How to Check Election Results (feat. Pólya's Urn) - Numberphile

Professor Ron Rivest discusses a technique for post election audits - taking small samples and using Pólya's Urn.
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[booodan]

Do you guys realize who he is?! This is Rivest of Rivest Shamir Adleman AKA RSA AKA the only way you can send your bank account info to Amazon without it getting stolen! This guy is a legend in crypto!

[Ceelvain]

Ron Rivest? The one from RSA and MD5? OMG! I want an autograph!
So many great people have been in numberphile.

[ARidley]

I just finish watching this video in a break on work on my dissertation, then I notice the name of the professor again, look down at the paper I'm reading and he's the author. What a coincidence!

[georgefowler]

You guys are being a bit cheeky using a man vs. woman ballot example on November 7th

[TheBlazeThrower]

I don't quite understand why the Polya's Urn technique is more useful than just looking at the sample. If the original sample has more Alice, then the Polya's will make it more likely for Alice to win the simulation vice versa. It's an unnecessary extra step.

[afbdreds]

5:08
I didn't get exatly what's the point in making the sample larger by randomly copying. I mean, the bigger copied sample won't be in general won by the one who was winning in the non copied small sample?

[krajorama]

Will you do a video on Pólya's approach to problem solving? I think it's very useful, not just in mathematics. I use it for troubleshooting software...

[JohnHarbot]

I'm over here in stitches LOL at the 4:55 minute marker. "in a probabilistic sense we are drawing from the posterior" !!! Professor Ron Rivest, I admire your wits!

[funkyspyspy]

The Singapore General Election 2015 used sample count to announce as part of election results as well, prior to actual results.

[kametrixomtikara]

I don't see how adding randomness is of any meaning. If we're going to take a sample with 8 votes and Alice wins 6 of them, it's most likely that Alice has about 3/4ths of the total votes, adding randomness doesn't add any more information.

A better option (I'm pretty sure) is to calculate how likely it is that Alice won based on the three variables total votes, sample size and sample votes for Alice.

Edit: I get it now, it makes sense, see explanations in the replies

[jacobjonsson]

For 16 it is fairly simple to analytically calculate all the possible vote situations that generated a sample 3A1B. There is one case where the remaining 12 votes are B, i.e. total vote of 3A13B, twelve cases of 1A11B, etc. down to one case of 12A. Why not just calculate all those cases and see how many of the total number of combinations contain a win for Alice? Wouldn't that give a better measure of the probability? Adding the uncertainty of a simulation seems unnecessary, and I would be surprised if this calculation is terribly hard for larger vote counts.

[DFPercush]

I don't see how duplicating votes and throwing it back in the urn is in any way connected to the original set of all votes. You just need to grow the actual sample size until the variation stabilizes.

[ninjafruitchilled]

Can these population estimates not be done analytically? It seems like a very simple system (at least for first past the post), I wouldn't have thought simulation was necessary.

[Scy]

Did someone steal this man's mustache? I demand justice!

[recklessroges]

Its nice to hear Rivest confirm that paper is still the best method known for presidential elections. I'm starting to think that the search for a safe digital ballot method is like a search for a perpetual motion.

[ulmeydasmile]

How is the sampling conducted?!? That I'd really like to know. Do all the ballots come together at one physical location? Per state? How do you draw from a pile where someone might have thrown a few handful ballots to where you are approaching the pile'o'ballots from?

[somitomi]

I am required by law to mention, that Hungarians don't pronounce Pólya like that (5:06)

[robertbrandemann]

Here in the Netherlands all votes are Made on paper and counted by hand, you can vote on certain locations all over the country each voting office counts the votes made there. Even if one person would want to influence the result he wouldnt be able to do it as the counters are forced to stay inside the office until all votes are counted.

[krazed]

this is great! I can follow easily because this was taught in my statistics class. thanks for including the possibility of (accidental) skewing and sample size variation

[kevnar]

This is all moot if electronic voting machines are used, with no exit polling, as was the case in the democratic primaries.