Donald Trump’s and Joe Biden’s ages and conditional probabilities of their dementia risk

The prior

Paul Campos posted something on the ages of the expected major-party candidates for next year’s presidential election:

Joe Biden is old. Donald Trump is also old. A legitimate concern about old people in important positions is that they are or may become cognitively impaired (For example, the prevalence of dementia doubles every five years from age 65 onward, which means that on average an 80-year-old is is eight times more likely to have dementia than a 65 year old).

Those are the baseline probabilities, which is one reason that Nate Silver wrote:

Of course Biden’s age is a legitimate voter concern. So is Trump’s, but an extra four years makes a difference . . . The 3.6-year age difference between Biden and Trump is potentially meaningful, at least based on broad population-level statistics. . . . The late 70s and early 80s are a period when medical problems often get much worse for the typical American man.

Silver also addressed public opinion:

An AP-NORC poll published last week found that 77 percent of American adults think President Biden is “too old to be effective for four more years”; 51 percent of respondents said the same of Donald Trump. . . . the differences can’t entirely be chalked up to partisanship — 74 percent of independents also said that Biden was too old, while just 48 percent said that of Trump.

The likelihood

OK, those are the base rates. What about the specifics of this case? Nate compares to other politicians but doesn’t offer anything about Biden or Trump specifically.

Campos writes:

Recently, Trump has been saying things that suggest he’s becoming deeply confused about some very basic and simple facts. For example, this weekend he gave a speech in which he seemed to be under the impression that Jeb Bush had as president launched the second Iraq war . . . In a speech on Friday, Trump claimed he defeated Barack Obama in the 2016 presidential election. . . . Trump also has a family history of dementia, which is a significant risk factor in terms of developing it himself.

Campos notes that Biden’s made his own slip-ups (“for example he claimed recently that he was at the 9/11 Twin Towers site the day after the attack, when in fact it was nine days later”) and summarizes:

I think it’s silly to deny that Biden’s age isn’t a legitimate concern in the abstract. Yet based on the currently available evidence, Trump’s age is, given his recent ramblings, a bigger concern.

It’s hard to know. A quick google turned up this:

On July 21, 2021, during a CNN town hall, President Joe Biden was asked when children under 12 would be able to get COVID-19 vaccinations. Here’s the start of his answer to anchor Don Lemon: “That’s under way just like the other question that’s illogical, and I’ve heard you speak about it because y’all, I’m not being solicitous, but you’re always straight up about what you’re doing. And the question is whether or not we should be in a position where you uh um, are why can’t the, the, the experts say we know that this virus is in fact uh um uh is, is going to be, excuse me.”

On June 18, after Biden repeatedly confused Libya and Syria in a news conference, The Washington Post ran a long story about 14 GOP lawmakers who asked Biden to take a cognitive test. The story did not note any of the examples of Biden’s incoherence and focused on, yes, Democrats’ concerns about Trump’s mental health.

And then there’s this, from a different news article:

Biden has also had to deal with some misinformation, including the false claim that he fell asleep during a memorial for the Maui wildfire victims. Conservatives — including Fox News host Sean Hannity — circulated a low-quality video on social media to push the claim, even though a clearer version of the moment showed that the president simply looked down for about 10 seconds.

There’s a lot out there on the internet. One of the difficulties with thinking about Trump’s cognitive capacities is that he’s been saying crazy things for years, so when he responds to a question about the Russia-Ukraine war by talking about windmills, that’s compared not to a normal politician but with various false and irrelevant things he’s been saying for years.

I’m not going to try to assess or summarize the evidence regarding Biden’s or Trump’s cognitive abilities—it’s just too difficult given that all we have is anecdotal evidence. Both often seem disconnected from the moment, compared to previous presidents. And, yes, continually being in the public eye can expose weaknesses. And Trump’s statements have been disconnected from reality for so long, that this seems separate from dementia even if it could have similar effects from a policy perspective.

Combining the prior and the likelihood

When comparing Biden and Trump regarding cognitive decline, we have three pieces of information:

1. Age. This is what I’m calling the base rate, or prior. Based on the numbers above, someone of Biden’s age is about 1.6 times more likely to get dementia than someone of Trump’s age.

2. Medical and family history. This seems less clear, but from the above information it seems that someone with Trump’s history is more at risk of dementia than someone with Biden’s.

3. Direct observation. Just so hard to compare. That’s why there are expert evaluations, but it’s not like a bunch of experts are gonna be given access to evaluate the president and his challenger.

This seems like a case where data source 3 should have much more evidence than 1 and 2. (It’s hard for me to evaluate 1 vs. 2; my quick guess would be that they are roughly equally relevant.) But it’s hard to know what to do with 3, given that no systematic data have been collected.

This raises an interesting statistical point, which is how to combine the different sources of information. Nate Silver looks at item 1 and pretty much sets aside items 2 and 3. In contrast, Paul Campos says that 1 and 2 pretty much cancel and that the evidence from item 3 is strong.

I’m not sure what’s the right way to look at this problem. I respect Silver’s decision not to touch item 3 (“As of what to make of Biden and Trump in particular — look, I have my judgments and you have yours. Cognitively, they both seem considerably less sharp to me than they did in their primes”); on the other hand, there seems to be so much direct evidence, that I’d think it would overwhelm a base rate odds of 1.6.

News media reporting

The other issue is news media coverage. Silver argues that the news media should be spending more time discussing the statistical probability of dementia or death as a function of age, in the context of Biden and Trump, and one of his arguments is that voters are correct to be more concerned about the health of the older man.

Campos offers a different take:

Nevertheless, Biden’s age is harped on ceaselessly by the media, while Trump apparently needs to pull a lampshade over his head and start talking about how people used to wear onions on their belts before the same media will even begin to talk about the exact same issue in regard to him, and one that, given his recent behavior, seems much more salient as a practical matter.

From Campos’s perspective, voters’ impressions are a product of news media coverage.

But on the internet you can always find another take, such as this from Roll Call magazine, which quotes a retired Democratic political consultant as saying, “the mainstream media has performed a skillful dance around the issue of President Biden’s age. . . . So far, it is kid gloves coverage for President Biden.” On the other hand, the article also says, “Then there’s Trump, who this week continued his eyebrow-raising diatribes on his social media platform after recently appearing unable, at times, to communicate complete thoughts during a Fox News interview.”

