Open AccessVoting on multiple issues: What to put on the ballot?
Author(s) -
Gershkov Alex,
Moldovanu Benny,
Shi Xianwen
Publication year - 2019
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te3193
Subject(s) - voting , dimension (graph theory) , mathematical economics , independent and identically distributed random variables , euclidean geometry , mathematics , anti plurality voting , cardinal voting systems , distribution (mathematics) , simple (philosophy) , combinatorics , computer science , statistics , political science , random variable , mathematical analysis , philosophy , geometry , epistemology , politics , law
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.