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

Alex Gershkov, Benny Moldovanu, Xianwen Shi

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageAmerican English
Pages (from-to)555-596
Number of pages42
JournalTheoretical Economics
Issue number2
StatePublished - May 2019

Bibliographical note

Publisher Copyright:
Copyright © 2019 The Authors.


  • D72
  • D78
  • D82
  • Multidimensional voting
  • budgeting procedure
  • mechanism design
  • rotation


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