My print column this week examines the debate over voting systems that theorists and reformers have backed to replace the system prevalent in the U.S. and many other places, in which each voter gets one vote and the candidate with the most votes wins. Among possible alternative systems include some where voters rank candidates and others where they assign candidates scores.

Instant runoff, the focus of my column, has gotten the most traction so far. But some mathematicians point out that the system could give rise to various troubling results. Two significant ones: Voters who decide to shift their support from one candidate to a second can hurt that second candidate; and voters can get a worse outcome if they choose to show up to the polls, inadvertently helping their least-favorite candidate (the no-show paradox). Robert Z. Norman, Dartmouth College professor emeritus of mathematics, has simulated three-candidate elections in which each candidate has at least 25% of support and finds that each of these apparent paradoxes occur about one in five times.

Rob Richie, Instant runoff’s leading advocate as executive director of the nonprofit advocacy group FairVote, counters that in practice, such paradoxes are rare — and can also arise in elections that have non-instant runoffs if no candidate gets a majority of the vote.

Researchers sometimes turn to simulations because it can be difficult to determine just how rare these occasions are because instant-runoff localities often don’t release full election results. Unlike in a simple, one-voter, one-vote race — the so-called plurality system, where election results are simply the number of votes each candidate received and the winner has the most votes — full instant-runoff results are much more complicated. In a three-party race, there are 15 different ways to rank the candidates (counting ballots with just one or two candidates ranked). But election boards often just release the final candidate totals in each round of the runoff, rather than the full voter preferences.

Full Article: The Mathematical Debate Over Instant Runoff and Other Alternative Voting Systems – The Numbers Guy – WSJ.