Comparing Election Methods Where Each Voter Ranks Only Few Candidates

Election rules are formal processes that aggregate voters preferences, typically to select a single candidate, called the winner. Most of the election rules studied in the literature require the voters to rank the candidates from the most to the least preferred one. This method of eliciting preferences is impractical when the number of candidates to be ranked is large. We ask how well certain election rules (focusing on positional scoring rules and the Minimax rule) can be approximated from partial preferences collected through one of the following procedures: (i) randomized-we ask each voter to rank a random subset of $\ell$ candidates, and (ii) deterministic-we ask each voter to provide a ranking of her $\ell$ most preferred candidates (the $\ell$-truncated ballot). We establish theoretical bounds on the approximation ratios and we complement our theoretical analysis with computer simulations. We find that mostly (apart from the cases when the preferences have no or very little structure) it is better to use the randomized approach. While we obtain fairly good approximation guarantees for the Borda rule already for $\ell = 2$, for approximating the Minimax rule one needs to ask each voter to compare a larger set of candidates in order to obtain good guarantees

Collecting, Classifying, Analyzing, and Using Real-World Elections

We present a collection of $7582$ real-world elections divided into $25$ datasets from various sources ranging from sports competitions over music charts to survey- and indicator-based rankings. We provide evidence that the collected elections complement already publicly available data from the PrefLib database, which is currently the biggest and most prominent source containing $701$ real-world elections from $36$ datasets. Using the map of elections framework, we divide the datasets into three categories and conduct an analysis of the nature of our elections. To evaluate the practical applicability of previous theoretical research on (parameterized) algorithms and to gain further insights into the collected elections, we analyze different structural properties of our elections including the level of agreement between voters and election's distances from restricted domains such as single-peakedness. Lastly, we use our diverse set of collected elections to shed some further light on several traditional questions from social choice, for instance, on the number of occurrences of the Condorcet paradox and on the consensus among different voting rules

Imputation, Social Choice, and Partial Preferences

A novel technique for deciding the outcome of an election when only partial preference ballots are submitted, using machine learning. An explicit connection between machine learning and social choice is discovered, which suggests many possible avenues of future work