et al.’s (2014a) experiment was only designed to test for positive MSoP because it only allowed positive adjustments of a rejected option. Therefore, it remains unclear if MSoPs overshooting the SI point result from the valuation process, which overvalues lotteries’ valuations compared to their SI points, or from spill-overs of mental evidence.

We assume that this spill-over e↵ect can only exist in MSoP tasks that occur straight after a choice. So as soon as DMs are not aware of the choice process anymore, they will not be able to access their mental evidence anymore. It follows that the spill-over e↵ect will disappear as soon as the MSoP task is sufficiently delayed in time from the respective choice. However, participants might still be

influenced; not by a spill-over of mental evidence but just by being aware that they made a certain choice in the past.

5.1.1.3 Consistency-Seeking Behaviour

BREUT can also incorporate consistency-seeking behaviour into its predictions, also predicting a positive MSoP mismatch. Unlike with spill-overs of mental evidence, we cannot assume that an MSoP mismatch resulting from consistency-seeking be- haviour disappears as soon as a participant is not aware of their choice anymore. If a participant has forgotten their choice but then sees the display of an MSoP task, she will be reminded of her past choice. The BREUT valuation model with consistency-seeking behaviour predicts that she will take this choice at face value and then base her reasoning on the fact that her preference supported that choice. Therefore, consistency-seeking behaviour cannot be removed from MSoP tasks.

But it would be possible to compare MSoP tasks immediately after choices to delayed MSoP tasks that are contingent on the same choices in the past. Thereby, we can distinguish if the MSoP mismatch originates from the choice or the valuation aspect of the MSoP task. An MSoP task using an immediate adjustment can be compared with a version where the participant needs to estimate her preference given one of herpast choices in an MSoP task using a delayed adjustment. This rules out an influence of the choice process on the MSoP valuation but keeps the influence of the choice display. So there is only a valuation process influencing the MSoP task along with the potential e↵ect of the choice display. This e↵ect is assumed to be consistency-seeking behaviour. Section 5.3.3 explains how hypotheses distinguish between consistency-seeking behaviour and spill-over e↵ects.