As noted when I blogged about the Washington Post column on the “Total Vote Runoff” variation of Ranked Choice Vote (co-authored with Eric Maskin), a mathematical feature of this method is that it will elect a Condorcet Winner–the candidate who is ranked higher on more ballots than each other candidate when compared head-to-head. The Washington Post column illustrated this point with the example of the recent Alaska special election, where Nick Begich was the Condorcet Winner based on all the ranked-ballots cast and would have won the Total Vote Runoff had that procedure been used, but was eliminated through the regular “instant runoff” method that Alaska employs.

Although not affecting the outcome of the Alaska special election under the TVR procedure, there is a detail that is necessary to include in order to assure in any future election that the mathematical property of electing a Condorcet Winner holds. The detail concerns ballots in which a voter leaves unranked more than one candidate. As noted in the Washington Post column, when a voter leaves only one candidate unranked, doing so is equivalent to ranking the candidate last, and any candidate ranked last on a ballot receives zero votes from that ballot under the Total Vote Runoff procedure (because the voter does not prefer that candidate to any other candidate). But when a voter leaves more than one candidate unranked, then it is necessary that the unranked candidates be treated as tied for all the positions on the ranked-choice ballot that are left unfilled.

Using the Alaska special election again as an example to illustrate the procedure, suppose one ballot ranked Palin first and did not rank either of the two candidates, Begich or Peltola. Then, Begich and Peltola are treated as tied for second place (as well as tied for last place, which is irrelevant since last place counts for zero votes), and thus for this ballot Begich and Peltola equally share the one vote that is allocated to second place on the ranked-choice ballot. In other words, Begich and Peltola each get half a vote by being tied for second place on this ballot. The same method applies to any ballot that ranks only Begich first, or ranks only Peltola first. (If one wishes, one can think of the half-votes involving these second-place ties as equivalent to each of the two tied candidates beating the other candidate half of the time–and thus entitled to half the share of these second-place votes.)

With this additional detail, one can provide a more complete calculation of the Total Votes for each of the three candidates in the Alaska special election (recognizing of course that these Total Votes derived from the state’s Cast Vote Record are necessarily a construct, since the state itself did not use this TVR procedure for the election). Building upon the chart of numbers included with the Washington Post piece, the TRV calculation identifies all the ballots on which each unranked candidate is treated as tied: Begich, 45142; Peltola, 32720; Palin, 35144. Awarding a half-vote for each of these ties adds the following for each candidate: Begich, 22571; Peltola, 16360; Palin, 17572. Including these half-votes-for-ties, along with the numbers already reported in the Washington Post column, yields these Total Votes for each candidate: Begich, 211444; Peltola, 186982; Palin, 167129. With these numbers, Palin has the fewest Total Votes and thus is eliminated, leaving Begich (the Condorcet Winner) to beat Peltola head-to-head.

Additional details about the Total Vote Runoff procedure, including how it applies to elections involving more than three candidates, will be discussed in my article for New Hampshire Law Review symposium, where the idea was presented. But because there has been some Twitter discussion related to this specific aspect of how TVR mathematically elects a Condorcet Winner, I thought it would be helpful to mention this detail here.