Egalitarian considerations play a central role in many areas of social choice theory. Applications of egalitarian principles range from ensuring everyone gets an equal share of a cake when deciding how to divide it, to guaranteeing balance with respect to gender or ethnicity in committee elections. Yet, the egalitarian approach has received little attention in judgment aggregation—a powerful framework for aggregating logically interconnected issues. We make the first steps towards filling that gap. We introduce axioms capturing two classical interpretations of egalitarianism in judgment aggregation and situate these within the context of existing axioms in the pertinent framework of belief merging. We then explore the relationship between these axioms and several notions of strategyproofness from social choice theory at large. Finally, a novel egalitarian judgment aggregation rule stems from our analysis; we present complexity results concerning both outcome determination and strategic manipulation for that rule.

Egalitarian considerations play a central role in many areas of social choice theory. Applications of egalitarian principles range from ensuring everyone gets an equal share of a cake when deciding how to divide it, to guaranteeing balance with respect to gender or ethnicity in committee elections. Yet, the egalitarian approach has received little attention in judgment aggregation-a powerful framework for aggregating logically interconnected issues. We make the first steps towards filling that gap. We introduce axioms capturing two classical interpretations of egalitarianism in judgment aggregation and situate these within the context of existing axioms in the pertinent framework of belief merging. We then explore the relationship between these axioms and several notions of strategyproofness from social choice theory at large. Finally, a novel egalitarian judgment aggregation rule stems from our analysis; we present complexity results concerning both outcome determination and strategic manipulation for that rule.

Condorcet extensions have long held a prominent place in social choice theory. A Condorcet extension will return the Condorcet winner as the unique winner whenever such an alternative exists. However, the definition of a Condorcet extension does not take into account possible manipulation by the voters. A profile where all agents vote truthfully may have a Condorcet winner, but this alternative may not end up in the set of winners if agents are acting strategically. Focusing on the class of tournament solutions, we show that many natural social choice functions in this class, such as the well-known Copeland and Slater rules, cannot guarantee the preservation of Condorcet winners when agents behave strategically. Our main result in this respect is an impossibility theorem that establishes that no tournament solution satisfying a very weak decisiveness requirement can provide such a guarantee. On the bright side, we identify several indecisive but otherwise attractive tournament solutions that do guarantee the preservation of Condorcet winners under strategic manipulation for a large class of preference extensions.

We study settings in which agents with incomplete preferences need to make a collective decision. We focus on a process of majority dynamics where issues are addressed one at a time and undecided agents follow the opinion of the majority. We assess the effects of this process on various consensus notions-such as the Condorcet winner-and show that in the worst case, myopic adherence to the majority damages existing consensus; yet, simulation experiments indicate that the damage is often mild. We also examine scenarios where the chair of the decision process can control the existence (or the identity) of consensus, by determining the order in which the issues are discussed.