Inconsistencies of Weighted Summation Voting Systems
- 1 November 1982
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Mathematics of Operations Research
- Vol. 7 (4) , 479-490
- https://doi.org/10.1287/moor.7.4.479
Abstract
Let αN be any ordinal ordering of N ≥ 3 alternatives. Select some one alternative and let αN−1 be some ordering of the remaining (N − 1) alternatives where αN−1, need not have any relationship to αn. It is shown for a voting system coming from a large class of weighted summation voting systems that there exist examples of voter profiles such that if the voters vote on N alternatives the aggregated result is αN, but if they vote on (N − 1) alternatives, the aggregated result is αN−1. This result holds even if the voting system changes with the number of alternatives.Keywords
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