News coverage in 2020

I recall that age was discussed a lot in the news media during the 2020 primaries, where Biden and Sanders were running against several much younger opponents. It didn’t come up so much in the 2020 general election because (a) Trump is almost as old as Biden, and (b) Trump had acted so erratically as president that it was hard to line up his actual statements and behaviors with a more theoretical, actuarial-based risk based on Biden’s age.

Statistical summary

Comparing Biden and Trump, it’s not clear what to do with the masses of anecdotal data; on the other hand, it doesn’t seem quite right to toss all that out and just go with the relatively weak information from the base rates.

I guess this happens a lot in decision problems. You have some highly relevant information that is hard to quantify, along with some weaker, but quantifiable statistics. In their work on cognitive illusions, Tversky and Kahneman noted the fallacy of people ignoring base rates, but there can be the opposite problem of holding on to base rates too tightly, what we’ve called slowness to update. In general, we seem to have difficulty balancing multiple pieces of information.

P.S. Some discussion in comments about links between age and dementia, or diminished mental capacities, also some discussion about evidence for Trump’s and Biden’s problems. The challenge remains of how to put these two pieces of information together. I find it very difficult to think about this sort of question where the available data are clearly relevant yet have such huge problems with selection. There’s a temptation to fall back on base rates but that doesn’t seem right to me either.

P.P.S. I emailed Campos and Silver regarding this post. Campos followed up here. I didn’t hear back from Silver, but I might not have his current email, so if anyone has that, could you please send it to me? Thanks.

63 thoughts on “Donald Trump’s and Joe Biden’s ages and conditional probabilities of their dementia risk

  1. I’d also check the interpretation of the facts. I dunno about the rest, but Eg:

    In a speech on Friday, Trump claimed he defeated Barack Obama in the 2016 presidential election

    The idea that (Hillary) Clinton and Biden are Obama’s puppets has been around for awhile, so that is what I’d assume was meant. I’d guess similar for most of the other quotes, they are taken out of context. Anyone who is recorded as often as them will have all sorts of goofy sounding quotes, so that provides little info on dementia.

    The constant stream of videos of Biden wandering around on stage are much more informative, because that is an appearance that other politicians manage to avoid.

    • Look, having nuclear — my uncle was a great professor and scientist and engineer, Dr. John Trump at MIT; good genes, very good genes, OK, very smart, the Wharton School of Finance, very good, very smart — you know, if you’re a conservative Republican, if I were a liberal, if, like, OK, if I ran as a liberal Democrat, they would say I’m one of the smartest people anywhere in the world — it’s true! — but when you’re a conservative Republican they try — oh, do they do a number — that’s why I always start off: Went to Wharton, was a good student, went there, went there, did this, built a fortune — you know I have to give my like credentials all the time, because we’re a little disadvantaged — but you look at the nuclear deal, the thing that really bothers me — it would have been so easy, and it’s not as important as these lives are — nuclear is so powerful; my uncle explained that to me many, many years ago, the power and that was 35 years ago; he would explain the power of what’s going to happen and he was right, who would have thought? — but when you look at what’s going on with the four prisoners — now it used to be three, now it’s four — but when it was three and even now, I would have said it’s all in the messenger; fellas, and it is fellas because, you know, they don’t, they haven’t figured that the women are smarter right now than the men, so, you know, it’s gonna take them about another 150 years — but the Persians are great negotiators, the Iranians are great negotiators, so, and they, they just killed, they just killed us, this is horrible

      • And? Weird quotes from politicians dont indicate dementia. It is too common and everyone can think of their own slipups or ramblings or someone taking what they said out of context.

        It is a basic application of Bayes’ rule. Where D = dementia, O = odd quotes, and H1:Hn are non-dementia explanations:

        p(D|O) = p(D)p(O|D)/B

        B = p(D)p(O|D) + [ p(H1)p(O|H1) + p(H2)p(O|H2) + … + p(Hn)p(O|Hn) ]

        Even though p(O|D) is large, the denominator is just too large for it to matter. As I said, it is more difficult for people to explain the stage wandering. First, most don’t have much personal experience with stages and public speaking. Second, we have not seen this behaviour from politicians before. So there is something requiring explanation in that case.

        • I don’t think either Trump or Biden have dimentia. I just think it’s really funny to twist yourself in knots trying to come up with some obscure context in which Trump’s quote makes sense. He says stuff that makes no sense all the time. For most of his off the cuff speaking, it’s difficult to interpret exactly what he’s claiming. I also think it’s ridiculous to claim that the way Trump speaks and his gaffes are just regular president stuff. His ramblings are absolutely unusual for a president.

          I’ve also never heard it said that Clinton was Obama’s puppet. But in any case, that’s not the reason why he said that, which took about a second to google. He just messed up a bunch of times.

          https://x.com/RpsAgainstTrump/status/1703224211399921939?s=20

          Very normal stuff

        • > He also said he was leading Obama “by a lot” in the 2024 presidential election polls.

          He prolly just said that also, because he thinks Biden is an Obama puppet.

        • “So let’s see what happens. But, you know, I’ve told the Obama campaign, I mean, the Obama — I’ve told the Biden campaign and the Biden transition, that they’re going to have to move really fast because let’s assume we take back the Senate,” said Clinton, who lost to President Trump in 2016.

          https://www.washingtonexaminer.com/washington-secrets/hillary-clinton-pelosi-ready-to-unleash-liberal-tsunami-after-biden-win

          Wow, how crazy of a quote that reveals something we always expected was true.

          The only people who care about this type of thing are the minority who identify as democrats + republicans.

          Most people do not care if it is a democrat or republican. It just makes little to no difference for their lives. If you identify as either you are a minority, even both combined together. Please understand that most people learn to ignore this type of he-said/she-said type of thing in high school.

          I am just describing reality, and the rational reasoning behind it.

        • What you have learned, in your attempt to seem like you’re above this, is to ignore all the specific facts of who and what you’re talking about. I am not a Democrat or a Republican and Biden sucks and Obama also sucks. But Trump and his communication style is 100% unusual for a president and the only way you can not see it is by not looking. The Clinton quote you posted has a verbal stumble and a quick return to topic (moving fast on the transition plan) while the Trump quote in context clearly has no message.

