Voting System - Evaluating Voting Systems Using Criteria - Experimental Criteria

Experimental Criteria

It is possible to simulate large numbers of virtual elections on a computer and see how various voting systems compare in practical terms. Since such investigations are more difficult than simply proving that a given system does or does not satisfy a given mathematical criterion, results are not available for all systems. Also, these results are sensitive to the parameters of the model used to generate virtual elections, which can be biased either deliberately or accidentally.

One desirable feature that can be explored in this way is maximum voter satisfaction, called in this context minimum Bayesian regret. Such simulations are sensitive to their assumptions, particularly with regard to voter strategy, but by varying the assumptions they can give repeatable measures that bracket the best and worst cases for a voting system. To date, the only such simulation to compare a wide variety of voting systems was run by a range-voting advocate and was not published in a peer-reviewed journal. It found that Range voting consistently scored as either the best system or among the best across the various conditions studied.

Another aspect which can be compared through such Monte Carlo simulations is strategic vulnerability. According to the Gibbard-Satterthwaite theorem, no voting system can be immune to strategic manipulation in all cases, but certainly some systems will have this problem more often than others. M. Balinski and R. Laraki, the inventors of the majority judgment system, performed such an investigation using a set of simulated elections based on the results from a poll of the 2007 French presidential election which they had carried out using rated ballots. Comparing range voting, Borda count, plurality voting, approval voting with two different absolute approval thresholds, Condorcet voting, and majority judgment, they found that range voting had the highest (worst) strategic vulnerability, while their own system majority judgment had the lowest (best).

Balinski and Laraki also used the same data to investigate how likely it was that each of those systems, as well as runoff voting, would elect a centrist. Opinions differ on whether this is desirable or not. Some argue that systems which favor centrists are better because they are more stable; others argue that electing ideologically purer candidates gives voters more choice and a better chance to retrospectively judge the relative merits of those ideologies; while Balinski and Laraki argue that both centrist and extremist candidates should have a chance to win, to prevent forcing candidates into taking either position. According to their model, plurality, runoff voting, and approval voting with a higher approval threshold tended to elect extremists (100%, 98%, and 94% of the time, respectively); majority judgement elected both centrists and extremists (56% extremists); and range, Borda, and approval voting with a lower approval threshold elected centrists (6%; 0.25%–13% depending on the number of candidates; and 6% extremists; respectively). However, their model did not take into account voters' strategic reactions to the system used, such as "lesser of two evils" voting under plurality.

Simulated elections in a two-dimensional issue space can also be graphed to visually compare election methods; this illustrates issues like nonmonotonicity, clone-independence, and tendency to elect centrists vs extremists.