# Transparent Task Delegation in Multi-Agent Systems Using the QuAD-V Framework
## 3 Delegation Model
### Evaluation Metrics  
As illustrated in Figure 1, the framework contains only one answer argument (\(A_{1}\)). The acceptance score (\(aS\in[0,1]\)) quantifies the partner's suitability based on past evaluations, reinforcing trust in consistently reliable partners while penalizing those with lower performance. If the answer argument is accepted (\(aS(A_{1})\geq 0.5\)), the partner can be selected as a delegate; otherwise, if rejected (\(aS(A_{1})<0.5\)), the partner should not be accepted. As presented in Figure 1, a partner is evaluated based on three dimensions:  
1. **Availability** (associated with arguments from class \(A_{2*}\)) (The asterisk (*) indicates that all arguments in a class have identifiers starting with a specific number. For example, arguments 21 and 22 belong to the Availability class, while arguments 31, 32, 321, and 322 belong to the Effectiveness class. ): This dimension reflects a partner's capability to accept task requests from delegators. As presented in Figure 1, a delegator votes for or against this class of arguments based on the partner's _rejection rate_ (\(RR(\beta,\tau)\in[0,1]\)),  
Figure 1: The proposed delegation model and its components. A vote is cast in favor or against an argument depending on whether the associated evaluation measure meets or exceeds a threshold value (\(Th\)). which represents the frequency with which a partner \(\beta\) has rejected a task \(\tau\) requested by its delegators over time: \[RR(\beta,\tau)=\frac{|(\beta,\tau)^{\circ}|}{|(\beta,\tau)^{\bullet}|}\] (5) where \(|(\beta,\tau)^{\circ}|\) is the number of times \(\beta\) rejected a task request for \(\tau\) from a delegator due to being occupied with another task or being unable to perform \(\tau\), and \(|(\beta,\tau)^{\bullet}|\) is the number of times \(\beta\) received a task request for \(\tau\) from its delegators. 2. **Effectiveness** (associated with arguments of class \(A_{3*}\)): This dimension estimates how often a partner successfully completes its tasks. A delegator votes for or against the arguments of this class based on the following measures: * **Success rate**(\(SR(\beta,\tau)\in[0,1]\)): This measure indicates the frequency with which a partner successfully completes a task, allowing its delegator to achieve its goal. The success rate is calculated as follows: \[SR(\beta,\tau)=\frac{|(\beta,\tau)^{+}|}{|(\beta,\tau)^{*}|}\] (6) where \(|(\beta,\tau)^{+}|\) is the number of times that \(\beta\) successfully completed \(\tau\), and \(|(\beta,\tau)^{*}|\) is the number of times that \(\beta\) attempted to execute \(\tau\), regardless of the success or failure in performing \(\tau\). * **Success confidence** (\(SC(\beta,\tau)\in[0,1]\)): This measure indicates the reliability of a partner's success rate (\(\beta\)) from the perspective of a delegator \(\alpha\), taking into account the number of iterations between them. The success confidence tends to increase as the number of iterations between \(\alpha\) and \(\beta\) grows [38]: \[SC(\beta,\tau)=I_{U}+(I_{L}-I_{U})*\left(\frac{I_{n}-|(\beta,\tau)^{*}|}{I_{n} }\right)^{2}\] (7) where \(I_{L}\) is the reliability lower bound, \(I_{U}\) is the reliability upper bound, and \(I_{n}\) is the number of interactions needed for \(\alpha\) to accurately infer \(\beta\)'s success rate. (The parameters \(I_{U}\), \(I_{L}\), and \(I_{n}\) are user-defined and configurable according to system needs. In our experiments, we assigned \(I_{U}=1\) and \(I_{L}=0\), meaning the confidence score starts at 0 and increases to 1 as interactions grow. We defined \(I_{n}\) as the number of task requests received by \(\beta\) from \(\alpha\). Thus, a partner \(\beta\) who frequently rejects task requests from a delegator \(\alpha\) tends to have lower reliability scores from \(\alpha\)'s perspective, since the number of interactions between \(\alpha\) and \(\beta\) remains low relative to the total task requests received by \(\beta\).) 3.