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Abstract
The purpose of this paper is to discuss the extent to which allowing for individuals to be indifferent among alternatives may alter the qualitative results that are obtained in social choice theory when domain restrictions are defined on profiles of linear orders. The general message is that indifferences require attention and careful treatment, because the translation of results from a world without indifferences to another where agents may be indifferent among some alternatives is not always a straightforward exercise. But the warning is not one-directional: sometimes indifferences complicate the statement of results, but preserve their essential message. Sometimes, they help to create domains where some rules work better than in the presence of linear orders. In other cases, however, their presence destroys the positive results that would apply in their absence. I provide examples of these three situations.

Two candidates competing for election may raise some issues for debate during the electoral campaign, while avoiding others. We present a model in which the decision to introduce an issue, or to reply to the opponent's position on one that she raised, may change the further list of topics that end up being discussed. Candidates' strategic decisions are driven by their appraisal of their expected vote share at the end of the campaign. Real phenomena observed during campaigns, like the convergence of the parties to address the same issues, or else their diverging choice on which ones to treat, or the relevance of issue ownership can be explained within our stark basic model. Most importantly, our analysis is based on a novel concept of equilibrium that avoids the (often arbitrary) use of predetermined protocols. This allows us to endogenously predict not only the list of topics that will be touched upon by each candidate, but also the order in which they will be addressed.

AbstractWe propose three mechanisms to reach compromise between two opposing parties. They are based on the use of Rules of k Names, whereby one of the parties proposes a shortlist and the other chooses from it. Methods of this class are used in practice to appoint Supreme Court justices and have been recently proposed for arbitration selection processes. Those we suggest are flexible and allow the parties to participate in the endogenous determination of the role of proposer and the shortlist size. They involve few stages, implement the Unanimity Compromise Set, and are robust to the strategic inclusion of candidates.

We study the possibilities for agenda manipulation under strategic voting for two prominent sequential voting procedures: the amendment procedure and the successive procedure. We show that a well known result for tournaments, namely that the successive procedure is (weakly) more manipulable than the amendment procedure at any given preference profile, extends to arbitrary majority quotas. Moreover, our characterizations of the attainable outcomes for arbitrary quotas allow us to compare the possibilities for manipulation across different quotas. It turns out that the simple majority quota maximizes the d omain of preference profiles for which neither procedure is manipulable, but at the same time neither the simple majority quota nor any other quota uniformly minimizes the scope of manipulation once this becomes possible. Hence, quite surprisingly, simple majority voting is not necessarily the optimal choice of a society that is concerned about agenda manipulation.