My Poll, Explained

So many have continued to ask me the same questions about my recent twitter poll, that I thought I’d try to put all my answers in one place. This topic isn’t that fundamentally interesting, so most you you may want to skip this post.

Recently, Christine Blasey Ford publicly accused US Supreme Court nominee Brett Kavanaugh of a sexual assault. This accusation will have important political consequences, however it is resolved. Congress and the US public are now put in the position of having to evaluate the believability of this accusation, and thus must consider which clues might indicate if the accusation is correct or incorrect.

Immediately after the accusation, many said that the timing of the accusation seemed to them suspicious, occurring exactly when it would most benefit Democrats seeking to derail any nomination until after the election, when they may control the Senate. And it occurred to me that a Bayesian analysis might illuminate this issue. If T = the actual timing, A = accurate accusation, W = wrong accusation, then how much this timing consideration pushes us toward final beliefs is given by the likelihood ratio p(T|W)/p(T|A). A ratio above one pushes against believing the accusation, while a ratio below one pushes for it.

The term P(T|A) seemed to me the most interesting term, and it occurred to me to ask what people thought about it via a Twitter poll. (If there was continued interest, I could ask another question about the other term.) Twitter polls are much cheaper and easier for me to do than other polls. I’ve done dozens of them so far, and rarely has anyone objected. Such polls only allow four options, and you don’t have many characters to explain your question. So I used those characters mainly to make clear a few key aspects of the accusation’s timing:

Many claimed that my wording was misleading because it didn’t include other relevant info that might support the accusation. Like who else the accuser is said to have told when, and what pressures she is said to have faced when to go public. They didn’t complain about my not including info that might lean the other way, such as low detail on the claimed event and a lack of supporting witnesses. But a short tweet just can’t include much relevant info; I barely had enough characters to explain key accusation timing facts.

It is certainly possible that my respondents suffered from cognitive biases, such as assuming too direct a path between accuser feelings and a final accusation. To answer my poll question well, they should have considered many possible complex paths by which an accuser says something to others, who then tell others people, some of which then chose when to bring pressure back on that accuser to make a public accusation. But that’s just the nature of any poll; respondents may well not think carefully enough before answering.

For the purposes of a Twitter poll, I needed to divide the range from 0% to 100% into four bins.
I had high uncertainty about where poll answers would lie, and for the purpose of Bayes rule it is factors that matter most. So I choose three ranges of roughly a factor of 4 to 5, and a leftover bin encompassing an infinite factor. If anything, my choice was biased against answers in the infinite factor bin.

I really didn’t know which way poll answers would go. If most answers were high fractions, that would tend to support the accusation, while if most answers were low fractions, that would tend to question the accusation. Many accused me of posting the poll in order to deny the accusation, but for that to work I would have needed a good guess on the poll answers. Which I didn’t have.

My personal estimate would be somewhere in the top two ranges, and that plausibly biased me to pick bins toward such estimates.  As two-thirds of my poll answers were in the lowest bin I offered, that suggests that I should have offered an even wider range of factors. Some claimed that I biased the results by not putting more bins above 20%. But that fraction is still below the usual four-bin target fraction of 25% per bin.

It is certainly plausible that my pool of poll respondents are not representative of the larger US or world population. And many called it is irresponsible and unscientific to run an unrepresentative poll, especially if one doesn’t carefully show which wordings matter how via A/B testing. But few complain about the thousands of other Twitter polls run every day, or of my dozens of others. And the obvious easy way to show that my pool or wordings matter is to show different answers with another poll where those vary. Yet almost no one even tried that.

Also, people don’t complain about others asking questions in simple public conversations, even though those can be seen as N=1 examples of unrepresentative polls without A/B testing on wordings. It is hard to see how asking thousands of people the same question via a Twitter poll is less informative than just asking one person that same question.

Many people said it is just rude to ask a poll question that insinuates that rape accusations might be wrong, especially when we’ve just seen someone going through all the pain of making one. They say that doing so is pro-rape and discourages the reporting of real rapes, and that this must have been my goal in making this poll. But consider an analogy with discussing gun control just after a shooting. Some say this is rude then to discuss anything but sympathy for victims, but others say this is exactly a good time to discuss gun control. I say that when we must evaluate a specific rape accusation is exactly a good time to think about what clues might indicate in what direction on whether this is an accurate or wrong accusation.

Others say that it is reasonable to conclude that I’m against their side if I didn’t explicitly signal within my poll text  that I’m on their side. That’s just the sort of signaling game equilibrium we are in. And so they are justified in denouncing me for being on the wrong side. But it seems a quite burdensome standard to hold on polls, which already have too few characters to allow an adequate explanation of a question, and it seems obvious that the vast majority of Twitter polls today are not in fact being held to this standard.

Added 24Sep: I thought the poll interesting enough to ask, relative to its costs to me, but I didn’t intend to give it much weight. It was all the negative comments that made it a bigger deal.

Note that, at least in my Twitter world, we see a big difference in attitudes between vocal folks who tweet and those who merely answer polls. That later “silent majority” is more skeptical of the accusation.

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