Implications of Bounds in Approval Voting

Abstract

We analyze and show the implications of required limitations on common voting system criteria for the three different versions of voting restrictions in the election website proposed for the Saudi Chamber of Commerce Business Awards. Electoral systems properties might be considered as performance indicators of a voting system. When presented with the same underlying voter preferences, different voting systems constraints might produce different results. Those voting systems may violate or satisfy voting properties. Distinct ways meet different requirements, and it was shown that no particular method can meet all of them.
The studied voting systems mechanisms on the aforementioned website are called: Single Casting, Limited Casting, and Unlimited Casting methods.
The first version permits the voter to vote for one unique candidate, and corresponds to the common Single Plurality Vote mechanism. The second version permits the voter to vote for three unique candidates at a time, and it is a new method that can be described as the Approval Voting with bounded ballot size. The third version permits the voter to vote for all candidates, and corresponds to the common Approval Voting mechanism.
In the long version analysis, we proved that one of the new voting schemes in the election website proposed for the Saudi
Chamber of Commerce Business Awards, a version of Approval Voting where the size of the ballot is bounded, a set of the properties of Approval Voting are lost, in particular Pareto efficiency, Condorcet criteria winner support, Condorcet criteria loser, and Independence to Irrelevant Alternatives.