What are the odds, II: the Venezuelan presidential election
terrytao.wordpress.com
terrytao.wordpress.com
There are a lot of different ways in which election results can 'look fishy', especially if you take combinations of different districts looking suspicious into account, and so on. Looking at digit distributions (Benford's Law) of various numbers (total votes, percentage), looking at exact numbers of votes, looking at exact percentages of votes, errors looking too much like a normal distribution or some other theoretical distribution, etc...
Since Terry Tao likely heard about this particular proposed anomaly and then looked into it, there is a selection bias: if a different metric had looked fishy, it would have been reported instead. But it is hard to know how many different things were looked at and not reported on because there was no anomaly. The end result is effectively cherry-picking the one thing that looks worst, and then doing statistics on that without all the other negative results being corrected for. This sort of thing plagues a lot of statistical research unfortunately.
That's not to say there was necessarily integrity in the Venezuelan election, but this type of analysis has to be taken with a grain of salt.
I was hoping for something like; "The probability of these apparently fake numbers being genuine is in the range 1/1500 to 1/130,000, depending on what other assumptions we make".
Maybe that's impossible in the same way that talking about the improbability of a shuffle revealing some specific series of cards says nothing about the reality of one such sequence after it's revealed.
You’d need to run that election 100 million times to expect an outcome with vote totals that landed on percentages that all rounded to exactly 0.1.
It more like, if you run that election 100 million times, it's very likely that these kinds of results would happen only once.
That once could be in the very first time you ran the elections, it could be in the 100 millionth, or anywhere in between.
> You’d need to run that election 100 million times
You don't. It might happen the very first time. It's as probable to happen this time as it is in any of the other 100 million times.
> The numerical anomaly is that if one multiplies the total number of voters {10,058,774} by the round percentages {51.2\%}, {44.2\%}, {4.6\%}, one recovers exactly the above vote counts after rounding to the nearest integer:
...
> giving credence to the theory of the election report being manipulated (though it is possible that the manipulation could occur through a third hypothesis {H_2} not covered by the original two hypotheses, such as a software glitch
Andrew Gelman's post on the counts is better written: https://statmodeling.stat.columbia.edu/2024/07/31/suspicious...
(The description and the conclusion aren't different; it's just easier to read.)
100% turnout, and the party-selected winners always win! You’re always free to non-anonymously vote for another candidate of course. What could go wrong?
In the Brazilian Old Republic (pre-1930), that was widely practiced. Historians call it "voto de cabresto" (loosely translated to "halter vote").
> why not simply oppress entire regions?
That's what in Brazil is called a "curral eleitoral" ("electoral corral").
The latter still exists and I imagine exists in many countries. Its effectiveness is highly curbed with anonymous voting though.
In the Old Republic, where voting was not anonymous, the electoral corral combined with the halter vote meant very few people were free to vote according to their wish. Local oppression is a powerful tool.
https://en.wikipedia.org/wiki/End-to-end_auditable_voting_sy...
As should be obvious, anonymous voting may be far from perfect if other parts of the electoral process are deeply rigged, but it at least prevents the blatant dangers of being personally afraid to even cast a vote against the leader even if you know your vote might get papered over with electoral rigging.
A government like Venezuela's wouldn't care if that level of transparency made their vote counts look like even more obvious frauds. Its electoral victories already look bad and it doesn't stop anything they do. But at least they can't tacitly coerce voters into not even casting the "wrong" vote.
This is Venezuela. If the people want the country back, they can't expect to simply lead regular lives.
>> But at least they can't tacitly coerce voters into not even casting the "wrong" vote.
Everything is a trade-off. I believe it is harder to coerce voters than to not bother looking at the votes at all and declaring victory.
With non-anonymous voting, the people would still be encouraged by that 1%, but also seeing 1% of voters lose their job/get beaten/go to jail/… puts a serious damper on that encouragement leading to “I’ll vote against next time”.
That’s why non-anonymous voting doesn’t work against despots.
I think this can be shorted to "voting doesn't work against despots".
Really, so in order to change their government they should be forced into even worse miseries of being exposed as so-called traitors to the ruling regime by having their specific vote known? What ridiculous logic. Anonymous voting at least gives that modest avenue of protest towards a change that might not require a personal blood sacrifice. It's grotesque to push for even more risk against civilians.
Your last sentence on the other hand is a complete non sequitur.