Multiwinner approval voting

Many multiwinner voting rules can be manipulated: voters can increase their satisfaction by reporting false preferences.

The most common form of manipulation is subset-manipulation, in which a voter reports only a strict subset of his approved candidates.

A multiwinner voting rule is called strategyproof if no voter can increase his satisfaction by reporting false preferences.

There are several variants of this property, depending on the potential outcome of the manipulation: Strategyproofness properties can also be classified by the type of potential manipulations:[11] Lackner and Skowron[11] focus on the class of ABC-counting rules (an extension of positional scoring rules to multiwinner voting).

[clarification needed] Utilitarian approval voting is the only non-trivial ABC counting rule satisfying both axioms.

[12] Specifically, the following three properties are incompatible whenever k ≥ 3, n is a multiple of k, and the number of candidates is at least k+1: The proof is by induction; the base case (k=3) was found by a SAT solver.

Lackner and Skowron[11] quantified the trade-off between strategyproofness and proportionality by empirically measuring the fraction of random-generated profiles for which some voter can gain by misreporting.

Barrot, Lang and Yokoo[13] present a similar study of another family of rules, based on ordered weighted averaging and the Hamming distance.

She proves that Thiele's rules (such as PAV) resist some common forms of manipulations, and it is strategyproof for "optimistic" voters.

Lackner and Skowron[11] define a strong extension called stochastic-dominance-strategyproofness, and prove that it characterizes the utilitarian approval voting rule.

[20] Bei, Lu and Suksompong[21] extend the committee election model to a setting in which there is a continuum of candidates, represented by a real interval [0, c], as in fair cake-cutting.

Lu, Peters, Aziz, Bei and Suksompong[22] extend these definitions to settings with mixed divisible and indivisible candidates (see justified representation).