We address the self-stabilizing bit-dissemination problem, designed to capture the challenges of spreading information and reaching consensus among entities with minimal cognitive and communication capacities. Specifically, a group of $n$ agents is required to adopt the correct opinion, initially held by a single informed individual, choosing from two possible opinions. In order to make decisions, agents are restricted to observing the opinions of a few randomly sampled agents, and lack the ability to communicate further and to identify the informed individual. Additionally, agents cannot retain any information from one round to the next. According to a recent publication in SODA (2024), a logarithmic convergence time without memory is achievable in the parallel setting (where agents are updated simultaneously), as long as the number of samples is at least $\Omega(\sqrt{n \log n})$. However, determining the minimal sample size for an efficient protocol to exist remains a challenging open question. As a preliminary step towards an answer, we establish the first lower bound for this problem in the parallel setting. Specifically, we demonstrate that it is impossible for any memory-less protocol with constant sample size, to converge with high probability in less than an almost-linear number of rounds. This lower bound holds even when agents are aware of both the exact value of $n$ and their own opinion, and encompasses various simple existing dynamics designed to achieve consensus. Beyond the bit-dissemination problem, our result sheds light on the convergence time of the "minority" dynamics, the counterpart of the well-known majority rule, whose chaotic behavior is yet to be fully understood despite the apparent simplicity of the algorithm.

Artificial intelligence is for lazy investors and this for two orders of reasons: it reduces the frequency of trading actions and it relieves you from the necessity of having an opinion. Any of our action requires an opinion and, in trading, our opinions are, usually, like TNT in the hands of a chimp. A lot of opinions to have, on gold, on oil, on the stocks, on the banks, on EVERYTHING!! I Must Have A Correct Opinion On EVERYTHING! Otherwise I Will Lose Money! In fact, it ends up that we lose money, confidence, respect, with rising tensions and crisis of any kind around, and still we have a very confused opinion on something, ignoring all the rest.

We investigate opinion dynamics in a fully-connected system, consisting of $n$ identical and anonymous agents, where one of the opinions (which is called correct) represents a piece of information to disseminate. In more detail, one source agent initially holds the correct opinion and remains with this opinion throughout the execution. The goal for non-source agents is to quickly agree on this correct opinion, and do that robustly, i.e., from any initial configuration. The system evolves in rounds. In each round, one agent chosen uniformly at random is activated: unless it is the source, the agent pulls the opinions of $\ell$ random agents and then updates its opinion according to some rule. We consider a restricted setting, in which agents have no memory and they only revise their opinions on the basis of those of the agents they currently sample. As restricted as it is, this setting encompasses very popular opinion dynamics, such as the voter model and best-of-$k$ majority rules. Qualitatively speaking, we show that lack of memory prevents efficient convergence. Specifically, we prove that no dynamics can achieve correct convergence in an expected number of steps that is sub-quadratic in $n$, even under a strong version of the model in which activated agents have complete access to the current configuration of the entire system, i.e., the case $\ell=n$. Conversely, we prove that the simple voter model (in which $\ell=1$) correctly solves the problem, while almost matching the aforementioned lower bound. These results suggest that, in contrast to symmetric consensus problems (that do not involve a notion of correct opinion), fast convergence on the correct opinion using stochastic opinion dynamics may indeed require the use of memory. This insight may reflect on natural information dissemination processes that rely on a few knowledgeable individuals.

In collective decision-making, designing algorithms that use only local information to effect swarm-level behaviour is a non-trivial problem. We used machine learning techniques to teach swarm members to map their local perceptions of the environment to an optimal action. A curriculum inspired by Machine Education approaches was designed to facilitate this learning process and teach the members the skills required for optimal performance in the collective perception problem. We extended upon previous approaches by creating a curriculum that taught agents resilience to malicious influence. The experimental results show that well-designed rules-based algorithms can produce effective agents. When performing opinion fusion, we implemented decentralised resilience by having agents dynamically weight received opinion. We found a non-significant difference between constant and dynamic weights, suggesting that momentum-based opinion fusion is perhaps already a resilience mechanism.