3 ms·

I don't get his reasoning about the Venezuela election. In theory, the chances one candidate get exactly 56.1% votes and 56.108174% votes are the same, right?

I don't get his reasoning about the Venezuela election. In theory, the chances one candidate get exactly 56.1% votes and 56.108174% votes are the same, right? We will need the prior probabilities of 1. Assuming we don't know the vote count, how likely it's rigged 2. Assuming it's rigged, how likely it's rigged in a way that the percentage is precisely XX.X% To calculate 3. Given the vote count we know now, how likely it's rigged Of course I practically know nothing about math compared to Tao, so I might completely miss his point.

energy123 2y ago
The chances are only the same if it wasn't rigged. If it was rigged, the chances aren't the same because humans tend to pick round numbers more frequently. Tao explains this in his longer blog post.
sahbasanai 2y ago
Yes, those chances are the same. But they’re also the same as the chances of the result being 56.108175% or 56.1081756%. So, using your number of decimal places (choosing this number of decimal places is a slight simplification but it doesn’t affect the point), there are 10 million numbers for which the probability was the same. It’s like saying “draw a random number from 0 to 10 million” and drawing exactly 1 million. He says that this unlikely event happened with multiple results in the election, and this would likely mean there is anomaly.
arnogau 2y ago
I think he's defining a round number as, for some precision Y, X number of consecutive most significant digits are 0. e.g. for a precision = 8 number, its "round" when the last 5 digits are 0, so like 32.300000 would be round. The probabilities of round vs non round are pretty skewed. There are far fewer round numbers (for reasonable definitions) than there are non round numbers.
- ithkuil 2y ago
  Not all numbers come out equally as likely. Round numbers are more likely to be picked by humans (or at least that's the argument)
  - raincole 2y ago
    That's why I said we need to know: > 2. Assuming it's rigged, how likely it's rigged in a way that the percentage is precisely XX.X% But I didn't realize he wrote a blog post about it. He actually addressed everything I listed (and more) in detail: https://terrytao.wordpress.com/2024/08/02/what-are-the-odds-ii-the-venezuelan-presidential-election/ https://terrytao.wordpress.com/2024/08/02/what-are-the-odds-... TL;DR: Yes, we need to know all these priori probabilities to get the exact answer. He made an assumption about them.

energy123 2y ago

The chances are only the same if it wasn't rigged. If it was rigged, the chances aren't the same because humans tend to pick round numbers more frequently. Tao explains this in his longer blog post.

sahbasanai 2y ago

Yes, those chances are the same. But they’re also the same as the chances of the result being 56.108175% or 56.1081756%. So, using your number of decimal places (choosing this number of decimal places is a slight simplification but it doesn’t affect the point), there are 10 million numbers for which the probability was the same. It’s like saying “draw a random number from 0 to 10 million” and drawing exactly 1 million. He says that this unlikely event happened with multiple results in the election, and this would likely mean there is anomaly.

arnogau 2y ago

I think he's defining a round number as, for some precision Y, X number of consecutive most significant digits are 0. e.g. for a precision = 8 number, its "round" when the last 5 digits are 0, so like 32.300000 would be round. The probabilities of round vs non round are pretty skewed. There are far fewer round numbers (for reasonable definitions) than there are non round numbers.

ithkuil 2y ago
Not all numbers come out equally as likely. Round numbers are more likely to be picked by humans (or at least that's the argument)
- raincole 2y ago
  That's why I said we need to know: > 2. Assuming it's rigged, how likely it's rigged in a way that the percentage is precisely XX.X% But I didn't realize he wrote a blog post about it. He actually addressed everything I listed (and more) in detail: https://terrytao.wordpress.com/2024/08/02/what-are-the-odds-ii-the-venezuelan-presidential-election/ https://terrytao.wordpress.com/2024/08/02/what-are-the-odds-... TL;DR: Yes, we need to know all these priori probabilities to get the exact answer. He made an assumption about them.