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How does this relate to things like nation-wide elections? For a 100 million population, a 99% confidence at 0.1 interval needs a sample size of only a million.

How does this relate to things like nation-wide elections? For a 100 million population, a 99% confidence at 0.1 interval needs a sample size of only a million. Does this mean it's not really important that every one must vote? Even an abysmal voter turnout is ultimately representative of the entire population?

YZF 1y ago
If it's a random sample then sure.
redtaperat 1y ago
For 100 million people and a confidence interval of 99% you only need 3000-4000 samples, depending on your moe.
- 01HNNWZ0MV43FF 1y ago
  At that point just elect them! https://en.wikipedia.org/wiki/Sortition https://en.wikipedia.org/wiki/Sortition
MrJohz 1y ago
A good sample needs to be random and representative of the population as a whole, otherwise you introduce sampling bias. Imagine trying to do a survey of what people's favourite fast food restaurants are, but doing it inside a McDonald's — it doesn't matter how large your sample is, it's going to be heavily biased. This is why survey companies spend a lot of effort trying to find random, representative samples of the population, and often weighting their samples so that they match the target population even more. If we treat elections like a survey, then they have a massive inherent bias to the sampling method: the people who will get "surveyed" are the ones who are engaged enough to get registered, and then willing to go to a physical polling station and vote. This will naturally bias towards certain types of people. In practice, we don't treat elections like a survey. If we did, we'd spend a lot of time afterwards weighting the results to figure out what the entire country really thought. But that has its own flaws, and ultimately voting is a civic exercise. You can do it, you can avoid it: that choice is yours, and ultimately part of your vote. In a way, you could argue that the sample size for an election is 100% of the population, where "for whatever reason, I didn't cast a vote" is a valid box to check on this survey. That said, the whole "samples can be biased" thing is very much relevant for elections because many political groups have an incentive to add additional bias to the samples. That could be as simple as organising pick-ups to allow their voters to get to the polls, or teaching people how to register to vote if they're eligible, but it could also involve making it significantly harder or slower for certain groups (or certain regions) to register or vote.
- potamic 1y ago
  A 100% sample is unattainable, not just practically, but fundamentally. Even if you made voting mandatory and ensured collection of every single vote, there will always be people who will fudge their vote because they are not interested in the process. I argue that any election is only representative of people engaged with the process and that fundamentally cannot change. Within that subset, you shouldn't need 100% sampling for high confidence. But agree that random distribution is key to this, but I don't see how that could change with the messaging that every one must vote, versus saying just vote if you're interested.
  - MrJohz 1y ago
    I mean that an election is (theoretically) an 100% sample because every eligible has the ability to interact with the voting process at the level that they choose. So the decision for some people to invalidate their vote, or to vote tactically, or not to vote at all, or whatever else: that's part of the act of taking part in an election. In that sense, you can't not take part in an election, if you're eligible to vote. This is important, because normally, once you take a sample, you need to analyse that sample to ensure that it is representative, and potentially weight different responses if you want to make it more representative. For example, if you got a sample that was 75% women, you might weight the male responses more strongly to match the roughly 50/50 split between men and women in the general population. But in an election, we don't do this, because the assumption is that if you spoil your ballot or don't take part, that is part of your choice as a citizen. But I think we're saying the same sort of thing, but in different ways: you can either see "the sample of an election is every citizen, regardless of whether they voted" or "the population of an election is everyone who voted", and in either case the sample is the same as the population, and we can therefore assume that it is representative of the population.
vouaobrasil 1y ago
Beyond simple statistics and random sampling, everyone voting is important because let's say 1000 people are required to determine the result beyond reasonable uncertainty. Then those 1000 consequently hold too much power and thus can be easily bribed and the result affected far more easily than if everyone voted. Of course, psychologically, everyone needs to vote to have a say. But beyond even that psychological thing, everyone voting is really a security measure against tampering.
- potamic 1y ago
  This is a problem even with a large turn out because swing voters are a thing and generally the target of manipulation. You may only need to target like a 1000 key swing voters to get your nose ahead of the other contestants. In fact, I would argue that making it easy to bribe would level out the playing field for contestants, otherwise the one with deepest pockets will tend to have the advantage.
- HPsquared 1y ago
  Democratic systems already have the problem of not accounting for how strongly each voter feels about something. Is it really fair for 51 people weakly in favour of something to overrule 49 who are very strongly against and consider the issue extremely important? That's surely a net negative decision. Forcing people to vote who aren't interested only makes this effect even worse.
  - vouaobrasil 1y ago
    I never said anything about forcing. Only giving people the chance to vote. As for your comments about democracy, well, I don't think democracy really works on a large scale. It's just probably the best system we have at the moment.
- jyounker 1y ago
  You nailed it vouaobrasil. The mark of an anti-democratic politician is that they seek to reduce the electorate's size.

