Author response:
We thank the reviewers for their thoughtful and constructive feedback on our work.
We have attempted to synthesize the main suggestions across both reviewers into four main areas, which we plan to address in a revised version of the manuscript.
(1) The relationship between covert attention, overt attention, and choice
While the current analyses address elements of relationship between covert attention, overt attention, and choice, the reviewers highlighted an opportunity to make full use of our rich gaze data to examine more explicitly how these processes are related to one another over the course of a decision. [Reviewer #1 Point 2, Point 3 i; Reviewer #2 Point 2 para 2]
(2) The role of decision difficulty and decision time
The reviewers point out that decision difficulty may i) account for the relationship between covert attention (probe response correctness) and choice; and ii) influence decision times, which are currently not analyzed; and that these considerations may affect how we interpret the relationship between covert attention and choice. [Reviewer #1 Points 2, 3 ii and iii; Reviewer #2 Point 1 paras 1 and 3]
(3) Evidence for competition between covert and overt attention
The reviewers requested more direct evidence for our claim that covert attention to higher-valued peripheral options occurs "at the expense of" overt attention [Reviewer #2 Point 2 paras 1 and 3, Point 3 para 3]
(4) Figure 6: Presaccadic vs. non-presaccadic attention
Reviewer 2 found the rationale behind the analysis distinguishing presaccadic from non-presaccadic covert attention difficult to follow and suggested and alternative to make this comparison more explicit [Reviewer #2 Point 3].
In response to these suggestions, we will include additional analyses in the revised manuscript which more directly examine the relationship between covert attention, overt attention, and choice. We will also introduce new analyses which more simply and directly depict: why decision difficulty cannot wholly account for the link between covert attention and choice; a competition/trade-off between overt and covert attention; and that value modulation existed at non-presaccadic options. In addition to these four main areas, we will clarify several elements of the task design and analysis which may not have been sufficiently clear in the manuscript.
Here, we offer a provisional response to each of the points above.
(2) The relationship between covert attention, overt attention, and choice
We agree that the relationship between covert attention, overt attention, and choice could be examined in more detail using the available eye-tracking data. In the revised manuscript, we plan to include further analysis looking at fixation and sampling measures before the decision is made.
For example, to investigate the relationship between covert attention and choice (as reviewer 1 suggested), we plan to include an analysis which asks about how decision accuracy changes as a function of decision difficulty (relative option value) when the unfixated probe is correctly reported, versus when it is not. This will straightforwardly test for the influence of probe report on choice, controlling for the influence of decision difficulty.
More generally, we will revise the manuscript to distinguish more carefully between associations demonstrated by the present data and stronger causal interpretations. To address this, we will either attempt more direct statistical tests of causality, or use more neutral language where the causal directionality between fixation, covert attention, and choice cannot be uniquely established by the present design.
An important clarification on the dynamics of the task is relevant to several of the reviewers’ comments concerning the last-fixation analyses. Probe performance was generally measured earlier than the final fixation and choice – as it was always at the first to third option visit by the participant (or only first to second option visit in Experiment 1). Only 10.4% of probes occurred during the final option visit, and on average, participants made 2.8 further option visits after probe presentation. We can see that our original presentation of these results may have been difficult to follow. We will make this clarification in the revised manuscript, particularly where we refer to “last-fixated” or “last-unfixated” options. These terms refer retrospectively to which option was ultimately visited or not visited last before choice, rather than to the fixation occurring at the time the probe was presented.
(2) The role of decision difficulty and decision time
We agree with the reviewers that decision difficulty and in turn decision time should be considered more carefully.
We will make explicit that relative option value was already controlled for in the existing analyses relating to covert attention and choice. Specifically, for the last-fixation analysis, relative value difference was included as a control variable in the regression. For the time-advantage analysis, we use a corrected dependent variable which is intended to remove possible influences of relative value (i.e., decision difficulty) on the fixation durations, following what has been done in previous work (e.g., Eum et al., 2023; Krajbich et al., 2010; Krajbich & Rangel, 2011).
We additionally plan to include new analyses which more directly examine the role of decision difficulty and decision time. In particular, we will test whether the relationship between peripheral probe performance and choice remains after accounting for decision difficulty, and whether decision time differs as a function of probe performance.
We would also like to take the opportunity to clarify that “time advantage” was operationalised as a relative measure: the difference in cumulative dwell time between the two relevant options, rather than the absolute cumulative dwell time on a single option. This definition will be stated more clearly in the main text and figure caption.