          Note that I am not claiming that Trump is stupid. The usual politician style is to have either a scripted speech or to be heavily briefed by your staffers on a list of specific talking points to hit and things to absolutely not say. Trump’s style doesn’t hit on specific talking points, but rather free associates positive words with himself and his actions and negative words with his opposition. This is great for sales, and it clearly works for him, but it also means he spends longer stretches saying nothing in particular and occasionally says outrageous stuff.

          Now, presidents have had their quirks like LBJ and his penis, and this isn’t in person speaking, but do you really think these constitute ordinary public communications from a president?

          Crazy Joe Biden is trying to act like a tough guy. Actually, he is weak, both mentally and physically, and yet he threatens me, for the second time, with physical assault. He doesn’t know me, but he would go down fast and hard, crying all the way. Don’t threaten people Joe!

          So interesting to see ‘Progressive’ Democrat Congresswomen, who originally came from countries whose governments are a complete and total catastrophe, the worst, most corrupt and inept anywhere in the world (if they even have a functioning government at all), now loudly….and viciously telling the people of the United States, the greatest and most powerful Nation on earth, how our government is to be run. Why don’t they go back and help fix the totally broken and crime infested places from which they came. Then come back and show us how….it is done. These places need your help badly, you can’t leave fast enough. I’m sure that Nancy Pelosi would be very happy to quickly work out free travel arrangements!

          Why would Kim Jong-un insult me by calling me “old,” when I would NEVER call him “short and fat?” Oh well, I try so hard to be his friend – and maybe someday that will happen!

          North Korean Leader Kim Jong Un just stated that the “Nuclear Button is on his desk at all times.” Will someone from his depleted and food starved regime please inform him that I too have a Nuclear Button, but it is a much bigger & more powerful one than his, and my Button works!

          (Note that the congresswomen in question were born in the United States, and mostly have parents born in the United States)

          Do you really see no difference in communication style between this and other presidents? And no, this is not “high school gossip” unless you think communication style does not matter at all for a sitting president.

          Oh but you are very cool for being above it all and not accepting media narrative and stuff, so incredibly cool

        • It isn’t “cool”, it is *normal* to not care. I mean, why would I care what a politician says in general? Its all BS anyway. This is how the majority of people think.

          Meanwhile, wandering around on stage like that is something new and exceptional. We haven’t seen this one before. So when normal people see that, they start suspecting dementia. Yea, no doubt it gets magnified by the “other side”. But that has always been the case, and we’ve never seen it to this extent.

          These are descriptive comments, not prescriptive.

        • Anon:

          Despite what you say here, for better or worse, in the U.S. it is normal to care about politics, at least at the national level. Voter turnout in presidential elections is about 60%, and most voters are consistent in how they vote by partisan. Strong partisanship here does not imply love of the Democratic or Republican party; it’s more like strong dislike of the opposite party.

        • You can believe whatever you want about what Joe ordinary thinks. My thoroughly blue collar, non-college graduate care all very deeply about what the presidents say, especially if they’re affiliated with any kind of union, and polling responds strongly as well. But again, you can believe whatever you want about your hypothetical mental constructs.

          My point is that Trump’s statements are not ordinary gaffes clipped out of context; he just has a wild, bloviating manner of speaking and writing that was obviously unusual for a president.

          As for whether it actually does matter, I guess it depends on what you care about. After Trump called for a “a total and complete shutdown of Muslims entering the United States” he issued an executive order banning travel from seemingly random countries, stranding many of my friends who had gone to their families for the holidays. He also threatened to fire the chair of the Federal Reserve for not printing enough money. But on domestic issues he’s of limited significance yeah; the executive order was essentially reversed in court and Jay Powell only printed the ordinary amount of money. Internationally, where the president can act almost unilaterally, it matters a great deal. Trump’s perceived lack of dependability combined with naked antagonism towards China and North Korea has led directly to a great deal of remilitarization and self-sufficiency efforts in the American protectorates of East Asia (South Korea, Japan, Taiwan).

          https://tradingeconomics.com/taiwan/military-expenditure

          So yeah, you can choose to ignore it if you don’t care about anything but it as a matter of fact affects the lives a lot of people, and many people I know personally.

          Even if it were all bullshit, what the president chooses to bullshit about reveals actual information. This kind of “it’s all bullshit anyways, all the same” is just empty truism, using a cynical attitude to paint a facade of wisdom.

      • > so that is what I’d assume was meant.

        You assume that based on what?

        > The constant stream of videos of Biden wandering around on stage are much more informative, because that is an appearance that other politicians manage to avoid.

        So their appearance in randomly assembled or algorithmically curated out of context clips that are often edited for the specific purpose of conveying a particular message is more reliable than what they actually said before you explained the actual meaning based on your assumptions.

        Sometimes it’s hard to believe you’re serious.

      • Trump accidentally breaks from 50 years of strategic ambiguity, calls Kim Jong Un short and fat and threatens to nuke North Korea on twitter: totally ordinary, nothing weird going, not interesting

        Biden doesn’t know where he’s supposed to go after his speech: historically unprecedented, extremely interesting

      • I have generally found that if you hear that Trump said something strange and you take the trouble to find the source of the quote in its context it sounds less strange. Some of the quotes mentioned appear to come from a mammoth speech with a textual transcript at https://www.rev.com/blog/transcripts/donald-trump-speaks-to-the-pray-vote-stand-summit-on-9-15-23-transcript and video at https://www.youtube.com/watch?v=e1ybKpY0p_4 I can find an example quoted in one of the articles linked to where he says World War II and clearly means World War III but carries on and does not correct himself. Searching for Obama, poll, and 2024 in the transcript finds nothing unusual. Make up your own mind from the transcript and the video, but the only change I can see from the Trump of the previous campaigns is that he seems less off the cuff and out of control, which could be down to the occasion not being exactly “Prime Time”.

        • Then there’s this from yesterday (as reported by the Associated Press):

          “We will immediately stop all of the pillaging and theft. Very simply: If you rob a store, you can fully expect to be shot as you are leaving that store,” he said, drawing loud applause. “Shot!” he added for emphasis.

          Maybe it was a temporary aberration to be less off the cuff and out of control. Or is it out of context?

