Engaging all content providers, including newcomers or minority demographic groups, is crucial for online platforms to keep growing and working.
A notable example is represented by reputation-based ranking systems, a class of systems that rely on users' reputation to generate a non-personalized item-ranking, proved to be biased against certain demographic classes.
First, we provide necessary and sufficient conditions for their structural state and input observability that can be efficiently verified in $O((m(n+p))^2)$, where $n$ is the number of state variables, $p$ is the number of unknown inputs, and $m$ is the number of modes.
Under mild assumptions, we show that: (i) the proposed method converges exponentially to the consensus of the regular agents; (ii) if a regular agent identifies a neighbor as an attacked node, then it is indeed an attacked node; (iii) if the consensus value of the normal nodes differs from that of any of the attacked nodes' values, then the reputation that a regular agent assigns to the attacked neighbors goes to zero.
To reduce this effect, we propose a novel post-processing approach that balances personalization and equality of recommended opportunities.
In this paper, we formulate the concept of disparate reputation (DR) and study if users characterized by sensitive attributes systematically get a lower reputation, leading to a final ranking that reflects less their preferences.
Also, by clustering users, the effect of bribery in the proposed multipartite ranking system is dimmed, comparing to the bipartite case.