YZF 1y ago

If it's a random sample then sure.

redtaperat 1y ago

For 100 million people and a confidence interval of 99% you only need 3000-4000 samples, depending on your moe.

01HNNWZ0MV43FF 1y ago
At that point just elect them! https://en.wikipedia.org/wiki/Sortition https://en.wikipedia.org/wiki/Sortition

MrJohz 1y ago

A good sample needs to be random and representative of the population as a whole, otherwise you introduce sampling bias. Imagine trying to do a survey of what people's favourite fast food restaurants are, but doing it inside a McDonald's — it doesn't matter how large your sample is, it's going to be heavily biased. This is why survey companies spend a lot of effort trying to find random, representative samples of the population, and often weighting their samples so that they match the target population even more. If we treat elections like a survey, then they have a massive inherent bias to the sampling method: the people who will get "surveyed" are the ones who are engaged enough to get registered, and then willing to go to a physical polling station and vote. This will naturally bias towards certain types of people. In practice, we don't treat elections like a survey. If we did, we'd spend a lot of time afterwards weighting the results to figure out what the entire country really thought. But that has its own flaws, and ultimately voting is a civic exercise. You can do it, you can avoid it: that choice is yours, and ultimately part of your vote. In a way, you could argue that the sample size for an election is 100% of the population, where "for whatever reason, I didn't cast a vote" is a valid box to check on this survey. That said, the whole "samples can be biased" thing is very much relevant for elections because many political groups have an incentive to add additional bias to the samples. That could be as simple as organising pick-ups to allow their voters to get to the polls, or teaching people how to register to vote if they're eligible, but it could also involve making it significantly harder or slower for certain groups (or certain regions) to register or vote.

potamic 1y ago
A 100% sample is unattainable, not just practically, but fundamentally. Even if you made voting mandatory and ensured collection of every single vote, there will always be people who will fudge their vote because they are not interested in the process. I argue that any election is only representative of people engaged with the process and that fundamentally cannot change. Within that subset, you shouldn't need 100% sampling for high confidence. But agree that random distribution is key to this, but I don't see how that could change with the messaging that every one must vote, versus saying just vote if you're interested.
- MrJohz 1y ago
  I mean that an election is (theoretically) an 100% sample because every eligible has the ability to interact with the voting process at the level that they choose. So the decision for some people to invalidate their vote, or to vote tactically, or not to vote at all, or whatever else: that's part of the act of taking part in an election. In that sense, you can't not take part in an election, if you're eligible to vote. This is important, because normally, once you take a sample, you need to analyse that sample to ensure that it is representative, and potentially weight different responses if you want to make it more representative. For example, if you got a sample that was 75% women, you might weight the male responses more strongly to match the roughly 50/50 split between men and women in the general population. But in an election, we don't do this, because the assumption is that if you spoil your ballot or don't take part, that is part of your choice as a citizen. But I think we're saying the same sort of thing, but in different ways: you can either see "the sample of an election is every citizen, regardless of whether they voted" or "the population of an election is everyone who voted", and in either case the sample is the same as the population, and we can therefore assume that it is representative of the population.

vouaobrasil 1y ago

Beyond simple statistics and random sampling, everyone voting is important because let's say 1000 people are required to determine the result beyond reasonable uncertainty. Then those 1000 consequently hold too much power and thus can be easily bribed and the result affected far more easily than if everyone voted. Of course, psychologically, everyone needs to vote to have a say. But beyond even that psychological thing, everyone voting is really a security measure against tampering.

potamic 1y ago
This is a problem even with a large turn out because swing voters are a thing and generally the target of manipulation. You may only need to target like a 1000 key swing voters to get your nose ahead of the other contestants. In fact, I would argue that making it easy to bribe would level out the playing field for contestants, otherwise the one with deepest pockets will tend to have the advantage.
HPsquared 1y ago
Democratic systems already have the problem of not accounting for how strongly each voter feels about something. Is it really fair for 51 people weakly in favour of something to overrule 49 who are very strongly against and consider the issue extremely important? That's surely a net negative decision. Forcing people to vote who aren't interested only makes this effect even worse.
- vouaobrasil 1y ago
  I never said anything about forcing. Only giving people the chance to vote. As for your comments about democracy, well, I don't think democracy really works on a large scale. It's just probably the best system we have at the moment.
jyounker 1y ago
You nailed it vouaobrasil. The mark of an anti-democratic politician is that they seek to reduce the electorate's size.