  2. I don’t think statistics is of any use here. First, there is the issue of using such data to make individual predictions – always subject to large uncertainty. Then there is the overlap between cognitive decline (in the medical sense), poor judgement, ethical limitations, basic intelligence, and strange beliefs. I don’t think anyone is capable of disentangling all these factors in a quantitative sense.

    On the subject of age, I don’t see the logic of imposing limitations. I am concerned about the age of many of these politicians. But given all the factors I allude to above, I don’t see the validity of singling out age as a bright line to draw. I’d rather have a senile 95 year old than an evil 60 year old (with some consideration of who they might appoint to assist with their decisions).

    • +1

      The available information is such poor quality, imo, I don’t see how it can be meaningfully useful for assessing probabilities. I would think that base rates, divorced of context such as open information from the people who spend time with BIden or Trump, are next to worthless. Biden- and Trump-specific information is far, far more useful. As would be cognitive assessments.

      An important aspect of all of this would also be Biden’s stutter – which with his strategy of alternative word-finding would enhance the appearance of cognitive impairment – as of course, would Trump’s long-standing strategy of bloviating and sensationalizing that predated the likelihood that there’s age-related cognitive decline.

      But I find myself feeling like “who cares?” Both candidates are so ridiculously bad, imo, as compared to some ideal notion of who I would want to be a president. And I wonder how much the president in office really matters as compared to who his/her managers are, who is in Congress, who is on the SCOTUS, etc.

      I mean I do care about whether Biden or Trump gets elected – i do think that will make a big difference – but I’m not sure how much I care about which one is more likely to be cognitively impaired, or how much they’re cognitively impaired one compared to the other.

    • “I’d rather have a senile 95 year old than an evil 60 year old”, I agree but if there were an age limit of, say, 80 years, then the senile 95-year-old wouldn’t be one of the choices.

      Looking at the other side, we have the seemingly (to me) absurd requirement that the president has to be at least 35 years old. OK, sure, we want some life experience, and I acknowledge that there’s some young age at which we can be sure people don’t enough of it, but I’d put the lower limit at 30 or maybe 28.

      But in both of these cases, how much should it really matter? Even if we set some crazily narrow range, like you have to be between 45 and 60, there would still be tens of millions of people who qualify on age. Let me pick from every US citizen in that age range (or any other 15-year age range) and I, at least, could find at least thousands of people who I think would be OK as president. To the extent that we have trouble finding good presidents — and we do seem to have trouble! — it’s because we’re not picking the best among the people available. If we set some upper limit that excludes some people, that might be objectionable on some sort of fairness grounds but it’s not realistically going to limit the ability to find a good president.

      I don’t feel strongly about an upper limit, but if we had one at, I dunno, 80 or 75 or even 70 (for the age on Election Day) I wouldn’t be out there marching to get rid of it.

      • The problem of finding good candidates that you refer to is a serious one. Age limits (low or high) will do nothing to address that. In your first paragraph, the 80 year limit would force us to have the evil 60 year old. That’s a bad deal. Age has little to do with it – the way we choose candidates is terrible, and the proof is in what we end up with.

        How could we improve it? That is a lengthy conversation and one that I have no particular expertise for. But I’d start with getting the money raising out of the selection process (sorry about the first amendment and corporate giving). I’d also like to see the 2 party system go. Beyond that, I’m open to suggestions.

        • No the age limit would force the 60 year old to run vs someone whose under 80 instead of the opposing party being able to run their candidate at 90+.

          The point of age limits is that politicianing is a process where you embed yourself in a power structure and that structure keeps you in place far longer than you should be… Feinstein should have been forced out a decade ago at a minimum (I’ve always hated her so I’d say she never should have made it to the Senate, but she really shouldn’t have continued until the day she died)

      • “that might be objectionable on some sort of fairness grounds but it’s not realistically going to limit the ability to find a good president. ”

        Badabing.

        The country has an interest in ensuring the leadership aren’t senile or confused. To that extent, what’s “fair” to a 90 year old loon who wants to run again isn’t necessarily what’s fair to the citizens, who have a right to demand mentally functional leadership, regardless of if it’s “unfair” to some crusty toad who’s been in the senate for five decades.

        Look at how much Obama aged during his presidency. High level office is a highly stressful job. It’s not a job for 80 year olds.

        So here you go:

        Can’t take office over age 65:

        President
        Vice President
        Cabinet or Major Agency leadership (Defense, State, CIA, NSC, others; also must retire by age 70)
        Senate

        Must retire by age 70:
        All non-elected Federal officials

        Cannot take office over age 70:
        House

  3. The ages of both candidates are a legitimate concern. But, one of those guys is going to be elected next year, and I cast my vote not for a person or personality, but for policies and policy outcomes. Realizable outcomes matter more than any hair-splitting predictions one might make given age or apparent cognitive ability of the candidates. In any conceivable future, a Biden second term will lead to better (far better) policies than another round of trump.

  4. There are reasons why pilots have a definite retirement age and State Supreme Court Justices have a definite retirement age. Notably, the U.S. Supreme Court Justices, unlike federal judges, do not have any retirement age stipulation. Should there be a mandatory retirement age for teachers of statistics, economics, philosophy, theology, etc.? If so, would the mandatory age be different depending on the discipline?
    As it happens, my fridge gave up the ghost two days ago. Upon investigation, the lifetime of a fridge is, according to what I found, is about 10 years, and mine was purchased in 2003. According to the latest demographic data

    https://www.verywellhealth.com/how-to-live-longer-for-men-2223908

    “From 2020 to 2021, the average life expectancy for U.S. males fell from 74 to 73 years—the lowest it has been since 1996. Between 2019 and 2021, the average life expectancy for U.S. males declined by three years overall.”

    Similar to my fridge, Biden and Trump, it seems that I am well past my expiration date. A new fridge is due to be delivered this coming Tuesday. It is unlikely that any of us will outlast the new fridge.

    • In my lifetime I don’t think I’ve ever had a refrigerator last less than 16 years, so if yours only lasted 10 that is bad luck, or maybe your refrigerator is under more strain than mine. I suppose higher indoor temperature, more usage of the fridge, and perhaps some other factors would affect the lifetime.

