Gallup doesn’t understand set theory


According to a Gallup Poll article, “Less than a third of Americans say they would be willing to vote for someone nominated by their party who is over the age of 80 or has been charged with a felony or convicted of a felony by a jury.” If that’s true and Trump and Biden are the major-party nominees in 2024, then two-thirds of Americans will sit out the election for that reason alone.

Is that what the poll actually shows? The article goes on to say, “The poll addressed the issues of felonies and candidate age with separate questions each asked of about half of the poll’s respondents.” That makes it impossible to draw the conclusion stated at the top of the article. It’s an issue of set overlap.

To illustrate this, let’s make a set of simplifying assumptions. Suppose (1) an equal number of Democrats and Republicans were polled, and nobody else was; (2) all Democrats find someone charged with a felony unacceptable, and 1/6 of them find someone over 80 unacceptable; (3) all Republicans find someone over 80 unacceptable, and 1/6 of them find someone charged with a felony unacceptable. This is just a made-up example to illustrate the point about sets.

With those numbers, 2/3 of those polled would find a candidate with felony charges unacceptable, and 2/3 would find a candidate over 80 unacceptable — but 5/6 of them would find one of the two acceptable. This presumes the greatest possible polarization consistent with a 2/3 result, so it isn’t realistic either; it gives the other end of a range of possibilities.

The actual numbers (which are visible only if you enable JavaScript — argh) say that 22% of Republicans, 24% of independents, and 53% of Democrats would vote for a “generally well-qualified” candidate over 80 nominated by their party, and that 46% of Republicans, 28% of independents, and 15% of Democrats would vote for a generally well-qualified candidate of their party who had been charged with a felony. This is an obvious case of people deriving their principles from the candidate they’ve decided to vote for and is far from random. It shows that at most, 47% of Democrats, 54% of Republicans, and 72% of independents would reject candidates from both categories, and the actual percentages are certainly less.

By the way, what does it mean to ask independents if they’d vote for a candidate of “your party”? Also, were people affiliated with minor parties allowed to say so? Shouldn’t there be an “other” category, even if its numbers were too small to be statistically meaningful?

The table doesn’t say how many people answered “undecided” or declined to answer, or whether that was an option at all. It isn’t safe to assume that everyone who didn’t answer “yes” answered “no.”

Further down, we’re told that “43% of respondents asked about voting for someone over 80 and someone charged with a felony say they would not vote for either type of candidate.” This contradicts the earlier statement that “less than a third” would vote for either type of candidate. Was this a separate question from the earlier two, which were given to disjoint sets of people? Why isn’t it listed in the data table?

The earlier statement includes the “nominated by their party” qualifier, but that doesn’t help the situation. The proportion of people who’d find a candidate acceptable should increase, not decrease, when the question is restricted to their own party.

Another oddity of the poll is that only one category in the list of questions is political in nature. The people polled were asked if they would vote for a “socialist,” but not whether they’d vote for a liberal, conservative, libertarian, progressive, Communist, Nazi, anarchist, etc. A candidate’s political views are a more solid reason for voting or not voting for a candidate than age, religion, or skin color. “Socialist” is grouped in “diverse types of candidates” along with gays, Muslims, and atheists, as if socialism were a private personal characteristic rather than a view of what governments should do.

Personal note: It’s depressing that only 70% of Democrats and fewer in the other categories would vote for a qualified atheist. With almost a third of Americans describing themselves as having no religious affiliation (though significantly fewer use the word “atheist” and many believe in some kind of vague Deity), that’s a large and growing part of the population they’ve rejected.

The reporting is sloppy, but the raw numbers are significant. If the respondents answered the questions honestly and with full understanding and are representative (a very dubious assumption), then less than half of Republicans would vote for Trump, and only a little more than half of of Democrats would vote for Biden. That’s not as serious as what the article claims, but it still indicates widespread dissatisfaction with both of the presumptive candidates. The 2024 election looks like a race to the bottom.