Stephen Broomell | Searcharxiv

arXiv2021

Capturing Richer Information -- On Establishing the Validity of an Interval-Valued Survey Response Mode

Obtaining quantitative survey responses that are both accurate and informative is crucial to a wide range of fields. Traditional and ubiquitous response formats such as Likert and Visual Analogue Scales require condensation of responses into discrete point values - but sometimes a range of options may better represent the correct answer. In this paper, we propose an efficient interval-valued response mode, whereby responses are made by marking an ellipse along a continuous scale. We discuss its potential to capture and quantify valuable information that would be lost using conventional approaches, while preserving a high degree of response-efficiency. The information captured by the response interval may represent a possible response range - i.e., a conjunctive set, such as the real numbers between three and six. Alternatively, it may reflect uncertainty in respect to a distinct response - i.e., a disjunctive set, such as a confidence interval. We then report a validation study, utilizing our recently introduced open-source software (DECSYS) to explore how interval-valued survey responses reflect experimental manipulations of several factors hypothesised to influence interval width, across multiple contexts. Results consistently indicate that respondents used interval widths effectively, and subjective participant feedback was also positive. We present this as initial empirical evidence for the efficacy and value of interval-valued response capture. Interestingly, our results also provide insight into respondents' reasoning about the different aforementioned types of intervals - we replicate a tendency towards overconfidence for those representing epistemic uncertainty (i.e., disjunctive sets), but find intervals representing inherent range (i.e., conjunctive sets) to be well-calibrated.

cs.HC↗

arXiv2014

When is a crowd wise?

Numerous studies and anecdotes demonstrate the "wisdom of the crowd," the surprising accuracy of a group's aggregated judgments. Less is known, however, about the generality of crowd wisdom. For example, are crowds wise even if their members have systematic judgmental biases, or can influence each other before members render their judgments? If so, are there situations in which we can expect a crowd to be less accurate than skilled individuals? We provide a precise but general definition of crowd wisdom: A crowd is wise if a linear aggregate, for example a mean, of its members' judgments is closer to the target value than a randomly, but not necessarily uniformly, sampled member of the crowd. Building on this definition, we develop a theoretical framework for examining, a priori, when and to what degree a crowd will be wise. We systematically investigate the boundary conditions for crowd wisdom within this framework and determine conditions under which the accuracy advantage for crowds is maximized. Our results demonstrate that crowd wisdom is highly robust: Even if judgments are biased and correlated, one would need to nearly deterministically select only a highly skilled judge before an individual's judgment could be expected to be more accurate than a simple averaging of the crowd. Our results also provide an accuracy rationale behind the need for diversity of judgments among group members. Contrary to folk explanations of crowd wisdom which hold that judgments should ideally be independent so that errors cancel out, we find that crowd wisdom is maximized when judgments systematically differ as much as possible. We re-analyze data from two published studies that confirm our theoretical results.

cs.SI↗