Not vouching for the election result, however, some kind of correction for multiple comparisons is probably needed here.
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.
One hesitates to criticize the great man but, as mmastrac has already pointed out, it's really difficult to parse out a conclusion, especially a straightforward probability estimate.
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.
TL;DR, and this took a while to parse out, but the post suggests a highly unlikely event that the vote was accurate.
> 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
Excellent idea. With de-anonymized voting, the not at all corrupt, totally non-violent ruling regime would never take advantage of the added ability to know and threaten specific people who voted for the opposition.
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.
With anonymous voting, resistance can grow over time. Election #1 may see 1% of voters vote against the despot. Encouraged by that, the people increases that to 10% in election #2. Further encouragement sees that go to 60% in election #3.
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.
>This is Venezuela. If the people want the country back, they can't expect to simply lead regular lives.
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.
Absolutely the hell not. Secret ballots are integral to free and fair elections. Once you lose anonymity, you open the door to a whole host of other issues, including the obvious potential for political oppression.
Everything is a tradeoff. It would be better than the current situation. Difficult to politically oppress wide swaths of the population on a person by person basis. Furthermore, voting regions are not anonymous (in some systems at least), why not simply oppress entire regions?
Which current situation are we referring to here? In Venezuela, if every vote were tied to a specific identified person, their government could still ignore that and doctor the result. The only thing that changes is that now there is a list of opposition voters in the hands of a hostile government. If the goal is to allow individuals to audit their vote and ensure that the government counted it correctly, it is possible to do that without compromising anonymity. If the goal is to release a public list of every person who voted and who they voted for... I think you're insane and drastically underestimate the capacity for voter coercion and political violence.
> Difficult to politically oppress wide swaths of the population on a person by person basis
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.
Fun fact: North Korea uses non-anonymous voting and it works great!
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?
No voting system can overcome such a regime on its own. I don't even know why NK bothers with elections. They should just claim they are a monarchy, ordained by God. No one believes their election results anyway.
You could have a pseudonymous voting system where you pick a unique username and when votes are published, you make sure your username is included in the data. That wouldn't prevent someone from inserting fake votes though.
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.