Winner Determination and Strategic Control in Conditional Approval Voting

Our work focuses on a generalization of the classic Minisum approval voting rule, introduced by Barrot and Lang (2016), and referred to as Conditional Minisum (CMS), for multi-issue elections. Although the CMS rule provides much higher levels of expressiveness, this comes at the expense of increased computational complexity. In this work, we study further the issue of efficient algorithms for CMS, and we identify the condition of bounded treewidth (of an appropriate graph that emerges from the provided ballots), as the necessary and sufficient condition for polynomial algorithms, under common complexity assumptions. Additionally we investigate the complexity of problems related to the strategic control of such elections by the possibility of adding or deleting either voters or alternatives. We exhibit that in most variants of these problems, CMS is resistant against control.

Condorcet Loser in 2016: Apparently Trump; Condorcet Winner: Not Clinton?

Using thermometer score data from the ANES, we show that while there may have been no clear-cut Condorcet winner among the 2016 US presidential candidates, there appears to have been a Condorcet loser: Donald Trump. Thus the surprise is that the electorate preferred not only Hillary Clinton, but also the two “minor” candidates, Gary Johnson and Jill Stein, to Trump. Another surprise is that Johnson may have been the Condorcet winner. A minimal normative standard for evaluating voting systems is advanced, privileging those systems that select Condorcet winners if one exists, and critiquing systems that allow the selection of Condorcet losers. A variety of voting mechanisms are evaluated using the 2016 thermometer scores: Condorcet voting, plurality, Borda, (single winner) Hare, Coombs, range voting, and approval voting. We conclude that the essential problem with the existing voting procedure—Electoral College runoff of primary winners of two major parties—is that it (demonstrably) allows the selection of a Condorcet loser.

Characterising scoring rules by their solution in iteratively undominated strategies

We characterize voting procedures according to the social choice correspondence they implement when voters cast ballots strategically, applying iteratively undominated strategies. In elections with three candidates, the Borda Rule is the unique positional scoring rule that satisfies unanimity (U) (i.e., elects a candidate whenever it is unanimously preferred) and is majoritarian after eliminating a worst candidate (MEW)(i.e., if there is a unanimously disliked candidate, the majority-preferred among the other two is elected). In a larger class of rules, Approval Voting is characterized by a single axiom that implies both U and MEW but is weaker than Condorcet-consistency (CON)—it is the only direct mechanism scoring rule that is majoritarian after eliminating a Pareto-dominated candidate (MEPD)(i.e., if there is a Pareto-dominated candidate, the majority-preferred among the other two is elected); among all finite scoring rules that satisfy MEPD, Approval Voting is the most decisive. However, it fails a desirable monotonicity property: a candidate that is elected for some preference profile, may lose the election once she gains further in popularity. In contrast, the Borda Rule is the unique direct mechanism scoring rule that satisfies U, MEW and monotonicity (MON). There exists no direct mechanism scoring rule that satisfies both MEPD and MON and no finite scoring rule satisfying CON.

Iterative Learning for K-Approval Votes in Crowdsourcing Systems

Crowdsourcing systems have emerged as cornerstones to collect large amounts of qualified data in various human-powered problems with a relatively low budget. In eliciting the wisdom of crowds, many web-based crowdsourcing platforms have encouraged workers to select top-K alternatives rather than just one choice, which is called “K-approval voting”. This kind of setting has the advantage of inducing workers to make fewer mistakes when they respond to target tasks. However, there is not much work on inferring the correct answer from crowd-sourced data via a K-approval voting. In this paper, we propose a novel and efficient iterative algorithm to infer correct answers for a K-approval voting, which can be directly applied to real-world crowdsourcing systems. We analyze the average performance of our algorithm, and prove the theoretical error bound that decays exponentially in terms of the quality of workers and the number of queries. Through extensive experiments including the mixed case with various types of tasks, we show that our algorithm outperforms Expectation and Maximization (EM) and existing baseline algorithms.

Reflecting People’s Will: Evaluating elections with computer aided simulations

The aim of this study is evaluate various single winner voting systems with the help of computer aided simulations. The impact of phenomena such as strategic voting, spoiler effect and centre squeeze are studied on various election systems such as First Past the Post, Ranked voting, Approval voting and Score voting. The democratic process gives great moral legitimacy to the winner as they are deemed to be chosen by the people, ergo the election system too needs to accurately reflect the will of all the people. Single winner systems or “winner takes all” systems have the advantage of decisive governments as compared to proportional systems but by its construct exclude parliamentary representation to a large percentage of voters who ended up on the losing side. It is therefore even more important that the single winner system mirror the voters mandate as accurately as possible. I conclude after evaluation that alternate systems such as Instant Runoff or Approval voting could be considered in lieu of the FPTP systems as they have fewer flaws and are more likely to give a truer representation of electorate’s choice.

Approval voting without ballot restrictions

We axiomatically study voting rules without making any assumption on the ballots that voters are allowed to cast. In this setting, we characterize the family of “endorsement rules,” which includes approval voting and the plurality rule, via the imposition of three normative conditions. The first condition is the well known social‐theoretic principle of consistency; the second one, unbiasedness, roughly requires social outcomes not to be biased toward particular candidates or voters; the last one, dubbed no single voter overrides, demands that the addition of a voter to an electorate cannot radically change the social outcome. Building on this result, we provide the first axiomatic characterization of approval voting without the approval balloting assumption. The informational basis of approval voting as well as its aggregative rationale are jointly derived from a set of conditions that can be defined on most of the ballot spaces studied in the literature.