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Contending with the NPV Dilemma

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The National Popular Vote Initiative (NPVI) enjoys considerable appeal, but we noted in a recent article that it presents us with a new problem if and when it should pass. In that event, a controlling number of electors sent by states to the Electoral College (EC) would be pledged to vote for the winner of the national popular vote. The trouble with that is that unless all states share the same voting system, presumably PV, then it is not clear how that national popular vote (NPV) should be computed.

apples and oranges and...
apples and oranges and...
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The problem is a real one since two of our states, Alaska and Maine have already adopted instant runoff voting (IRV) rather than PV in presidential elections. Fortunately though, in the special case of IRV there is a close enough similarity with plurality voting (PV) that a path for managing the problem is apparent. IRV simulates a series of PV elections and we might just take the results of some particular PV election in that series to use in computing the NPV. We might, for example, take the first of the runoff elections and in fact this was proposed by Bruce Poliquin, the loser in Maine's Congressional election in 2018. No doubt Poliquin was influenced by the observation that this choice would have made Poliquin the winner in that 2018 election. But the Maine courts did not see things his way.

The difficulty with that choice would be that in the minds of voters, PV elections are between just two viable candidates whereas that initial PV election encourages voters to choose among all of the candidates and that added choice certainly influences the voting. The more comparable situation would be between the PV election and the very last iteration of the IRV counting which in fact is between only two candidates. In the example of Maine's 2018 election this approach was in effect how the court decided by confirming of the defeat of Poliquin.

The similarity of PV with the last iteration of IRV is incomplete of course. Some voters in the IRV election surely have submitted abbreviated lists to show their preferences, effectively dropping out before the final iteration of vote counting. Perhaps those may be the same voters who would fail to turn up for a PV election but probably this is at best a rough approximation. But this is a problem that can be addressed by scaling up the vote-counts for both winner and loser so that their combined votes match the actual number of ballots.

More worrisome, as we noted in another recent article, with IRV there are many reasons why IRV votes may be at odds with voters' intent. With PV elections, a voter will more often vote strategically, but the ballot will generally express what the voter intends. The voting in the last round of IRV is different from a PV election; still, less than perfect solutions are commonly adopted to deal with real-world problems when, as is all too often the case, no perfect solution is apparent.

What is interesting is that this approach will generalize to other, perhaps all other, voting systems. Other voting systems may lack the great similarity with PV, but generally other voting system do identify some ranking of the candidates. Generally a single-winner election, whatever the voting method, will determine both a winner and a runner up. Exceptions to this would usually be in the highly improbable event of a tie, but let us put off consideration of tie votes.

Suppose, for the purpose of computing the NPV, each state would be required to submit a report of their state-wide election that specifies three positive numbers:

  • B of submitted ballots (the vote-count),

  • V 1 for the winner and

  • V 2 for the first runner-up.

In preparation for tallying the NPV, the vote-counts for the reported candidates are scaled by a factor of B/(V 1 + V 2 ). This computation helps adjust for the fact that different states use different voting systems and so may have a different notion of what constitutes the number of votes a candidate receives; it ensures that the two vote-counts add up to the number of voters. This also puts the weight of the entire voting population behind the choice of the top two winners, much as what happens with PV. The influence a particular state has on NPV is weighted according to the actually number of ballots cast and this will encourage states to avoid voter suppression.

The requirement that V 1 and V 2 must be positive may appear to present a difficulty for balanced voting systems in which a net vote for candidates could be zero or negative. However, a state that uses such a system is free to define, within reason, the reported vote-count as it deems appropriate. In particular, the state is free to add a (conservatively chosen) positive number as an offset to the net vote so that the reported values are made positive. That number would not need to be greater than B.

Returning now to the question of tie-votes in an election, my suggestion would be to relax the restriction to only two vote-counts and allow states to submit vote counts for additional candidates. The denominator of the scaling factor would be the sum of additional vote-counts. The intended use for this flexibility would be to accommodate ties or near-ties. Of course states would not be allowed to skip over candidates; when a vote count is submitted for a given candidate, one must also be submitted for every candidate who scores the same or better in the state-wide election.

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Attended college thanks to the generous state support of education in 1960's America. Earned a Ph.D. in mathematics at the University of Illinois followed by post doctoral research positions at the Institute for Advanced Study in Princeton. (more...)

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