What are the odds, II: the Venezuelan presidential election

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.

Related Suspicious data pattern in recent Venezuelan election (886 points, 3 days ago, 514 comments) https://news.ycombinator.com/item?id=41123155

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

Have to drop anonymity from voting. Yes, I know there are down sides but large scale corruption on a transparent system is difficult.