The media is spreading a fallacy in ever more imaginative ways

I already did the math and it says that a 26% vote share for the winner of a 6-way race is about the same as a 60% vote share in a 2-way race. (The second error is to treat a 60/40 split as a blowout. It is not.) Many people actually intuitively grasp this. It does not take a math degree to recognize that when more people are sharing the pie, each gets less.

The media is trapped in this fallacy and can't get out. In this post, I keep track of all the articles that pretend that vote shares in an 10-plus-person election are equal to vote shares in a 2-person election.

No matter how many times they repeat this talking point, it is still wrong.

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Benjamin Wallace-Wells (New Yorker): Bernie Sanders Leads a Jumbled New Hampshire Primary

In 2016, Sanders won sixty per cent of the vote in New Hampshire; this time, his totals were less than half that.

Hunter Woodall, Nicholas Riccardi (Chicago Tribune): A victory for Bernie Sanders, but

And Pete Buttigieg, the former mayor of South Bend, Indiana, again made a case to be that choice with another impressive performance, winning votes across broad demographic groups, by running close to Sanders, who defeated Hillary Clinton by 22 percentage points in 2016.

Sam Stein, Hanna Trudo (Daily Beast): Bernie Sanders Wins New Hampshire

The Vermont independent scored a far smaller percentage of the electorate than in 2016, when he breezed to victory in New Hampshire with 60 percent of the vote

Ruby Cramer (Buzzfeed): Bernie Sanders Won the New Hampshire Primary

Sanders, who spoke to supporters on Tuesday night at the Southern New Hampshire University field house, finished with a smaller margin of victory than his finish four years ago against Hillary Clinton

Ryan Lizza (Politico): Sanders ekes one out

Independents were a larger share of the electorate, but they did not break nearly as decisively for Sanders as they did in 2016. He received support from just 29 percent of self-described independents this time, as opposed to 73 percent (!) in 2016.

[Note: Subsetting to Independents does not do away with the fallacy.]

John Whitesides, Amanda Becker (Reuters): Sanders narrowly beats Buttigieg

For Sanders, who won New Hampshire in 2016 with 60% of the vote against eventual nominee Hillary Clinton, the results offered new momentum but not the overwhelming win he had hoped for given his history in the state. Exit polls showed he only won about two-thirds of his 2016 primary supporters.

[Note: if he kept all those supporters, he would have obtained similar vote share as in 2016. It's still the same fallacy at play here.]

Washington Post: Bernie Sanders wins New Hampshire

While he has emerged as one of the candidates everyone else is chasing — an unfamiliar spot for a politician much more accustomed to running as an insurgent underdog — his narrow winning percentage was on course to be historically low, below Jimmy Carter’s 28.6 percent in 1976.

[Note: Wiki says there were five candidates in 1976. There are over 10 candidates in 2020.]

Laura Bronner (FiveThirtyEight): Liveblog

[Note: FiveThirtyEight is still the class act here, and they have said many things that I agree with. This post is from their LiveBlog, so it is not as well thought out. This is a standard plot comparing vote shares in one election versus another. But it only works when the race has similar number of candidates. If Sanders's margin is going to sit above the diagonal, he probably would be running away with the nomination already.]

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Meanwhile, this lady who voted in New Hampshire stated the obvious. (link) She even claimed she was so upset by the media repeating this fallacy that she voted for Sanders.

Comments

[Tom Dietterich]

If you group the candidates into left-wing vs. centrist, the centrist vote was larger than the left-wing. So I don't think you can say that this is equivalent to Bernie winning 60%. What is the underlying stochastic model?

[Kaiser]

TD: I'm framing the problem as looking for equivalence in terms of strength of the winner in a N-person versus 2-person contest. I want something that works generally, regardless of who the candidates are. The goal is to put some rigor behind the intuitive notion that the vote shares can't be directly compared.

I thought about a stochastic model but couldn't get past the need to model migration behavior. In the counterfactual scenario, what would the #4 candidate's voters do if there were only 2 contestants? That requires arbitrarily setting a large number of parameters, with no data to support them.

Separately, any analysis that adds together left-wing and centrist groupings makes several assumptions: (a) that all voters make decisions primarily based on their identification with those factions, and (b) that voters consider the candidates within each grouping as exchangeable.

Also, Bernie winning 60% is not the blowout that the media portrayed it to be. An even match is 50/50; 60/40 is a good win but not huge. Clinton won most states on Super Tuesday by a bigger margin than 60/40!

[Noah Motion]

A new instance from Megan McCardle, in a slightly different context:

“The most important theory these primaries should have killed is that of our nascent socialist revolution. That theory was plausible in 2016, when Bernie Sanders (I-Vt.) won New Hampshire with 60 percent of the vote. It is less so now that he’s leaving the same state with only a quarter of its votes. Even if every one of Andrew Yang’s and Warren’s voters had picked him, he’d still only have gotten a bit over a third, and his polls suggest that’s about where he’d be nationally, too. So what looked, four years ago, like a sharp leftward shift in the electorate now seems more like a mass protest against the party’s slavish fealty to the Clintons.”

From:

https://www.washingtonpost.com/opinions/2020/02/12/theories-that-collapsed-new-hampshire/