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GOP primary elections use flawed math to pick nominees

Ismar Volić, Wellesley College, The Conversation on

Published in News & Features

Republicans around the country are picking a nominee to run for president. However, their process – designed and run by the party, not government officials – is a mess of flawed mathematics that can end up delivering a result that’s in conflict with the person most voters actually support.

As a mathematics professor and co-founder of the Institute for Mathematics and Democracy, I watched this contradictory process play out in 2016, shaping the political landscape ever since. Elements of it are visible again in 2024.

There are many ways bad mathematics interferes with our democracy, as I explain in my forthcoming book, “Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation.” Here’s how the Republican primaries can manage to defy democratic ideals and deliver a nominee even though most voters prefer someone else:

In 2016, former President Donald Trump became the Republican choice, having won 44.9% of the votes cast in primaries. That was nearly twice the share of votes won by the runner-up, Ted Cruz, who had 25.1% of the primary votes.

But during primary season, polls suggested that in head-to-head primaries, Trump would have lost not only to Cruz, but also to third-place Republican finisher John Kasich and Marco Rubio, who placed fourth.

In other words, a majority of Republican voters preferred Cruz, Kasich and Rubio to Trump. But none of the three took the lead because of the party’s nomination system, which assigned Trump 58.3% of the delegates at the Republican National Convention – the formal process by which the nominee is selected.


The Republican Party says its primaries are meant to encourage proportional assignment of delegates to candidates. So if a candidate wins, say, 40% of the votes, she should win as close to 40% of the delegates as possible.

This sounds reasonable, and it aligns with most people’s notion of fairness. For primaries taking place before March 15, the Republican Party mandates proportional allocation, but with lots of exceptions that can effectively turn the election into winner-take-all or winner-take-most. After March 15, the exceptions become the norm, pulling the outcome further from proportional representation.

The Democratic Party has a more centralized system and mandates proportionality for all its primaries.

The process begins with the states each receiving a number of delegates that will later be assigned to candidates.


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