      Doesn’t this seem ridiculously short, by the way? (10, 15, whatever). It does to me. I’ve recently been pondering what it would look like if everything I’ve ever owned, that is now in a landfill or a scrap pile, were piled up in a big pile. There would be lots and lots of plastic packaging etc., but also a big pile of refrigerators and dishwashers and clothes washers and dryers, plus a couple of cars and some cameras and computers… multiplied by the number of people in the U.S. it seems like, and is, a heckuva lot.

      A couple of years ago we had a problem with our clothes washer, I forget what it was exactly but something that I didn’t want to get involved with trying to fix myself. I called our appliance repair guy , and he asked the age of the washer, which was about 13 years. He said ‘at that age, you can expect it to break in the next few years anyway. I suggest that you get a new one: if I fix this part, it’s pretty likely something else will break soon.” But I felt bad throwing away a washer that seemed perfectly fine except for one bad part. I spent a few hundred dollars to have him replace the part with a new one. Within six months one of the bearings went bad and the washer made a horrible grinding sound and shuddered terribly when used. Sigh. It’s like the “fabulous one-horse shay”, except instead of lasting “100 years to the day” it lasts 14.

      I recently bought a used power tool called a “ShopSmith”. Mine is a sort of Frankenstein (or, rather, Frankenstein’s monster, whose name was, boringly, ‘Paul’), parts of which date back to before 1962. The guy who sold it to me gave me a box of stuff that goes with it, which includes some old parts that show that he, or perhaps a previous owner, had done some service to replace worn-out parts. The switch is a little balky so I’ve just ordered a replacement, doing my part to keep this thing going. It’s older than I am and if I fix things as they wear out I should be able to pass it along to someone after I die and there’s no reason they can’t keep it going until it’s 100.

      No particular point here, it’s just that I’m getting old so I ramble. (j/k).

      • Phil,
        I think you misread my fridge lament. I wrote, “mine was purchased in 2003,” so it lasted 20 years rather than 10 years. With that in mind, I wrote “It is unlikely that any of us (Trump, Biden or me, born in 1936) will outlast the new fridge. The race officially begins this coming Tuesday when the new fridge arrives. The warranty on the new fridge is for one year. If I pay extra, the warranty is extended. No such option available for Trump, Biden or me.

      • Phil:

        With a fridge, stove, etc., the need for replacement is annoying because the new one isn’t so different from the old. At least when you get a new TV, it’s a lot better than the previous version!

        And, yeah, we’ve had the same experience with you regarding appliances. A year or so ago, our stove had some little problem with one of the burners not completely firing up, so we had a guy come to fix it. He charged . . . umm, I don’t remember, certainly over $100, probably over $200 (“parts and labor”), and then a couple weeks later it broke again, more charges, etc. Now we have a similar problem on another burner. At this point it seems to make more sense to just buy a new stove, even though it’s just some little part that’s needed. So annoying!

  5. I’m two years older than Biden, and all else equal would prefer a younger president. You don’t learn things are quickly when you are old. However, all else in not equal. For one thing, the alternative is autocracy, and for another, Biden knows the job.

  6. My initial reaction (above) was that statistics has nothing to offer on this question. At the same time, it is sort of a fun mental exercise to apply Bayesian logic to the probability of dementia risk for the 2 candidates. That got me to thinking about himmicanes, power poses, and shark attacks – these, too, can be fun mental exercises. So, is there a difference between those exercises (which we, myself included, have chastised) and this one? Of course, the difference is that this is a blog and such silly or destined-to-be meaningless exercises are perfectly reasonable to do on blogs. But to do these things in journals and claim that the results shed light on meaningful real phenomena is not so good.

    So, I believe there is a difference. But I also think it is worth considering how these “fun” thought exercises are similar. It suggests to me that academics exhibit a sort of stunted emotional development when they fail to distinguish between a fun exercise on a blog and a serious attempt to say something about the world. The journals and incentives (promotion, tenure, grants) reinforce this, but they are also populated by the same sort of people. The inability to recognize when fun interferes with, or differs from, meaningful insights is what disturbs me.

    • Dale:

      I think you’re missing the point. Or maybe it would be more accurate for me to say that I haven’t made the point clearly.

      I’m not bringing up the dementia thing because it’s a “fun mental exercise.” I’m bringing it up because it’s an important policy issue, if the leader of a country has diminished mental capacity. This is a potential big deal. Not the biggest deal in politics, but not nothing either. It’s also something that’s being discussed in the news media and which concerns many voters. And it’s a problem where there is uncertainty and there is a challenge of combining information. So a serious statistical problem as well as an important policy issue.

      The tentative conclusion of my above post is that I don’t know what to do about this problem. We have solid base-rate information (prior odds of 1.6 times higher dementia risk of the person who is 3.6 years older), along with tons of difficult-to-evaluate direct evidence. One option here is to give up entirely, another option is to just use the base-rate information, another option is to combine that with some assessment of the direct evidence. None of these options seem completely satisfying, hence the post. I don’t see this as a “fun” thought exercise at all.

      For that matter, I don’t see the research on himmicanes, power pose, and shark attacks to be merely “fun mental exercises.” I think all of that research is, for scientific and statistical reasons, mistaken, but if it were not mistaken—that is, going by the assumptions and methods used by those researchers—these are legitimate and important topics of study: how human behavior can be affected by seemingly irrelevant factors. That’s a topic that is big if true.

      • In that case, I take issue with your intent in this post. First of all, dementia is not a binary problem. A little dementia may not impede someone’s function very much. Enough dementia becomes a real problem. But the focus on these two people and whether or not the exhibit dementia (aside from the statistical issues) is not an “important policy issue” in my mind. At least, not any more important than whether a candidate exhibits honesty, integrity, or ethical behavior. So, the focus on the degree of dementia I agree is seen as important to many voters, but I find that disturbing – unless it is balanced by at least as much attention to those other criteria.

        There are several other politicians currently or recently exhibiting either dementia or other debilitating health problems. Does this disqualify them for political office? I would say that Santos is far more easily disqualified. While he may have some legitimate medical diagnosis, he very well may not. But he is disqualified in my mind far more quickly than any number of these others.

        • And, for that matter, I view almost all presidents I have lived through exhibit either some degree of mental impairment or serious ethical flaws – and I view the latter as more serious than the former.

