A theoretically interesting issue in the domain of recognition memory concerns the decision variable that participants use to decide whether an item was previously encountered. In a standard old/new recognition procedure, the decision variable is simply the memory signal generated by the singular item presented on a given test trial. The nature of this memory signal can be conceptualized in terms of recollection vs. familiarity, item vs. associative information, or verbatim vs. gist memory—but however it is conceptualized, the stronger that memory signal is, the more likely the test item is to be declared “old” and the higher the participant’s confidence will be.

When more than one item is presented on a given test trial, other decision variables become possible. In a standard two-alternative forced-choice (2-AFC) procedure, for example, the item chosen on a given trial is presumably the one that generates the stronger memory signal. However, the participant’s confidence in that choice could be based either on the strength of the winning item’s memory signal considered in isolation (i.e., without regard for the strength of the losing item), or it could instead be based on the difference in memory strength associated with the two test items, in which case confidence would be higher the more the strength of the winning item exceeds that of the losing item. Ignoring the strength of the losing item is suboptimal in the sense that it leaves useful information on the table, but the results of a several recent studies have suggested that participants do just that (e.g., Hanczakowskia, Butowska, Beaman, Jones, Zawadzka, 2021; Jou et al., 2016, Miyoshi et al., 2018, Zawadzka et al., 2017).

Similar theoretical issues arise when more items are presented on a test trial, such as in the case of a police photo lineup. A typical photo lineup consists of six or more faces that are arranged in one of two possible configurations. A target-present lineup consists of one previously seen “old” face (i.e., the target) surrounded by five or more new “fillers” (i.e., lures) that are drawn from a pool of photos all of which are matched to the target on basic characteristics like race, gender, hairstyle, and approximate age. A target-absent lineup is similar except that the target is replaced by another filler to serve as the “innocent suspect.” An innocent suspect in an actual police lineup is special from the perspective of the police (being the only person in the lineup suspected of having committed the crime), but from the perspective of the witness, the innocent suspect is not special and is functionally just another filler (i.e., an innocent person who matches the other lineup members with respect to general physical characteristics). When presented with a lineup, participants can choose one of the faces as having been seen before or they can reject the lineup by indicating that the target is not present.

As in 2-AFC, if a face is chosen from a lineup, it is presumably the one that generates the strongest (MAX) memory signal. However, once again, confidence in a positive identification might be based solely on the absolute strength of the memory signal associated with the chosen face (without regard for the strength of the other faces in the lineup) or it might instead be based on a difference score. A signal detection model known as the Independent Observations model assumes that confidence in a positive identification from a lineup is based on its absolute memory signal (Wixted et al., 2018). An alternative signal detection model known as the Ensemble model assumes that confidence in a positive identification from a lineup is instead based on a difference score. According to this model, confidence in a positive ID is based on the MAX signal minus the mean memory strength signal across all faces in the lineup. In that case, confidence would be high not merely when the MAX signal is strong (as is true of the Independent Observations model) but only when its high strength stands out sufficiently from the “crowd” of memory signals in the lineup (Akan et al., 2021, Wixted et al., 2018).

The research reported here does not address the absolute vs. relative issue for positive IDs but instead focuses on the largely unexplored decision variable that underlies confidence for negative IDs (i.e., for lineup rejections). Critically, unlike in the case of positive IDs, no face is selected when a lineup is rejected. In that case, is confidence still determined by the memory signal associated with the unchosen MAX face (either its absolute memory strength or its memory strength relative to the other faces in the lineup)? Or is it instead based on a collective memory signal, such as the average (AVG) of the memory signal generated by all the faces in a lineup?

It seems fair to say that the default view is that the confidence in lineup rejections is based on the MAX signal, just as is true of confidence in positive identifications (e.g., Akan et al., 2021). However, picking up on an idea suggested by Brewer and Wells (2006) and Lindsay et al., 2013, Yilmaz et al., 2022 hypothesized that confidence in lineup rejections might be determined by the average memory signal. The rationale for deviating from the default perspective was based on the empirical observation that the confidence-accuracy relationship for lineup rejections, unlike the confidence-accuracy for positive IDs, is often weak (e.g., Brewer & Wells, 2006) and is sometimes completely flat (e.g., Dodson & Dobolyi, 2016). One possible reason for that asymmetry is that a different decision variable is used for positive vs. negative IDs. It seems plausible that a different decision variable might be used because, for positive IDs, confidence is provided in relation to a single face (i.e., the MAX face), whereas for negative IDs (i.e., lineup rejections), confidence is provided to the set of rejected faces. Here, using a model-fitting approach, we investigate whether the MAX memory signal or the AVG memory signal underlies confidence in lineup rejections.

The primary goal of our model-fitting approach is to rule out the least viable model, leaving the winning model as a viable candidate. As noted by Roberts and Pashler (2000), the mere fact that a model provides a better fit cannot be assumed to validate that model. However, Wixted et al. (2018) argued that a model that provides a qualitatively poor fit relative to other models can be reasonably rejected. For example, for the fits reported by Wixted et al. (2018), the Integration model (according to which the decision variable is based on the sum of the memory signals associated with the individual faces in the lineup) provided a far worse fit to the data than the Independent Observations and Ensemble models. On those grounds, the Integration model was ruled out as a viable candidate. Our goal here is to determine if, for lineup rejections, the assumption of a MAX decision variable similarly provides a qualitatively worse fit to the data than a model based on an AVG decision variable, perhaps helping to explain the weak confidence-accuracy relationship when the witness decides that the perpetrator is not in the lineup.

To investigate this issue, we (1) modified both the Independent Observations model and the Ensemble model to use either a MAX decision variable or an AVG decision variable to determine confidence in lineup rejections (yielding two versions of each model) and then (2) fit those models to empirical lineup data to determine which better characterizes the results. According to the MAX version of each model, the weaker the (absolute or relative) signal associated with the MAX face is, the more confidently the lineup is rejected. According to the AVG version, the weaker the average signal associated with the set of faces in the lineup is, the more confidently the lineup is rejected.

Because the Independent Observations and Ensemble models used in prior research already assume that the MAX face determines confidence for positive IDs, extending that assumption to confidence in negative IDs required only minor changes. By contrast, modifying the two models to allow for the possibility of an AVG decision variable for lineup rejections was more involved because it required modifying the likelihood functions for positive IDs derived by Wixted et al. (2018). The next section describes how the Independent Observations model and the Ensemble model conceptualize confidence in positive IDs and then provides an overview of how their likelihood functions were modified to allow for the possibility that an AVG memory signal is used for confidence in lineup rejections (with the mathematical details presented in the Appendix).