Analyzing a networked social algorithm for collective selection of representative committees

A recent work (Hernández, et al., 2018) introduced a networked voting rule supported by a trust-based social network, where indications of possible representatives were based on individuals opinions. Individual contributions went beyond a simple vote-counting and were based on proxy voting. This mechanism selects committees with high levels of representativeness, weakening the possibility of patronage relations. By incorporating the integrity of individuals and its perception, we here address the question of the resulting committee’s trustability. Our results show that this voting rule provides sufficiently small committees with high levels of representativeness and integrity. Furthermore, the voting system displays robustness to strategic and untruthful application of the voting algorithm.

I have read carefully the paper entitled as "Analyzing a networked social algorithm for collective selection of representative committees" by Hernández et al., submitted to PLoS ONE for publication. The paper builds on an earlier work published by the same set of authors recently [1], which proposes an algorithm to construct representative committees using personal and collective preferences in networked populations. In this paper they extend their earlier findings by considering committee's trustability.
I have some comments what I suggest to the authors to consider: - Figure 1 has been already published in [1] and this fact is not acknowledged in the actual manuscript.
Thanks for pointing out this issue, we corrected that in the revised version.
-It is not clear what is novel algorithmically and in terms of results as compared to the previous paper of the authors [1]. Please highlight.
The new ingredient in the algorithm appears in equation (2) where the overlap is multiplied by the perceived integrity. In the previous paper, the transfer of votes depends only on opinion's overlap. The introduction of this term allows us to study the performance of the algorithm with respect to the committee's integrity. We write it explicitly on the revised version in order to make this clearer.
-Their method assumes global network knowledge about the underlying social network what is commonly unknown. The authors (implicitly) argue that this is not a problem as their method is meant for online social networks where social ties are mapped with high precision. However, it is usually not the case as (a) detailed online social network data is not available but only for the provider, (b) it may contain several non-real social ties and non-human actors (e.g. bots), and (c) it may not capture all social ties (e.g. offline relationships) which at the same time might be important for opinion formation. I would suggest to the authors to address these questions and show how the outcome of their process is changing by assuming incomplete knowledge about the network structure.
Thanks for pointing out this very important issue. In order to illustrate the robustness of the algorithm, we ran new simulations where we considered a fraction of users as unavailable (in the sense of participating as representatives).
In practice, it washes out the participation of a fraction of the committee representatives with their respective voting trees. Our results show that even for very high values of this fraction (0.8) the algorithm performs pretty well. These results makes it possible to reasonably think that incomplete knowledge of the network structure would not jeopardize our conclusions. We mention these results in the body of our manuscript and include figures and description in the new supplementary material.
-In page 4 the authors explain that a representative committee can be selected in two steps: first identifying cycles in the representative graphs and then by thresholding to select people by the number of votes they gained in their downstream tree structure.
In my opinion, it is a possible scenario that a group of people agree in advance to bias the first step of this process to vote such that they form a cycle. This way they would increase the probability that some of them will be selected from the cycle in the committee. The authors address resilience issues in the end of the manuscript (starting from line 218) but miss to address the problem when fraud is not individual but organized between a larger group of people.
Thanks for raising this interesting question. To address this issue we considered a slightly different situation. We introduced a fraction of individuals who refuse to transfer their votes, making them self-candidates to the resulting committee. Again we observe the system to be very robust and even for a very high fraction of self-declared individuals (0.8), we find it to behave properly, achieving committees with high levels of representativity and integrity. These results are also included in the new supplementary material and commented on the body of our manuscript.
-In the paragraph starting from line 119 the authors discuss that they tested their algorithm on three conventional network models while they were concentrating on the dependencies of the selection outcome on generic network properties like degree heterogeneity, average connectivity, or shortest paths. One important characteristic missed here is community structure, which can largely influence the outcome of the committee selection algorithm. I would suggest to the authors to use one of the many (Planted L-partition model, NG benchmark, LFR benchmark) community network model to test the effect of intra/inter community link density on the outcomes.
Thanks again, this is also a very interesting point.
In order to answer this question, we generated random networks with a specific number of communities and modularity. The results are described in the new supplementary material and commented on the body of the article. Again the system presents a robust behavior allowing the conformation of a committee with high values of representativity and integrity even for highly modular networks.
-For validation purposes it would be necessary that the authors explore their model via data-driven simulations where they take a real social network as an underlying structure and model the committee selection process on the top. Simulating the process only on synthetic overly simplified network models is important for exploration but may provide results far from reality.
Thanks again. We ran new simulations considering the network structure of two online social networks: one from a music streaming service (Deezer) and the other from a free online social network (Orkut). In both cases the results are consistent with the ones obtained for synthetic networks. We include these results in the manuscript.

List of Changes (summary):
 In line 85, we clarify the algorithmic contribution of the paper.  In Fig. 1