Voting on multiple issues: What to put on the ballot?

Abstract

We study a multidimensional collective decision under incomplete information. Agents have Euclidean preferences and vote by simple majority on each issue (dimension), yielding the coordinate-wise median. Judicious rotations of the orthogonal axes-the issues that are voted upon-lead to welfare improvements. If the agents' types are drawn from a distribution with independent marginals, then under weak conditions, voting on the original issues is not optimal. If the marginals are identical (but not necessarily independent), then voting first on the total sum and next on the differences is often welfare superior to voting on the original issues. We also provide various lower bounds on incentive efficiency: in particular, if agents' types are drawn from a log-concave density with independently and identically distributed marginals, a second-best voting mechanism attains at least 88% of the first-best efficiency. Finally, we generalize our method and some of our insights to preferences derived from distance functions based on inner products.

Agenda-Manipulation in Ranking

“…Specifically, this paper belongs to the literature on agenda-setting under incomplete information about voters' preferences. This literature long consisted of a single pioneering paper (Ordeshook and Palfrey, 1988), but has recently received interest from Kleiner and Moldovanu (2017), Gershkov et al (2017Gershkov et al ( , 2019 and . We depart from these papers by considering a committee tasked not with choosing a single alternative, but rather with ranking all of the alternatives.…”

Aggregation over Metric Spaces: Proposing and Voting in Elections, Budgeting, and Legislation

“…The spatial model of elections (Enelow & Hinich, 1984) considers voter ideal elements and infers voter preferences using an underlying Euclidean metric. This model was later extended to Hilbert spaces (Gershkov, Moldovanu, & Shi, 2019), normed spaces (Peters, van der Stel, & Storcken, 1993), and semi-inner product spaces (Gershkov, Moldovanu, & Shi, 2020). Here, we consider general metric spaces, including discrete and not limited to complete and well-structured ones.…”

Monotonic norms and orthogonal issues in multidimensional voting

“…15;16 What is missing for DIC in more than two dimensions is an additivity on the left property. 17 Gershkov, Moldovanu and Shi [2019] maximize utilitarian welfare over the class of marginal median mechanisms in Hilbert spaces. 18 Technically, they maximize over the continuum, multiplicative group of linear isometries (rotations).…”

“…A comparison of the two mechanisms from an utilitarian perspective (for the case p = 2) is conducted in Gershhkov, Moldovanu and Shi [2019]. There, we also establish the relations between theses two mechanisms and the bottom-up vs. top-down budgeting procedures used by legislatures (see for example Ferejohn and Krehbiel [1987], Groves [1994], and Poterba and von Hagen [1999]) 47 .…”

“…The case p < 1 does not yield a normed space, and it is not considered here.3 Recall that Auerbach's theorem yields at least two DIC mechanisms.4 It is interesting to note that the welfare analysis in Gershkov, Moldovanu and Shi[2019] for the Euclidean case focused precisely on these coordinates.5 Shepsle proposed the structure-induced equilibrium as a response to the lack of equilibria in multidimensional models where voting is not formally constrained by institutional arrangements. See also Feld and Grofman[1988] and Kramer[1972],[1973].…”