Our work introduces a new voting paradigm about which many questions remain unanswered and many variations and extensions remain to be explored. Listed below are several areas that look especially attractive for future exploration.
Acceptability. We conducted a limited acceptability study by surveying a group of well-educated people about one type of DSV. Further work is needed to gauge the acceptability of other types of DSV and the acceptability of DSV among a more general population. In addition, we recommend conducting a study in which a professional organization or other voting body conducts a DSV election shadowing an actual election after its members are educated about DSV and their current voting system.
DSV combined with approval voting or other voting rules. We have limited our study to DSV systems that use the plurality voting rule. Our simulations with many alternatives (especially our trajectory selection simulations) highlighted the fact that the plurality rule prevents the selection of an alternative that does not receive a large number of first-place votes, regardless of the number of second-place votes that alternative receives. DSV systems that use an approval voting rule would not have this problem. The combination of DSV with approval voting, Borda count voting, and other voting rules should be explored.
Tie-breaking rules. We introduced the concept of tie-breaking rules to augment the expected-utility model of voting. However, more work is needed to determine what types of tie-breaking rules are useful in actual voting situations and the impacts of these rules on the behavior of DSV systems.
Uncertainty. As we demonstrated, uncertainty is an important factor in the calculation of pivot probabilities. We introduced a method for accounting for the uncertainty of predictions in ballot-by-ballot DSV and suggested some possible approaches to account for uncertainty in batch DSV. Further work is needed to explore ways of incorporating voters' attitudes towards risk, the entire set of voter preferences, or the maturity of the election in the calculation of uncertainty for batch DSV.
Stability. In many actual voting situations, voters are unlikely to accept an unstable voting system. We have demonstrated that batch DSV is stable, assuming the use of an arbitrary factor for uncertainty and an arbitrary termination condition in case it fails to converge. However ballot-by-ballot DSV is generally unstable. Further work is needed to develop a DSV system that is stable without relying on arbitrary factors. We envision a system that would allow stability to be adjusted depending on the importance of picking a single winner versus preventing manipulation or gaining a greater understanding of the preferences of the electorate.
Dependent alternatives. We have only explored the use of DSV for decisions between independent alternatives. However, decision-makers must often select several dependent alternatives. The use of DSV in decisions involving dependent alternatives should be explored.
Sophisticated strategies. We demonstrated that batch DSV systems may be manipulable by voters who use sophisticated strategies. Further work is needed to determine the extent to which sophisticated strategies are feasible to develop in actual voting situations as well as the possibility of designing a strategy formulator that can formulate optimal sophisticated strategies for voters.
Analysis of election and survey results. One of the positive characteristics of DSV systems is that they provide complete (and likely sincere) cardinal preference information for the entire electorate. This data should prove useful to decision-makers using a DSV survey to guide their decisions, and to analysts interpreting the results of a DSV election. Further work is necessary to determine what methods are most useful for interpreting DSV data.
These areas are a few of the many areas where further work might be focussed. In the process of introducing this new paradigm we have attempted to sketch a rough overview of this previously unexplored concept, filling in as many details as is possible during a first exploration. In trying to map out this paradigm we encountered many unexpected problems. Happily, we also encountered some unexpectedly simple solutions. But as we conclude our work, we leave many problems unsolved, and probably many more undiscovered. It is our hope that other investigators will find some of these problems worthy of their attention.