Evaluation of single-prioritization voting systems in controlled collective Parrondo’s games

We examine an ensemble of individuals playing three individually losing games. With three games to choose from, what happens when players are allowed to vote for the game that will be played by the entire ensemble? The collective choice cannot conform to the preference of all the players simultaneously. As such, a subset of players will have to implement strategies to force the outcome of the vote to favour their preferences. How does this affect the outcome of playing these three games? We show that for plurality voting, the introduction of the spoiler option significantly changes the outcome of Parrondo’s games. Rank choice and approval voting are not susceptible to the spoiler effect. However, the complexity associated with rank choice and approval voting implies that other systemic flaws, such as the centre squeeze and the Volunteer’s dilemma, emerge.