      • To the extent that the risk of dementia is felt to be important (not very much to me, including my own risk!), at least let’s use a more complete picture of the risks. We could use something like a dementia risk calculator (e.g., https://www.projectbiglife.ca/dementia or https://alzheimerdementiacalculator.wustl.edu/) for more meaningful base rates that relying on age alone. While age may be the most important factor, several others matter. From Canadian data, it appears that one in 4 Canadians of age 85 have dementia. So, even if that were the posterior probability, as you suggest I don’t know what to do with that.

        The more pertinent question might be whether the person is able to do the job. When I look at McConnell I believe he has had at least two episodes where he has been unable to function. Does that disqualify him? I don’t think so. There are few things that Congress does that require instantaneous and real time decision making. Even in those two instances, he had support staff that, arguably, enabled him to function. The standard for a President would be somewhat higher since there is the possibility that immediate action would be required. I don’t believe Biden has exhibited behavior that fall short of that standard, nor is the probability of him developing that incapacity large enough to disqualify him (of course, we have the 25th Amendment which could handle all but sudden and immediate cases of incapacity). On the other hand, I have a fairly long list of politicians (past and present) that I believe should be disqualified on grounds of dishonesty, lack of integrity, and/or evil character. As you say, mental impairment is far from the most important factor.

      • Hi Andrew,

        Just came across this blog and found it interesting– I imagine it wouldn’t be too difficult to quantify the direct evidence, although figuring how to interpret it/weight it’s importance relative to the prior odds could be challenging.

        For example, if one had enough time, looking at transcripts of three randomly selected full speeches and/or interviews from 2016, 2020, and now would allow for comparison of several different statistics (sentence complexity, frequency of losing the train of thought or suddenly switching topics, etc.) For Trump in particular, it would be interesting to look at his tweets (previously) or whatever he currently posts on Truth Social — increased “clusters” of tweets, increased emphasis on people personally out to get him, overall skew towards negativity versus promises for positive change could be interesting indicators to track (as well as just the total frequency of how often he is posting things.)

        I don’t know if any of this can specifically predict dementia and, given that I am not his clinician, would be hesitant to try anyways. But it might provide useful information about how certain aspects of his state of mind are deteriorating or not.

  7. Am I the only one who is angry that our political process is going to leave the voters to choose between two candidates who, for good reasons, are historically unpopular? It is, to me at least, so blatantly obvious that neither Trump nor Biden is fit to be president–based on policy matters having nothing to do with age or even with possible cognitive decline. And yet, this is what our parties have on offer.

    I know I won’t be voting for either of these wretches. I hope I can find a suitable third party candidate.

    • Clyde:

      In comparison, 2008 was a year in which both of the major-party candidates were popular. In 2016, both major-popular candidates were unpopular, which gave hope to third parties. But the third-party candidates were unappealing in their own ways. They did better than third-party candidates usually do, but ultimately didn’t get a large share of the vote.

    • My first opportunity to vote was for either Humphrey or Nixon. I too decided I was not going to vote for either of the wretches. In hindsight, I should have voted for Humphrey. I believe if Trump is elected you will have similar regrets. In my view, there is something wrong with most politicians (mainly due to the money involved, as previously commented), but some are much worse than others.

      The third-party aspirants I know of (e.g., Cornel West, RFK Jr.) are far worse than Biden, in my opinion.

      In other news, a bit more on topic, at about Trump’s age, I have definitely suffered impairment in memory, energy, and health, but still manage to complete, e.g, computer programming tasks. Impairment is not dementia–yet. I do need to double-check all the things my memory tells me about world and personal history, though.

  8. Checking this thread this morning I am disheartened to see some commenters actually supporting an age limit. Maybe it is because I am getting old that I am sensitive on this point. But how many examples of young politicians that are unfit for office (due to dishonesty, evil intentions, or stupidity) are required before we can throw out this ridiculous idea that age limits are a wise thing (I wouldn’t impose a minimum age requirement either)? In brief: first, while age is a (the) greatest factor affecting the probability of cognitive decline, it is not the only factor and we have better information than relying on age alone. So, if we are going to conduct a statistical exercise to determine the probability of a candidate’s decline, then let’s at least use a more sophisticated risk calculator. Of course, the effort to develop and approved calculator that will actually be used to determine a candidate’s right to run for office will turn into the worst of what we’ve seen in academic modeling disputes.

    Second, I doubt we can agree on what cognitive decline actually means. Compared to what? Compared to what someone could do when they were younger, compared to what the “average” person of age x could do, compared with some “objective” measure of ability to think? Actually I sort of like the last one of these, but I doubt that age is the most significant determinant of that one.

    Third, while I share people’s distaste with current candidates and past politicians, I think a little more generosity is in order. We have a number of current and past office holders who clearly exhibit the declines of age, both physically and mentally. Before you declare them unfit for office, I’d suggest you take a more complete look at their experience as well as the lack of experience of many younger politicians. As much as I detest what goes on in Congress, there are real political and ethical debates and compromise is a necessary feature of a government (at least one that I want to see). Many of these old politicians have a proven ability to compromise that younger people may not have. They may also have better judgement about who to surround themselves with as advisors. Of course, they may not – but, again I don’t think age is the determining factor either way.

    Fourth, I’ve seen (on other blogs) plenty of people state that there should be an age limit for academics – retirement should be forced after a certain age, tenured or not. I’d suggest the same issues arise in that case. There’s plenty of “dead wood” in academia, but there are also plenty of young academics who are either unqualified, ill-suited, or otherwise should not be permitted to teach classes. Singling out age as a qualification of academia is perverse in the same way that it is for public office.

    I am truly disappointed to see a number of people actually considering an age limit as a good idea.

    • > (I wouldn’t impose a minimum age requirement either)?

      you really think 2 years old isn’t too young to be president?

      The point of imposing an age limit is so that we don’t have people embedded in a political machine extending their stay beyond where we can reasonably believe with high probability that they will be fit for duty physically.

      If you’ve been a politician all your life and reach some age (72 say) and haven’t been elected president, then it’s time for you to leave it to someone else.

      fitness for duty in terms of ethics and such are also an issue. I would argue that if you are nominated to either the Democrats or the Republican party this disqualifies you from being fit for duty as president. Unfortunately my view doesn’t matter.

