Robustness Among Multiwinner Voting Rules

Abstract

We investigate how robust are results of committee elections to small changes in the input preference orders, depending on the voting rules used. We find that for typical rules the effect of making a single swap of adjacent candidates in a single preference order is either that (1) at most one committee member can be replaced, or (2) it is possible that the whole committee can be replaced. We also show that the problem of computing the smallest number of swaps that lead to changing the election outcome is typically NP-hard, but there are natural FPT algorithms. Finally, for a number of rules we assess experimentally the average number of random swaps necessary to change the election result.

A Quantitative Analysis of Multi-Winner Rules

“…Another approach to understanding the nature of different multi-winner rules is to analyze how these rules behave on certain subdomains of preferences, where their behavior is much easier to interpret, e.g., on two-dimensional geometric preferences [16], on party-list profiles [11], or on single-peaked and single-crossing domains [2]. Other approaches include analyzing certain aspects of multi-winner rules in specifically-designed probabilistic models [21,23,30,34], quantifying regret and distortion in utilitarian models [12], assessing their robustness [9], and evaluating them based on data collected from surveys [31,39].…”

How Similar Are Two Elections?

“…Choosing Elections to Evaluate Algorithms On. There is a growing body of work in computational social choice that provides experimental analyses of elections (see, e.g., the works of Narodytska and Walsh (2014), Aziz et al (2015), Caragiannis et al (2017), and Bredereck et al (2017)), often using the PrefLib database (Mattei and Walsh 2013). Designing convincing experiments, however, requires care.…”

Algorithms for destructive shift bribery

“…First, one could always study more election rules. Second, one can analyze the robustness of various election rules based on the number of backward shifts of the winner needed to change their outcome [36,5]. This direction can also be seen as studying a more fine-grained extension of the Margin of Victory problem.…”

“…In recent years, Constructive Shift Bribery received quite some attention. The problem was defined by Elkind et al [16], as a simplified variant of Swap Bribery (which itself received some attention, for example, in the works of Bredereck et al [5], Dorn and Schlotter [13], Faliszewski et al [19], Knop et al [24], and papers regarding combinatorial domains, such as those of Mattei et al [27] and Dorn and Krüger [12]; importantly, Shiryaev et al [36] studied a variant of Destructive Swap Bribery and we comment on their work later). Elkind et al [16] have shown that Constructive Shift Bribery is NP-hard for the Borda, Copeland, and Maximin voting rules, but polynomial-time solvable for the k-Approval family of rules.…”

“…2 This work is very closely related to ours, but the definition of the problem is somewhat different (more general types of swaps but less general price functions). Very recently Bredereck et al [5] studied an analogous setting (Destructive Swap Bribery with unit prices) for the case of multiwinner voting rules.…”