The Facebook + Cambridge Analytica thing is a trainwreck on multiple levels, but the impact of psychological profiling on the election is overblown. Let me break down the numbers and show why: 1/
One of the few open sources on persuasion profiling (Matz et al, 2017) showed uplifts in conversions up to 50% with personality based targeting of ads. Whether this is predictive of performance on voting behavior is unclear, but lets work with this number for now 2/ 
The same report also gives some insights on the raw numbers you can expect with campaigns like this on facebook. From ads against 3,129,993 users, they ultimately got 390 conversions. Even if the uplift they got is impressive, the overall impact of a campaign is tiny 3/
Now, according to NYT, Cambridge Analytica had data on 50 million accounts, where only 270,000 actually took a personality test and the rest were their friends. So compared to Matz et al, these personality profiles are mostly derived from likes rather than a survey 4/
Depending on what research you look at, this might be not as precise. Markovikj et al (aaai.org/ocs/index.php/…) seems to find a high level of precision, Ortigosa a bit less (sciencedirect.com/science/articl…). Overall let's assume you can get a fairly good personality profile 5/
However, based on the actual numbers on impact from the first experiment, 50 million users would get you about 6000 conversions. Let's assume that we'd like to flip MI, WI and PA - enough electoral votes to change the outcome, and the 3 states with the overall slimmest margin 6/
The total difference is not very big - there was an total overall GOP majority in these states of 77,744 voters. Sounds flippable. But the 50 million accounts were not all there - assuming they're distributed equally to voters, about 5m would be in these 3 states 7/
Meaning a campaign like Matz et al, would get around 600 conversions. And that was a campaign for making you buy a trivial beauty product. A political campaign in the middle of an election? It's hard to know the baseline, but this gives an idea of what the necessary impact: 8/
The Cambridge Analytica campaigns would have to be 100x as impactful as the only publicly known Facebook campaign based on personality profiling to flip the 3 easiest to flip states. 9/
It's not necessarily impossible, but it demonstrates the limitation and scope of what you can manage with Facebook campaigns, even if targeting on personality 10/
By the way: I am assuming here that the most effective campaign tactic would not be to flip peoples voting preference, but suppress democratic voters to not vote and vice versa. If they were flipping people, you'd need half - so it would need to be 50x as impactful... 11/
This also generally seem to reflect my own experiences with facebook ads. I'd be interested to hear if others have results on FB that actually are more towards the 100x of Matz et al. I'll reconsider my take on fb campaigns if so.. 12/