Finally, to address the possibility that peripheral probe report errors reflect a general dual-task cost or increased response noise, we will examine decision accuracy as a function of decision difficulty separately for trials in which the peripheral probe was reported correctly versus incorrectly. This will help determine whether successful peripheral probe report is associated with poorer decision performance.
However, we should note that a closer examination of Figure 4 offers clues to this question; it suggests that correctly reporting the probe at the last-unfixated item makes people more accurate, rather than happening at the expense of decision accuracy. To explain this:
When objectively Option 1 is worse than Option 2 (i.e., to the left of x-axis center), choice for a last-fixated Option 1 (solid line) is unfairly boosted; but if the last-unfixated probe was correctly reported, then the choice proportion is correctly closer to 0%.
When objectively Option 1 is better than Option 2 (i.e., to the right of x-axis center), choice for a last-unfixated Option 1 (dotted line) is unfairly discounted; but if the last-unfixated probe was correctly reported, then the choice proportion is correctly closer to 100%.
That is, the bias-attenuation effect of correctly reporting the probe at the last-unfixated item seems to operate on 1) reducing choice boosting of the objectively-worse fixated option (left of x-axis center, solid line is further down on right panels than left panels); and 2) increasing choice boosting of the objectively-better unfixated option (right of x-axis center, dotted line is further up on right panels than left panels).
(3) Evidence for competition between covert and overt attention
To address more directly the question of whether covert attention occurs at the expense of overt attention, we will add an analysis testing whether successful report of a probe at an unfixated option negatively predicts report of the simultaneous probe at the fixated option. A negative relationship would provide a more direct test of the predicted trade-off between attentional allocation to the fixated and peripheral locations. We will revise the strength of the corresponding language in the manuscript according to what this analysis supports.
(4) Figure 6: Presaccadic vs. non-presaccadic attention
We agree that the rationale underlying the current Figure 6 analysis is too implicit in the current manuscript.
To clarify the underlying rationale: The key logic of the analysis was to ask whether value modulation of probe performance is present at an unfixated option even when that option is not the target of the upcoming saccade. In the original analysis, we only compared attention at peripheral options that had previously been viewed: we compared attention at peripheral options that had previously been viewed and were subsequently fixated next, with those that had previously been viewed but were not subsequently fixated next. The requirement that the option had previously been viewed arose because, in the gaze-contingent “hidden” condition, the value information of an unvisited peripheral option would not yet have been available to the participant, and therefore there would be no possibility of any value modulation effects existing at that location.
Although this analysis was intended to distinguish value modulation at likely presaccadic targets from value modulation at other peripheral locations, we now see that its rationale is not immediately transparent. In the revised manuscript, we therefore plan to replace or supplement this analysis with a simpler visualisation and analysis that addresses the same question more directly.
We will also revise text associated with the time-to-saccade analysis. Our use of the term “monotonic” was imprecise. The intended point was not that a purely presaccadic account predicts a strictly monotonic change across the full time-to-saccade interval, but rather that the observed U-shaped relationship is difficult to reconcile with a simple presaccadic-only account, because probe performance remains elevated even when the upcoming saccade is relatively distant. We will clarify this point and more carefully distinguish evidence inconsistent with a simple presaccadic-only explanation from the stronger claim (which we did not intend to make) that presaccadic contributions have been completely excluded.
(5) Additional clarifications
We agree with Reviewer 1 that the task can reasonably be described as perceptual rather than strictly value-based, but we believe that our central concerns regarding how covert and overt attention interact with multi-alternative decision-making still stand.
We will clarify why the secondary probe task was not incentivized. The probe task was intended to provide an incidental measure of covert attention while participants performed the primary decision task. Incentivizing probe performance could have encouraged participants to explicitly trade off performance on the two tasks or to alter their allocation of attention in response to the secondary task.
In summary, the revisions will combine clarification of several existing analyses with the addition of new analyses that more directly test the reviewers’ central concerns. In particular, we will more explicitly address whether the relationship between covert attention and choice remains after accounting for option value/decision difficulty; whether peripheral and fixated probe performance show evidence of an attentional trade-off between overt and covert attention; how decision time and richer measures of overt sampling relate to covert attention; and whether value modulation is present at peripheral locations that are not the target of the upcoming saccade. We will also moderate causal and mechanistic language where the current data do not uniquely establish directionality.