## 1 Introduction
### Information Content of Risk Warning eHMI  
Risk-warning eHMIs are interfaces designed to alert pedestrians to risk levels for crossing based on the AV's time-to-arrival (TTA) [12; 13; 11]. When the AV is far away (TTA \(\geq\) 5.1 s), the eHMI could signal low risk; as the AV approaches (3.7 s \(\leq\) TTA \(<\) 5.1 s), the eHMI could signal medium risk; and when the AV is very close (TTA \(<\) 3.7 s), the eHMI could signal high risk [12; 14]. A low-risk signal allows pedestrians to cross confidently. A medium-risk signal could prompt pedestrians to either hasten their crossing or wait. A high-risk warning could advise pedestrians to refrain from crossing. While these visual cues serve as proactive guidance for pedestrians, AVs still retain the ability to dynamically adjust their driving behavior, such as slowing down or performing emergency braking, based on pedestrians' actual crossing behaviors. By introducing a risk-warning communication mechanism, AVs are no longer required to automatically yield upon every instance of pedestrian detection. Accordingly, risk-warning eHMIs offer a promising approach to enhance pedestrian safety while improving traffic efficiency [11]. Building on the risk level classification, risk-warning eHMIs can be designed to convey a single-level (low, medium, or high), two-level (low-medium, medium-high), or three-level (low-medium-high) of risk levels. An explicit, 'always-on' three-level low-medium-high risk warning eHMI could offer greater transparency, leading to clearer mental models. However, it may not be necessary for the eHMI to explicitly announce all levels of risk. Not explicitly conveying a message can also serve as a form of communication. Therefore, it is crucial to investigate whether reducing the explicit conveyance of one or two risk levels could minimize visual clutter and mental workload (MW) in dynamic traffic scenarios while still enabling optimal communication. According to the definition by [15], MW \"represents the degree of activation of a finite pool of resources, limited in capacity, while cognitively processing a primary task over time\". Due to the limited capacity of human cognitive resources, an increase in MW for task execution can impair situation awareness (SA) by competing for cognitive resources necessary to maintain SA [16; 17]. SA refers to an individual's ability to perceive, comprehend, and predict their environment [18]. In pedestrian-AV interactions, SA involves pedestrians predicting vehicle behavior based on their perception and comprehension of vehicle and road features [19]. Therefore, eHMI designs should effectively reduce MW, or at the very least, ensure that they do not increase MW compared to conditions without such interfaces, as emphasized by [20] and [PERSON], [PERSON], and [PERSON], as cited in [21]. Previous studies have also suggested the possibility of reducing the explicit conveyance of one or two risk levels. Ref. [11] reported that for larger time gaps, pedestrians are able to make crossing decisions more easily, adhering to their traditional crossing behavior, which in turn reduces the effectiveness of low-risk signals. Therefore, they suggested that the risk levels presented by the eHMI may be more advantageous in high-risk situations. Additionally, research on both single-level low [22] and single-level high [13] configurations has reported that they can aid pedestrians in street-crossing decision-making. Moreover, previous studies have highlighted the different impacts of risk signals (high-risk, medium-risk, and low-risk) on pedestrians' street-crossing behavior and perceivedurgency [12; 13]. Ref. [13] speculated that pedestrians tend to exhibit lower compliance with prohibitive alerts (i.e., high-risk signal) compared to permissive alerts (i.e., low-risk signal). Once a crossing decision is made, pedestrians are more likely to disregard high-risk warnings and proceed without stopping. Additionally, medium- and high-risk signals tend to elicit a stronger sense of urgency compared to low-risk signals [12].