Information sharing in democratic mechanisms (Q776856)

This paper starts from the notion of a mechanism, designed in terms of a map from messages to outcomes and a decision-making process in which a designer announces the mechanism, then, citizens report their types and, finally, the outcome that the mechanism associates to the reported type profile is implemented. The paper proposes a concept of democratic mechanism, modifying that notion of mechanism in three ways: first the space of messages is restricted: only binary messages are allowed; secondly, a status quo can only be replaced by a new policy if the majority of citizens agree; finally, a selfish agenda-setter chooses the feasible alternative which is then voted upon. Once the state of nature has been revealed, the agenda-setter may want to use this knowledge for his own benefit, rather than work ``in good faith'' towards the implementation of the Condorcet winner. Such strategic behavior by the agenda-setter is called exploitation throughout this paper. An impossibility result and an existence result are presented: first, it is shown that the simplest possible (baseline) democratic mechanisms, which rely on a single voting stage preceded by binary communication fails to generally implement the Condorcet winner. Implementation fails because citizens manipulate information sharing or because the agenda-setter exploits information sharing. The existence result is that a democratic mechanism can be built which is immune to both the voters' and the agenda-setter's attempts to manipulate or exploit information sharing, and which therefore implements the Condorcet winner. This democratic mechanism relies on two features: It grants a conditional privilege to a small random sample of the population, and requires a two-stage voting procedure.