Stephen B. Broomell

Stephen B. Broomell, Christian Wagner

Information aggregation is a vital tool for human and machine decision making in the presence of uncertainty. Traditionally, approaches to aggregation broadly diverge into two categories, those which attribute a worth or weight to information sources and those which attribute said worth to the evidence arising from said sources. The latter is pervasive in the physical sciences, underpinning linear order statistics and enabling non-linear aggregation. The former is popular in the social sciences, providing interpretable insight on the sources. While prior work has identified the need to apply both approaches simultaneously, it has yet to conceptually integrate both approaches and provide a semantic interpretation of the arising aggregation approach. Here, we conceptually integrate both approaches in a novel joint weighted averaging operator. We leverage compositional geometry to underpin this integration, showing how it provides a systematic basis for the combination of weighted aggregation operators--which has thus far not been considered in the literature. We proceed to show how the resulting operator systematically integrates a priori beliefs about the worth of both sources and evidence, reflecting the semantic integration of both weighting strategies. We conclude and highlight the potential of the operator across disciplines, from machine learning to psychology.

Zack Ellerby, Christian Wagner, Stephen Broomell

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.