Responsibility Gap in Collective Decision Making

TL;DR

This paper formalizes responsibility gaps in collective decision making by modeling mechanisms as trees with binary outcomes and agents who may have imperfect information. It proves a sharp dichotomy: in perfect information, a gap-free mechanism is exactly an elected dictatorship, and each such dictatorship guarantees no responsibility gap; in imperfect information, the gap-free class is strictly sandwiched between elected epistemic and elected semi-epistemic dictatorships, showing that epistemic constraints alter accountability. The authors introduce epistemic responsibility via knowledge-aware winning sets $\text{ewin}_a(o)$, and define new dictator notions (epistemic and semi-epistemic) to map the landscape of accountable mechanisms. The results illuminate how to design or analyze collective decision processes when accountability and knowledge constraints matter, and they argue that non-dictatorial gap-free designs require alternative concepts of responsibility beyond simple dictatorships.

Abstract

The responsibility gap is a set of outcomes of a collective decision-making mechanism in which no single agent is individually responsible. In general, when designing a decision-making process, it is desirable to minimise the gap. The paper proposes a concept of an elected dictatorship. It shows that, in a perfect information setting, the gap is empty if and only if the mechanism is an elected dictatorship. It also proves that in an imperfect information setting, the class of gap-free mechanisms is positioned strictly between two variations of the class of elected dictatorships.

Figures (8)

• Figure 1: Two-person Rule mechanism.
• Figure 2: (a) There is a responsibility gap at nodes $v_1$ and $v_4$. The Vice President is a dictator at node $u_2$. (b) The mechanism is gap-free. The Dean is a dictator at root node $u_1$.
• Figure 3: Drawing Straws mechanism.
• Figure 4: A single-agent decision-making mechanism with imperfect information. Dashed lines represent the relation $\sim_A$.
• Figure 5: Mechanism $M$ with imperfect information. The names of actions are only shown for the nodes in which the acting agent does not have complete information about the current node.

Theorems & Definitions (46)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Definition 6
• Definition 7
• Definition 8
• Theorem 1
• Definition 9