# The Sense of Agency in Human-Machine Interaction Systems
## 2 The SoA: Definition and Influencing Factors  
### The Definition of the SoA  
The SoA refers to the subjective experience of controlling one's actions and, through them, external events [33; 34]. [PERSON] [35] considered the SoA to contain two layers. The first layer is body agency, which is the SoA that people have over controlling their bodies. The second layer is the feeling of controlling external events, i.e., external agency. For example, the light is turned on by pressing a switch. The feeling of controlling the body by pressing the switch is the body's agency. And, the light is turned on as an outcome of the action of pressing the switch, which is the external agency. In HMI systems, only external agency is considered relevant [36].  
There are two explanations for how one attributes agency to oneself [37]. The first one is the comparator model (CM) [38; 39; 40; 41; 42], which is also the most common explanation, as shown in Figure 4. An HMI system is usually intended to complete tasks or achieve goals. Before taking an action, the agent forms an intention and translates it into a motor plan. The motor plan predicts the outcome of the intended action. The agent then performs the action according to the motor plan. After taking the action, the agent compares the perceived outcome of the action with the predicted outcome. When the comparison is consistent, the agent obtains a strong SoA, while an inconsistency results in a weak SoA.  
The second explanation is the multifactorial weighting model (MWM), which is an extended model of [42; 43; 44; 45; 46]. The SoA can be separated into two related concepts: feelings of agency (FoAs) and judgments of agency (JoAs). The FoA refers to the pre-reflective, experiential sense of being an individual agent of action, involving implicit, low-level sensorimotor processes, similar to the components of the CM. The FoA is influenced by feed-forward cues, proprioception, and sensory feedback. The JoA refers to the cognitive assessment of an agent's control over their actions and outcomes; higher-order factors, including thoughts, intentions, social cues, and situational cues, all contribute to the JoA, as shown in Figure 5 [42]. The SoA is a dynamic interplay between the JoA and FoA, where the FoA provides the experiential basis and the JoA offers the cognitive evaluation of agency.  
Although many cues have been found to promote agency [41; 43; 47; 48; 49], previously studied systems mainly relied on a single cue. There are usually multiple cues available, so the SoA produced by a single cue is weaker than that elicited by multiple cues. According to the context, the reliability of these cues is weighted for agency attribution toward a stronger SoA [43], because multiple cues improve the consistency between outcomes and expectations. In short, the consistency between outcomes and expectations is the key to a high SoA. Both the CM and MWM produce a strong SoA when the outcomes and expectations are congruent. In addition, [PERSON] [36] believes that in an autonomous driving system, whether the vehicle's movements match the driver's intentions is a higher-level comparison that is more conducive to maintaining the SoA. On the other hand, [PERSON] et al. [37] proposed that the SoA also depends on the action-effect relationship after the operation, that is, the post hoc inference account. However, this review believes that the post hoc inference account can be included in the MWM.  
Figure 4: The comparator model.