We consider the effectiveness of multiobjective counterfactual explanations (MOCEs) in helping individuals learntactics, or rules of thumb, to apply when required to select a course of action in a specific context. In this setting, a counterfactual explanation compares one course of action against another. A MOCE presents this comparison by highlighting how the two options differ across a range of objectives or metrics. We conduct a study in which participants are presented with various scenarios alongside courses of action that could be implemented in those scenarios. Counterfactual explanations, including those involving multiple objectives, are used to identify the positive and negative aspects of the provided options. Participants were then required to identify the best course of action in various contexts. Participants trained with MOCE outperformed those given no explanations in seven of eight scenarios and those given single-objective counterfactual explanations (SOCEs) in four. SOCEs gave participants an aggregated outcome (expected rewards) without breaking these into specific objectives. MOCE improved tactic learning, but participants provided with SOCE or no explanation performed better in multitactic scenarios. These findings suggest that MOCE enhances tactical decision-making, but further research is needed for multitactic integration.

Mistakes made by humans, or machines, commonly arise when managing ballots cast in an election. In the 2013 Australian Federal Election, for example, 1,370 West Australian Senate ballots were lost, eventually leading to a costly re-run of the election. Other mistakes include ballots that are misrecorded by electronic voting systems, voters that cast invalid ballots, or vote multiple times at different polling locations. We present a method for assessing whether such problems could have made a difference to the outcome of a Single Transferable Vote (STV) election – a complex system of preferential voting for multi-seat elections. It is used widely in Australia, in Ireland, and in a range of local government elections in the United Kingdom and United States.

The single transferable vote (STV) is a system of preferential voting for multiseat elections. Each ballot cast by a voter is a (potentially partial) ranking over a set of candidates. No techniques currently exist for computing the margin of victory (MOV) in STV elections. The MOV is the smallest number of ballot manipulations (changes, additions, and deletions) required to bring about a change in the set of elected candidates. Knowing the MOV gives insight into how much time and money should be spent on auditing the election, and whether uncovered mistakes (such as ballot box losses) throw the election result into doubt—requiring a costly repeat election—or can be safely ignored. We present algorithms for computing lower and upper bounds on the MOV in STV elections. In small instances, these algorithms are able to compute exact margins.

Computing the margin of victory (MOV) in an Instant Runoff Voting (IRV) election is NP-hard. In an IRV election with winning candidate w, the MOV defines the smallest number of cast votes that, if modified, result in the election of a candidate other than w. The ability to compute such margins has significant value. Arguments over the correctness of an election outcome usually rely on the size of the electoral margin. Risk-limiting audits use the size of this margin to determine how much post-election auditing is required. We present an efficient branch-and-bound algorithm for computing exact margins that substantially improves on the current best-known approach. Although exponential in the worst case, our algorithm runs efficiently in practice, computing margins in instances that could not be solved by the current state-of-the-art in a reasonable time frame.

We consider the short-term production scheduling problem for a network of multiple open-pit mines and ports. Ore produced at each mine is transported by rail to a set of ports and blended into signature products for shipping. Consistency in the grade and quality of production over time is critical for customer satisfaction, whereas the maximal production of blended products is required to maximise profit. In practice, short-term schedules are formed independently at each mine, tasked with achieving the grade and quality targets outlined in a medium-term plan. However, because of uncertainty in the data available to a medium-term planner and the dynamics of the mining environment, such targets may not be feasible in the short term. We present a decomposition-based heuristic for this short-term scheduling problem in which the grade and quality goals assigned to each mine are collaboratively adapted—ensuring the satisfaction of blending constraints at each port and exploiting opportunities to maximise production in the network that would otherwise be missed.