How Not to Tabulate the 2028 US Democratic Primary

The US Democratic Party introduced a novel electoral system in 2020, combining instant runoff voting (IRV) and proportional representation (PR) with a 15% viability threshold. This tabulation system was chosen over more established methods, such as single transferable vote (STV), as a way to incorporate ranked-choice ballots into a PR system with a 15% viability threshold, which is deeply embedded in the party's rules. Ahead of the 2028 presidential nomination process, party leaders have expressed a desire to expand the IRV+PR system. However, the system has received little attention from the mathematics and public choice communities. We introduce new optimal transport metrics to measure the misalignment between the ensemble of ballots cast and the distribution of delegates awarded. These metrics have the advantage of separating the alignment measure from the tabulation process and from treating all ballots uniformly. These metrics do not restrict their attention to the match between individual ballots and the candidates whose tallies they increment during tabulation; rather, they treat each cast ballot as an equal amount of probability mass to be transported optimally (not via tabulation) to the delegate distribution. We compare eight potential tabulation schemes, including the "fair reflection" winner: a loss-minimizing tabulation per an optimal transport cost (which, while NP-hard to tabulate in general, can be calculated for many elections). We find that this IRV+PR tabulation scheme fails to improve overall delegate alignment with voter preferences. Moreover, the use of ranked-choice ballots introduces paradoxical outcomes, such as the no-show paradox and generalized non-leader outcomes (candidate A wins strictly more delegates than B while most ballots rank B above A). In fact, under the IRV+PR scheme, Condorcet losers win strictly more delegates than other candidates in simulated delegate-allocation elections using real cast ballot records of US ranked-choice voting elections. Thus, we recommend that the DNC Rules and Bylaws Committee discourage the use of this novel tabulation scheme. If the desire to incorporate ranked-choice ballots for this delegate-allocation task persists, we recommend the use of STV using large statewide delegate pools and further mathematical, legal, and logistical study of a mixed-integer program to minimize the optimal transport misalignment cost and interpretable heuristic approximations thereof. We also recommend the party cease awarding delegates by candidate performance within a district and weighting the totals by the strength of the Democratic ticket in past elections. Such an approach violates "one person one vote," masks the signal voters express with quantization noise, and-in the wake of Callais-dilutes minority representation, without advancing the aims of McGovern-Fraser. The signal-to-quantization-noise ratio increases with the square of the pool size; for each tabulation method, awarding all of a state's delegates based on the statewide vote totals for each candidate improves the optimal transport cost.