      • Note that my suggestion specifically was not a given age, but rather an age at which the overall frequency of dementia is objectively low in the population, so the prior probability would be that a person isn’t in significant cognitive decline.

        https://statmodeling.stat.columbia.edu/2023/09/29/donald-trumps-and-joe-bidens-ages-and-conditional-probabilities-of-their-dementia-risk/#comment-2266625

        If we have medical technology that lets most people live to 200 years old and dementia hits 3% typically around 180 then you’d set the age to 180

        A fixed age is not a good plan I agree with that. But also, a supposed evaluation of the individual is not a good plan either because the politics of getting a reliable evaluation is impossible.

        • Sorry, but I don’t go along with your suggestions. First of all, while 2 years old is extreme, what about 11? There are exceptional 11 year olds that I might prefer to most of the current politicians. But the more important fact that you overlook is that it is for the voters to decide. It will be hard for a 2 year old to convince people to vote for them. An 80 year old will still have to convince people. Now, I am as disturbed as you by what people will vote for – but as Churchill implied, the alternatives are all worse.

          The idea of a cutoff probability of cognitive decline doesn’t work for me either. First of all, that probability is affected by many things and I would foresee many unresolved fights about what the risk calculator should look like. And then, what do we do about the error ranges around those estimates?

          Further, I repeat: cognitive decline relative to what? More precisely, how does cognitive decline affect your ability to do your job? I don’t think that question is straightforward.

          In the end, it is the voters that choose who to vote for. All sorts of conditions (physical and mental) will impact how an individual performs. I’m all for disclosure, but then leave it to the voters to decide. Using an age cutoff, even derived from a model of the probability of “significant cognitive decline” seems like a poor way to restrict voters’ choices. I could list dozens of criteria I would use before using age.

        • Dale:

          The 2-year-old doesn’t have to convince anyone. All that is necessary is for the 2-year-old’s representative to convince people to vote for him. I think this could definitely happen if the 2-year-old is an heir to a political family.

        • Andrew
          You seem to be getting more skeptical. If it “definitely could happen” due to family heritage and a representative’s convincing, then it seems even more possible that shark attacks influence voters. At times you seem to reject how fickle voters may be and at other times you portray them in the most fickle terms. Voting for a 2 year old seems quite fickle to me.

          Perhaps more common ground is to say that many voters will vote their party allegiance almost regardless of who is running. That I may, unfortunately, believe. And if the 2 year old is supported by their party, then it definitely could happen. But in that case, I’d say the cure is not to put a minimum age limit – I believe it indicates far more serious problems with our political system. I’m perfectly serious saying that having a group of 2 year olds in Congress might be just what we need if our system is that broken.

        • Dale:

          I say that people would vote for a 2-year-old because, historically, people have often voted for unqualified political heirs, and I suspect that they’d vote for the 2-year-old heir if he or she seemed like the only possibility.

          Also, I think that shark attacks could very well influence voters! What I wrote on the topic was: (a) I don’t think the research claiming to show the influence of shark attacks actually showed what it claimed to show, and (b) I expect that any effects of shark attacks would depend very much on context, hence I doubt we’d see large average effects.

        • Andrew
          I seriously ask you: if people would elect a 2 year old from a family dynasty “if he or she seemed like the only possibility,” doesn’t that suggest some serious problems with our political system? I’m not denying the fact that it could happen, but I find it disturbing enough that I think the “solution” to not permit 2 year olds to run for office is no real solution at all. It keeps the 2 year old from being elected but does nothing for the underlying problem that (a) people would cast their votes that way, and (b) that there was not other possibility on offer.

        • Dale:

          I don’t think it’s a problem with “our political system”; it seems like a more general political problem, given that this sort of thing has happened all over the world in some form or another. No one would hire a 2-year-old to fix their pipes or do their taxes, but the 2-year-old political leader seems like a more legitimate possibility because presumably someone else would be running the show.

        • Dale, I’ll give you zero age limits provided you give me score voting on a 0 to 5 scale (zero default if no mark made), and a minimum of 10 candidates for every office with no primary elections at all. I’m open to discussion as to how to determine who’s on the ballot.

          I honestly think that’d solve a LOT of the US’s problems.

        • Daniel
          I’ll agree to that – unfortunately it is not my place or capability to deliver what you want. I’ll offer an alternative – if we change the discussion from biological age to mental age, I’m prepared to support both minimum and maximum age restrictions on holding pubic office.

      • If we’re having zero age limits for candidates, can we have zero age limits for voters as well, please? My 8 year old would love to vote in the next election.

        • We have all sorts of age limits applied to children – voting, drinking, owning guns, driving, serving in the military, financial and legal responsibilities, etc. These are all problematic, although most people just accept them. It is true that younger people have brains that are still developing in some ways that have implications for their ability to make decisions and be responsible for them. It is also true that many parents are not really better at making decisions than their children would be. I can’t imagine developing and using some sort of mental capacity test for these activities (e.g., voting). At the same time, having somewhat arbitrary age limits doesn’t strike me as particularly attractive either – the main justification for each applied age limit is probably the existence of the age limits for the other activities. There is a circular logic to saying that minors should not vote because minors are not legal adults.

          So, I’m not sure how sarcastic you are being in saying that your 8 year old would love to vote. Yes, it is pretty ludicrous, but I also think it is ludicrous that we permit some 40 year olds to vote. I’m willing to agree that the average 40 year old is better able to cast a rational vote than the average 8 year old (although I’m not sure how far I’d be willing to push that logic). The best defense I can offer for not permitting 8 year olds to vote is that it would upset a whole set of legal restrictions we have about age and legal responsibilities. I think that can of worms is probably left mostly unopened. It is convenient to not have to debate and reexamine every age restriction we live with. But that is not quite the same thing as saying that these restrictions make sense in themselves. In other words, I don’t find it completely ridiculous to think of your 8 year old being able to vote.

        • Dale the thing about age limits is that they are objectively verifiable. Has it been more than 18 years since the birthdate listed on an official record? That’s pretty easy for everyone to verify, document forgery notwithstanding.

          Do you have a “mental age of at least 18 years but less than 70 years?” Yeah, according to who? At least with my suggestion for an age at which 3% of the population exhibits dementia it’s somewhat objectively verifiable, it’s a statistic about the population at large. If you ask “does person X have dementia?” then it can easily become a political football: who are the people making the determination, how much have they been paid off, how much does their personal desire for particular political outcomes affect their judgement, how much have they been threatened with credible death threats, etc etc etc.

