# Robot Swarms Decide under Perception Errors in Best-of-N Problems
## 5 Results
### Consensus Accuracy
#### 5.2.2 Experiments Set II  
In this set of experiments, we allow measurement errors to occur at both sites (A and B)--i.e., a robot belongs to a particular population e.g., the overestimating population will overestimate the quality value of any site it visits during its exploration trip. Figure 5 depicts the evolution of collective decision over time for the configuration of equal populations--i.e., \(\{70,70,70\}\). In Figure 5a, we show the results when the basic behavioral model is applied, while in Figure 5b, we show the results when the distance-based algorithm for robot classification is used (when the extended model is applied). As we can observe, the difference is minor between these results and the ones obtained when measurement errors were allowed only at site A. One remarkable difference (especially in the case (a) of the basic model) is a smaller standard deviation around the number of committed robots. This results from enabling the entire swarm to measure with errors, hence contributing to a larger sample of the random variable--i.e., the quality measure. Another difference is the faster convergence time of the collective decision in comparison to the case when errors were allowed only at site B only. Similarly, the speed to achieve a consensus drops when applying the distance-based algorithm due to the time spent by the robots in the classification phase. In terms of decision accuracy, the basic behavioral model was able to achieve 64% decision accuracy without exploiting any robot classification, whereas the distance-based algorithm achieved only 60% decision accuracy. Next, we examine the accuracy of the collective decision for different compositions of the swarm of 210 robot. The results are reported in Table 4 as the percentage at which the swarm committed to any of the two sites. Different from the case where the measurement errors were only enabled at site A (red), when these are allowed at both sites, the results summarized in Table 4 show an improvement in the decision accuracy for similar population compositions. The improvement is observed particularly when using the basic behavioral model. This counterintuitive result can be explained as the population evaluating site A splits into overestimating, underestimating, and accurate instead of only \begin{table}
\begin{tabular}{|c|c|c|c|c|} \hline \multirow{2}{*}{**Population Composition**} & \multicolumn{2}{c|}{**Basic Model**} & \multicolumn{2}{c|}{**Distance-Based Algorithm**} \\ \cline{2-5}  & **\% Site A** & **\% Site B** & **\% Site A** & **\% Site B** \\ \hline
105 A, 105 U, 0 O & 0\% & 100\% & 0\% & 100\% \\ \hline
0 A, 210 U, 0 O & 0\% & 100\% & 0\% & 100\% \\ \hline
30 A, 120 U, 60 O & 30\% & 70\% & 46\% & 54\% \\ \hline
70 A, 70 U, 70 O & 33.33\% & 66.67\% & 23\% & 77\% \\ \hline
60 A, 120 U, 30 O & 43\% & 57\% & 50\% & 50\% \\ \hline
105 A, 0 U, 105 O & 46\% & 54\% & 50\% & 50\% \\ \hline
90 A, 90 U, 30 O & 46.66\% & 53.34\% & 26\% & 74\% \\ \hline
60 A, 30 U, 120 O & 53\% & 47\% & 40\% & 60\% \\ \hline
0 A, 105 U, 105 O & 73\% & 27\% & 46\% & 54\% \\ \hline \end{tabular}
\end{table} 
Table 3: Comparing the accuracy of consensus accuracy when using the basic behavioral model vs. the distance-based algorithm for different swarm compositions. Errors in measurements can occur only at site A (red). accurate. Hence, both the parts of accurate and underestimating will reinforce the commitment to site B instead of site A, contributing to the shift of the collective decision to the higher-in-quality site--i.e., site B. Finally, our results show a high sensitivity of the distance-based algorithm to parameter \(\zeta\). \(\zeta\) is used as a lower-bound of number of interactions, above which a non-accurate robot starts to classify itself as accurate. In order to illustrate the role of parameter \(\zeta\), we run the decision experiment after disabling the use of this parameter. Consequently, overestimating and underestimating robots do not have the chance to classify themselves as accurate at any time of the experiment.