Suppose we magically intervene on the USA to make there be a snap election for the office of President. The incumbent (the existing president) goes up against X, where X is a randomly selected eligible person (e.g. adult, citizen, etc.) Voters have one month of campaigning before they decide, so X isn't a total stranger by the end.

What is the probability that the President wins?

Is the probability substantially different for Biden than it was for Trump? What about Obama?

What is the probability that the President loses in a massive landslide (getting e.g. only 40% of the vote or less)?

ETA: I've changed the title to stop giving the impression that I am looking for a yes or no answer. I'm not looking for a yes or no answer, I'm looking for a probability.

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Yes. The politician wins. Focus groups and polls are clear on this, they won't vote for random people. Trump would also beat them easily.

(Obviously some probability you get someone effectively not random from a random draw, but it's very low.)

I'm interested in the probability. Sorry for giving the impression I wanted a yes or no answer; I've edited the title accordingly.

ETA: Another way of putting my question is: How many eligible Americans are there who, if they magically ended up running against the current president in a 1v1 race, would win? Is it zero? Is it ten thousand? Is it a million? Ten million?

My guess is about a thousand, mostly because if you have a 'strange general election' where you have two Rs or two Ds then Biden and Trump both are highly polarizing without being highly unifying, and Biden has the economy as an albatross around his neck right now, so I'd expect - if the other candidate was reasonable - them to lose the other party and still lose some of their own party, which lets otherwise much worse candidates have a chance. But we're still talking about e.g. 900 politicians and 100 business people and maybe a handful of very famous celebrities. and that's it.  Technical note: Most of the time that Biden or Trump loses it is because they literally died during the month of campaigning, or had a huge health issue where they are obviously no longer able to serve. It's not that unlikely. 
2Daniel Kokotajlo1y
Wow. Yeah, as Charlie pointed out I basically asked the wrong question given what I'm interested in; it should have been something like "how many Americans are there who would have a >40% chance of winning were they to be selected." Thanks for the answer. I find your answer ... well, on the one hand it seems plausible for the reasons you mention + efficient-market style intuitions. But on the other hand... I get the sense that there are millions of Americans who are generally well liked by a majority of people on both sides of the aisle (or would be if they were more famous), and also very smart/impressive/competent etc. And I get the impression that Trump (and to some extent Biden) are hated by half the country. So this makes me feel like the answer should be "millions."
Being well-liked is not the same thing as being a good candidate. People will not vote for someone who is not either a professional politician or someone who is famous in a relevant profession (such as lawyer or finance).
  My theory is that being a politician in the way that presidents have to be is genuinely extremely difficult.  Of course they make gaffs and make stupid mistakes, but that’s because they have the difficulty level set to “stupidly insane”.  And that most people that are in those roles would actually seem much more impressive if you swapped them with the millions of americans you’re talking about. There’s some intuitiveness about this: Look at any modern day campaign trail — it’s public speaking, Q&A, many flights, traveling, remembering a lot of stuff day-in and day-out while working 10-12 hour days.  Very few of the most competent people I know would be able to do that at all, much less do it with the small number of gaffs that politicians actually make.

Random person most likely has an IQ of 100 which is a standard deviation or two below a random president. Random person most likely has less talent and experience at politics, promotion and attack than a politician. Random person is most likely less physically attractive, less charismatic, and less wealthy than a politician. Random person doesn't have a gigantic support apparatus behind them (although even if they do they're probably still screwed because it's not enough to make up for the rest of the deficiencies). As others say it won't even be close. Random person will predictably be slaughtered. 

Not a very principled answer, but: 98%

There is already a substantial preference for incumbents (about 65-35 I think), and I think this would be much stronger if the challenger was completely unaffiliated with politics (I want to say something like 90-10 if challenger and sitting president were equally electable otherwise, maybe 75-25 if the challenger is actually substantially better than the president, 99-1 if they're just average).

Say there's 5% chance they're equally or more electable, 2% they're substantially more electable. Then there's 0.5% on them being equally electable and winning, 0.5% on them being substantially more electable and winning and 1% on them being less electable but winning anyway.

So 98% overall.

Edit: didn't consider that the major party might organise in support of the candidate, this changes things a lot. Say there's a 20% chance that the out-of-power party campaigns for the rando (40% the rando is somewhat-aligned, 50% conditional that the party can get their shit together to campaign for them); then the incumbency advantage will be more like the standard 65-35, assuming equal presidentiality (but I still think they're probably a lot less presidential)

All told...this gets me to 96% chance the sitting president wins.

You are the only person who has actually answered the question; thank you.

