conditional probability
Currently, betting markets suggest that the Democrats have a 54% chance to win the presidential election in 2028.
Brian Tannehill claims, however, that the chances of a Democrat actually taking office in 2029 are nearly zero.1
The path for a Democrat to be sworn in on 20 January 2029 is so narrow that I deem it to be nearly impossible, and so should leaders within the Democratic party...To summarize, here is what must happen:
- A Democrat who can win has to make it to election day outside of federal custody
- A Democrat must overcome attempts to suppress votes, and win the electoral college
- They must overcome potential skullduggery by Dominion to manipulate vote counts
- They must prevent local and state officials from refusing to certify the election
- They must get SCOTUS to prevent ALL attempts to overturn election results
- They may have to overcome another fake electors scheme
- They must control the House of Representatives, despite all of the election challenges above (gerrymandering, end of the VRA, Dominion, polling place intimidation, fights over mail-in voting, etc…)
- They must get the House of Representatives sworn in and seated by January 6th.
- They must get the Vice President (presumably JD Vance) to certify the election
- They will likely have to get Republican Senators to defy the administration at great personal risk to vote to certify the election
- They must avoid or prevent Trump from using law enforcement, the military, or the mob to prevent Congress from certifying the election results
- They must successfully get the Democratic nominee sworn in despite whatever efforts Trump and the GOP use to prevent it from occurring.
If any one of those things doesn’t happen, then a Republican ends up President regardless of how people voted.
That's quite a list! I want to set aside the plausibility of each of these steps actually being prevented from happening---they range from that is indeed a bit concerning to batshit insane conspiracy theory---because that's a secondary issue for a different blog post. Here we are focused on the math of Brian's conclusion:
Even if you charitably assume that the Trump administration only has a 50-50 chance at succeeding at each of these steps, the probability that a Democrat is president on January 21st 2029 is less than one tenth of one percent (.0975%). Or, it’s a one-in-a-thousand chance, at best.
This is bad thinking about probability.2
The problem is Tannehill is making the assumption that the events are independent, like flips of coin. Each hurdle the Democrats must clear is a different flip. Fail on any of the 12 flips, no presidency. The only way to win is if the coin comes up heads 12 times in a row, and that is indeed a very small chance.
But, of course, these events aren't independent at all; they are highly correlated.3 Especially in tandem. If the first eight things are accomplished by the Democratic candidate, the probability they accomplish the last four skyrockets. And that's because the underlying mechanism controlling the events (public opinion, norms, etc) is similar/identical for each event.
Indeed, if we imagine they are perfectly correlated, then the probability of Brian's hypothetical---using his own numbers---shoots all the way from 1-in-1000 up to 50%! Instead of dealing with 12 coin flips, we're considering 12 cups of punch drawn from a single punch bowl, which has a 50% chance of being poisoned.4
As a computational matter, once things are correlated, you need to start using conditional probability. That is, p(A and B) = p(A) * p(B|A), which can be read as "the probability of A and B happening is the probability of A happening times the probability of B happening given that A already happened."
Back to Tannehill's example, imagine that the first 11 steps miraculously happened: a Dem wasn't put in jail, won the vote and the EC, overcame Dominion, local certification problems, and the Court, avoided all fake elector schemes, Dems controlled the House, seated the House, Vance certified the election, GOP Senators certified the election, and no mob appeared at the Capitol.
What's the conditional probability that the last event---the Dem nominee is sworn in "despite whatever efforts Trump and the GOP use to prevent it from occurring"---happens given that the first 11 did?
It's essentially 100%. Because the correlation between (the first 11 things happening) and the 12th happening is almost certainly near perfect.
I do not know the probability that the 2028 election ushers in a competitive authoritarian system because Trump and the GOP successfully rig the game. It's certainly not zero! But I do know that you cannot figure it out by listing potentially ways the system can fail, assigning each of them a probability, and then multiplying them together as independent events. That's not how the world works.
And, of course, if you actually believe the Democrats have less than a 1-in-1000 chance of holding the presidency in 2029, you should immediately get your money in the betting markets and get rich.
This is technically a slightly different claim. The betting markets are setup to resolve upon major news outlets agreeing on the winner, with the actual inauguration as a fallback if the outlets don't agree. Tannehill is making a claim about the inauguration, which in theory could be correct even if the betting markets resolved the other way, though in many cases the two will be correlated.↩
It's also literally bad math. (.5)^12 is 0.0244%, or 1-in-4096.↩
Some of them almost perfectly so. Like, if the Vice President certifies the election, Republican Senators almost certainly would as well.↩
This would be a dark place to use a very old bridge joke. "What's the probability Trump becomes a dictator?" "50-50, he either does or he doesn't."↩