Context. Modeling how cold giant planets form around M dwarfs remains a challenge, both because their protoplanetary disks can lack sufficient mass and because such planets are expected to migrate inward while interacting with the disk. Moreover, it remains unknown whether inner rocky planets can survive in systems that host a cold giant around very low-mass stars, which could have important implications for the habitability of rocky worlds. Aims. We investigated the conditions required for the formation of giant planets at large orbital distances (1- 3 au) around a 0.1 M_· star, and explored the circumstances under which a close-in rocky planet can survive. Methods. We performed N-body simulations in which planetary embryos grow through pebble accretion, followed by gas accretion during the disk lifetime. Assuming a local disk turbulent viscosity (α_t) of 10^{- 4}, we included planet-disk interactions throughout the disk evolution, using a new prescription that accounts for the onset of outward migration when the planet-to-star mass ratio (q) exceeds 0.002. Results. We find that a cold giant planet can form around a late M dwarf, even with an initial pebble mass of only 6 M_·, provided the disk gas mass is 10% of the stellar mass. This outcome requires a compact 20 au disk in which the inner, viscosity-dominated region has a high gas surface density set by a low accretion viscosity (α_g=10^{- 4}), that planet- planet collisions assemble a a∼ 5 M_· core within 1 Myr, and that the gas disk survives for 10 Myr. In addition, an inner rocky planet can survive in a close-in orbit if it migrates into the inner disk cavity before the outer body grows into a giant. Conclusions. The initial dust mass required for giant planet formation around very low-mass stars does not need to be as extreme as previously thought. A combination of planet- planet collisions, efficient pebble accretion, and a long disk lifetime plays a key role in enabling the formation of cold giant planets with masses between those of Saturn and Jupiter.

We adopt an emerging and prominent vision of human-centred Artificial Intelligence that requires building trustworthy intelligent systems. Such systems should be capable of dealing with the challenges of an interconnected, globalised world by handling plurality and by abiding by human values. Within this vision, pluralistic value alignment is a core problem for AI– that is, the challenge of creating AI systems that align with a set of diverse individual value systems. So far, most literature on value alignment has considered alignment to a single value system. To address this research gap, we propose a novel method for estimating and aggregating multiple individual value systems. We rely on recent results in the social choice literature and formalise the value system aggregation problem as an optimisation problem. We then cast this problem as an ℓ_p-regression problem. Doing so provides a principled and general theoretical framework to model and solve the aggregation problem. Our aggregation method allows us to consider a range of ethical principles, from utilitarian (maximum utility) to egalitarian (maximum fairness). We illustrate the aggregation of value systems by considering real-world data from two case studies: the Participatory Value Evaluation process and the European Values Study. Our experimental evaluation shows how different consensus value systems can be obtained depending on the ethical principle of choice, leading to practical insights for a decision-maker on how to perform value system aggregation.