Restricted Manipulation in Iterative Voting: Condorcet Efficiency and Borda Score

Introduction to Computational Social Choice

“…In a paper that initiated a great deal of activity in this area, Meir et al (2010) proved for the plurality rule that, if voters update their ballots one at a time and adopt a myopic best-response strategy, then the process converges to a Nash equilibrium, whatever the initial state. Other voting rules and other assumptions on voter behavior were considered by several authors (e.g., Chopra et al, 2004;Lev and Rosenschein, 2012;Reyhani and Wilson, 2012;Grandi et al, 2013;Obraztsova et al, 2015a). Reijngoud and Endriss (2012) added the assumption of incomplete knowledge regarding the voting intentions of others and Meir et al (2014) added the assumption of uncertainty regarding this information.…”

A local-dominance theory of voting equilibria

“…In particular, in Example 1 voter v does not have a response that is better than his current action (c). More recent papers on the iterative setting suggested other myopic strategies (Grandi et al, 2013), which suffer from similar problems.…”

Computational Social Choice: The First Ten Years and Beyond

“…For instance, one can consider settings where voters submit their ballots one by one; the appropriate solution concept is then subgame-perfect Nash equilibrium [58,133]. Alternatively, one can consider dynamic mechanisms, where voters take turns changing their ballots in response to the observed outcome, until no voter has an incentive to make a change: this line of work was initiated by Meir et al [97], who focused on better/best-response dynamics of plurality voting, and has been subsequently extended to other voting rules (see, e.g., [84,93,104,116]). Convergence and complexity of iterative voting depends on whether voters get to observe the full set of current ballots or just some aggregated information about the ballot profile [68,98,115], whether voters compute their best responses at each step, or may use other heuristics [84,105], and whether voters exhibit secondary preferences, such as laziness or truth bias [113]; see the recent survey by Meir [96].…”