The thing that interests me about this is that it seems like if you are right, both major parties are doing a terrible job of selecting candidates to run against the sitting president. There seem to be millions of people who would win. Maybe they care about more than just winning the election? Or maybe even though there are millions of people who would win, there's no one who has a legibly higher chance of winning than [whatever candidate the GOP ends up selecting?]

7Charlie Steiner1y
I think that's the deadly bagel fallacy. Or at least close enough that I get to link the video. (To belabor the point: A 98% probability doesn't mean that 2% of the people are the destined winners, it can represent uncertainty about things that have nothing to do with the person running, like their opponent's mistakes or whether we're at war.)
4Daniel Kokotajlo1y
Yeah, good point. I should have asked "how many people are there who would have a >40% chance of winning if they were selected." Seems like David's answer would be about 5% (so, a few million) given the breakdown given above.
3David Johnston1y
That's what you're after, right?
2Daniel Kokotajlo1y
Yes, exactly. That's why I said "millions."
3David Johnston1y
If there are 2% of the population more electable "all else equal" to the sitting president (and this is a pretty wild guess), then I think you'd need a pretty good selection procedure to produce candidates who are, on average, better than the current procedure.
2Daniel Kokotajlo1y
Really? I feel like there are loads of selection procedures that reliably discern much smaller populations than that. For example, I would guess that if you were an elite university and you wanted a selection process such that the people you admit are each probably within the top 0.1% of the nation by academic ability, you can do that. (SAT tests, GPA, etc.) I would also guess that athletes in the Olympics are in the top 0.1% of the world, plausibly top 0.001% or more.

Politicians are good at campaining. Most people are not. A moderately successful politician at the national level would shred through any random people.

I disagree with this. At the president level, politicians are more like a brand, than a source of labor. Most of the work is done by specialists; all they need is good acting skills, and specialists are good enough to figure out all sorts of ways to make the random person play to their strengths on the podium (there would even be game theory between them and the politician during the debate).

If it was the case, it would be much easier for people who already have a brand to convert it into a political brand. Well, the USA have a tradition of actors turned politicians but in (saner ?) country this kind of things are really uncommon.

To add to the consensus— if a random person actually had a favorable matchup against a career politician of any stripe, that would be a massive low-hanging fruit for existing political actors to capitalize on. The RNC and DNC would be falling all over themselves to present "average joe" candidates if doing so provided a consistent advantage. They're not, so it follows that either those organizations are both highly un-optimized for winning elections (probably not; too much money at stake) or else that the evidence doesn't bear out that they should.

I don't buy this. I think RNC and DNC are not just trying to win votes; the individuals within those orgs are mainly trying to preserve and increase their own power, which entails winning votes, but it also entails a bunch of internal coalition stuff. 

Grabbing an excelent non-politician, and grooming him or her for power, and then attempting to put him in a position of power, without "climbing the ranks", isn't obviously in the interest of any of the party officials of either party. 

The VAST majority of adult citizens would decline rather than suffering the scrutiny of the public, and the unpleasant work of internalizing and repeating the lies needed to win, especially with the expectation that it would get even worse if they actually won.

General Sherman had this one right.  

There's enough magic/counterfactual assumptions in the question that I don't think I can provide a probability - it's a different universe than I live in, so presumably has different voters and different populace.  

Current president of Poland went from being relatively unknown parliament member (I'd bet, less than 5% of general public knew who he was? Also there's another public figure with the same last name, so maybe even some people who knew the name were confusing him with the other guy) to being the president within one year. So with longer timescale, big support from one of leading political powers, and some political backlog it is possible. There are surely similar stories around the world, of outsiders rising to leaders. Of course what you're asking is much more extreme, but that provides some staring datapoint.

Even an unknown member of parliament has still been tested against a competitive market, has at least met many or all the key power brokers, etc. They're much closer to the president end of the spectrum than the random citizen end.

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These answers don't take into account the possibility that the party not in power, organizes to support the random candidate. 

The political science keywords here I would be looking at are 'polarization', 'slate voting', 'split ticket' and 'downballot/downticket'. Essentially, how many voters are voting for X solely and completely because X is now their party's nominee and that's that, they neither know nor care anything about the candidates, because you simply can't let the Y party win? Rapid career rises are thought-provoking but too qualitative (who ever heard of Barry Obama before he gave that speech and began his run for president? Or imagine if John McCain had died a few years earlier - who outside Alaska, a tiny state population-wise, not even 0.8m people, had ever heard of Sarah Palin? I sure hadn't, but unclear what that means). This can be quantified by looking at the increase in straight party voting, and also by natural experiments: obviously, the presidential candidate hasn't died during campaigning recently so no examples there, but there are a lot of elections out there and many candidates will die or otherwise be incapacitated, and their replacement will be effectively an unknown and probably not all that heavily selected in terms of a political career.

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