          What are people going to do about population stats from the Census? Threaten every doctor in the country that if they don’t add/reduce the rate of dementia diagnosis bad things will happen to them and their family? The overall rate in the population is way less gameable. The only thing about setting age limits at the upper end is that medical technology etc has improved a lot. If you were to set a “healthy maximum age to be president” for people in 1900 you’d have probably chosen maybe 60-65, today it’d probably be closer to 70-75.

          Judgements to be made about individuals will always be gamed, and so heavily gamed that they will look nothing like reality. For example Dianne Feinstein should have been forced out *years* ago. And it’s just not reasonable to say that the world loses out because we can’t elect 90 year olds. Sorry, as much as some 90 year olds may be wonderful and even competent people, the world would be better if the maximum age for taking office as president was closer to say 60. There just isn’t a lack of qualified candidates between the ages of 35 and 60.

        • Daniel
          I agree with everything you said, except the last paragraph. Certainly age limits are more verifiable and less gameable than “true” measures of capability. That would make them much more suitable as legal requirements – if the relationship between the objectively measured age and the “true” measure is close enough to warrant its use. It is that second part that I don’t believe. Even if we accept that each year of age beyond X adds Y% to the probability of cognitive decline on average (and that “if” is far from unambiguous), applying it to individuals is subject to much greater uncertainty. Your claims that the costs of mistakes is small (eliminating the 90 year old politicians because of the qualified candidates between the ages of 35 and 60) I don’t find convincing. There are also many unqualified candidates between the ages of 35 and 60 and what you need is confidence that we have a good process of ensuring that the better qualified candidates are the ones we would end up with. Also, despite your obvious dislike of Feinstein, I am not seeing evidence that it was costly that she continued to be in office at her advanced age.

          I think you have answers for this – I’ve seen you refer to many changes in our political process which would improve the selection process – many of which I would agree with. However, absent those changes, I’m not convinced that the age limit would result in a better choice of candidates.

        • > what you need is confidence that we have a good process of ensuring that the better qualified candidates are the ones we would end up with.

          Dale. Age disqualifies by more reasons than just physical and mental competence in my opinion. In most cases it also disqualifies on the basis of incorrect frame of reference and on embedding in a political “machine”. People tend to hold on to opinions and policy ideas long after the concepts on which they are based are accurate assessments of the current state of affairs (ie. they tend to be come “out of touch”), and the more they are embedded into political power structures the more corrupted they become. Age limits are kind of like term limits, they limit the damage that people can do from accumulation of power. In that sense I’d welcome older outsiders more than older “statespeople” but I think there’s huge advantages to limiting the total time you can be a part of the US govt.

          Yes, you’re right I absolutely detested Feinstein, she was a stateist elitist in my opinion and an enemy of the US people and US constitution, she routinely proposed bills directly infringing on the Bill of Rights with absolutely no compunction. She proposed many pro-law-enforcement anti-privacy and anti-individual laws directly opposing the protections of the 1st, 2nd, and 4th amendment, she was pro spying pro PATRIOT act, (co-sponsored bills to expand wiretapping and limit the protections of the american people from all sorts of electronic SIGINT gathering), a patsy to Hollywood and the recording industry, she was responsible for much of the way in which industries stole our cultural heritage (in the form of essentially “forever copyrights” the DMCA and similar acts). She believed that Marijuana should remain a Schedule 1 drug, and that we should continue to prosecute the war on drugs. She directly sponsored the behind-the-counter status of Pseudoephedrine which is directly responsible for millions of deaths, the methamphetamine epidemic we have today, and a dramatic increase in chronic medical conditions in the US. She was basically horrible.

        • Daniel
          We’ve probably reached the end of productive discussion. I would only point out that your accurate (mostly in my view) perceptions of the age-party politics links should be balanced against the age-selfish ambition dimension. Much as I suspect you disagree, I find most of the current and recent very old politicians have some real belief in “public service.” I believe very few of the young politicians really believe in the term and instead mask their pursuit of power with the appearance that it is “good” for the country. I don’t expect you to agree with that, but I think you totally discount the positive aspects that age can bring to the job. I have little respect for the views espoused by many old time politicians (think back to the Strom Thurmond era, a racist, in my view) but I do think they shared something that seems to be missing in most of today’s politicians – they believed they were serving their constituents rather than the other way around.

          You can have the last word unless you want to take this offline.

        • Hi Dale, no worries as you should know by now i respect your view and I do in this case think you have good points. I’m normally against arbitrary rules, so I’ll just say that if we have age limits I’d argue for them to be based on features of the growth and survival curves of the population because those are less gameable than supposed individual evaluations.

          In any case, at any time on any post if things go far enough afield and someone wants to continue it off-blog I have found that discussions on mastodon have a public forum style that is very similar to this blog, and I’d encourage people from this blog to discuss those “offtopic” or “extra detailed” topics by public message there, I can be tagged by @[email protected] it’s important to me that Mastodon is a decentralized universally accessible cooperative of servers and it’s not a commercially controlled “walled garden”

  9. Of course a major risk factor for developing severe dementia is already having mild dementia. I don’t think untrained observers watching someone on TV (or other media) can reliably assess the degree of dementia (if any) that they have. But I think an independent panel of doctors after an examination could offer an useful assessment. Sufficient public pressure could make this a norm with a political price for violating it.

    • Joshua:

      Yes, Reagan’s second term did not go well, and in retrospect given the economy it seems pretty clear that just about any Republican could’ve replaced him and won the 1984 election. The Republicans lost in the 1982 midterms, though, so with the 1984 elections coming up they weren’t as confident as maybe they should’ve been.

  10. Despite what you say here, for better or worse, in the U.S. it is normal to care about politics, at least at the national level. Voter turnout in presidential elections is about 60%, and most voters are consistent in how they vote by partisan.

    This is a misreading of what I wrote: “Most people do not care if it is a democrat or republican. It just makes little to no difference for their lives. If you identify as either you are a minority, even both combined together.”

    Can we agree that the majority of the US population is either non-voter or “independent”? This is something like 70-80%.

    And for sure I agree Trump doesn’t act “presidential”. But there also are not dozens of videos of him wandering around on stage like he is lost.

    And I personally want a president with the least charisma possible, so have no problem with Biden having dementia. It is actually a good thing imo.

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