Imprecise Data Sets as a Source of Ambiguity: A Model and Experimental Evidence

Abstract

In our model an individual forms beliefs over events based on the frequencies of occurrences of the events in past cases. However, in some cases, he might not know whether or not a speci…c event has occurred. Our model suggests that ambiguity may arise due to this sort of partial information and that attitude towards ambiguity can be explained by the way the individual process such imprecise cases. An individual who tends to put low weight on the possibility that an event occurred in these imprecise cases will turn out to be ambiguity averse, whereas an individual who tends to put high weight on the possibility that this event occurred will turn out to be ambiguity loving.The model is followed by an experiment designed to test the main features of the model. It is corroborated that given precise data subjects are ambiguity neutral while given imprecise data subjects are ambiguity averse.We wish to thank Anat Bracha, Itzhak Gilboa, Dotan Persitz, Ariel Rubinstein, Ella Segev, Peter Wakker and participant of the PhD seminar at Tel Aviv University for many helpful comments and suggestions.

Exploring uncertainty perception as a driver of design activity

“…Krippendorff's alpha (Krippendorff, 1981) was calculated for the core action codes using two raters on a data sample with continuous coding intervals of 1 s. This resulted in alpha values of 0.93, 0.95, and 0.98 for information action, knowledge sharing action, and representation action respectively. The (Langer & Roth, 1975); confident, confidence, not confident (Lawrence & Makridakis, 1989); imprecise, imprecision (Arad & Gayer, 2012); vague, vagueness, vaguely (Ellsberg, 2001); ambiguous, ambiguity (Ellsberg, 2001); x%, probable, probability, probably (Bedford & Cooke, 2001); likely, unlikely ; uncertainty modelling techniques such as Sensitivity analysis or Monte Carlo (Beynon, Curry, & Morgan, 2000); unknown, not known, don't know (Soanes, 1928); ignorance, ignore, ignorant (Walker et al, 2003); Interval statement (e.g. maximum, minimum, worst case, best case, biggest, smallest, heaviest, lightest) ; on average, mean, around (Langer & Roth, 1975) Implicit…”

Cautious Belief Formation

“…The beliefs (EG and ours) require that agents are able to ignore this difference, which might be fine if agents have experienced already a situation in which they actually estimated according to that objective precision and know her induced perception of that precision (as in our work). However, if an agent has never experienced 22 From that perspective, our representation is even more convincing than the perfectly objective imagination-free representation (2), in which the cautiousness and confidence is altered for each case, putting the agent in different moods of cautiousness and confidence for each piece of information.…”

“…However, the perception of this precision needs not to be imagined, since the agent estimates according to an already experienced precision and cautiousness level 4 (experienced for c 2 ). Arad and Gayer (2012) analyze beliefs based on datasets containing imprecise pieces of information in the sense that "it is not entirely clear what occurred in them ". Roughly speaking, their approach models this sort of imprecision (ambiguity) by assuming subjective capacities.…”

“…) intersects for all 0 ≤ z ≤ a l (defined above (12)) with the lines (g (1,3) l (z), g (2,3) l (z)) which are parallel to the line (f 1 , f 2 ) and also with all lines (g (1,2) l (z), g (1,3) l (z)) which are parallel to (f 2 , f 3 ). By Lemma B.4 this yields, that all simplicical points of the (l + 1)-th partition, which lie on the line (b 1 l+1 (1), b 3 l+1 (1)) are satisfying equation (11).…”

Ambiguity, data and preferences for information – A case-based approach

“…The empirical relationship between ambiguity and data is largely unexplored. Some recent experimental studies by Arad and Gayer (2010) and Hau, Pleskac and Hertwig (2010) examine, however, behavior when information is provided in the form of data. Both studies report signi cant behavioral effects of the form in which data is provided.…”