Absolutely, shutting up and multiplying is the right thing to do.
Assume: simple majority vote, 1001 voters, 1 000 000 QALY at stake, votes binomially distributed B(p=0.4), no messing with other people’s votes, voting itself doesn’t give you QALY.
My vote swings iff 500 ⇐ B(1001, 0.4) < 501, with probability 5.16e-11, it is advised if takes less than 27 minutes.
Realistically, usefulness of voting is far less, due to:
actual populations are huge, and with them chance of swing-voting falls;
QALY are not quite utils (eg. other’s QALY counts the same way as your own);
You will rarely see such huge rewards (if 1 QALY ~ 50 000$, our scenario gave each voter free $50 M )
So, people who ‘need your vote’ in real-world scenarios are either liars or just hopeless.
My town, with more than 1001 voters in each ward, had around twenty elections last year and two of them were decided by one vote. Your model says that this should happen somewhere in America much less than once in a billion years. The fact of the matter is, voters are not binomially distributed (sometimes this lowers the probabilities further, but sometimes it raises them a lot)
Also, elected officials change their behavior based on margins, and on the size and habits of the population of voters. Politicians pay a lot more attention to vote-giving populations than non-vote-giving populations, for instance. The number of minor thresholds that can have some impact is large.
And that’s before you multiply the impact of your reasoning by the population who might follow it.
Let 20% wards be swung by one vote, that gives each voter 1 in (5 * amount of voters) chance of affecting a vote cast on the next level, if that’s how US system works?
… elected officials change their behavior based on margins …
Which is an exercise in reinforcing prior beliefs, since margins are obviously insufficient data.
Politicians pay a lot more attention to vote-giving populations...
Are politicians equipped with a device to detect voters and their needs? If not, then it’s lobbying, not voting that matters.
...impact of your reasoning by the population who might follow it.
Population following my reasoning: me.
P.S. Thanks for hinting at other question, which might be of actual use to me.
1 - No. This was an election for members of the town council, so those two 1-ballot-difference votes decided who got two jobs.
2 - I’m not sure what you mean there. A way of measuring the strength of this effect is to see how voting patterns differ between representatives who win by landslides vs representatives who squeak by. The vulnerable representatives act much more cautiously—and for good reason.
3 - Who voted in each election is public information, so the first answer is YES except for the requirement that there be a special device for it which you tacked on. For identifying your needs, there’s exit polling (there is no way to make sure that you get exit-polled), in which you are often asked what the most important issue is for you. For other polling, I suppose you can lie and say you vote regularly when called, but you might consider that unethical.
The simplest form of lobbying is letters to representatives. Again, I suppose you could lie.
4- Follow it, not you. The population of people who face the same situation with the same logical premises and habits. Copies of computations are the same computation.
Perhaps you would find the fraction of people that would need to be voting so that your voting is no longer ‘worth it’. Then you would vote or not with that probability.
So learning how 900 of the voters (other than you) voted won’t shift your beliefs about how the remaining 100 voters voted in the slightest? No, I don’t think so.
Absolutely, shutting up and multiplying is the right thing to do.
Assume: simple majority vote, 1001 voters, 1 000 000 QALY at stake, votes binomially distributed B(p=0.4), no messing with other people’s votes, voting itself doesn’t give you QALY.
My vote swings iff 500 ⇐ B(1001, 0.4) < 501, with probability 5.16e-11, it is advised if takes less than 27 minutes.
Realistically, usefulness of voting is far less, due to:
actual populations are huge, and with them chance of swing-voting falls;
QALY are not quite utils (eg. other’s QALY counts the same way as your own);
You will rarely see such huge rewards (if 1 QALY ~ 50 000$, our scenario gave each voter free $50 M )
So, people who ‘need your vote’ in real-world scenarios are either liars or just hopeless.
My town, with more than 1001 voters in each ward, had around twenty elections last year and two of them were decided by one vote. Your model says that this should happen somewhere in America much less than once in a billion years. The fact of the matter is, voters are not binomially distributed (sometimes this lowers the probabilities further, but sometimes it raises them a lot)
Also, elected officials change their behavior based on margins, and on the size and habits of the population of voters. Politicians pay a lot more attention to vote-giving populations than non-vote-giving populations, for instance. The number of minor thresholds that can have some impact is large.
And that’s before you multiply the impact of your reasoning by the population who might follow it.
Let 20% wards be swung by one vote, that gives each voter 1 in (5 * amount of voters) chance of affecting a vote cast on the next level, if that’s how US system works?
Which is an exercise in reinforcing prior beliefs, since margins are obviously insufficient data.
Are politicians equipped with a device to detect voters and their needs? If not, then it’s lobbying, not voting that matters.
Population following my reasoning: me.
P.S. Thanks for hinting at other question, which might be of actual use to me.
This isn’t a great assumption in general, but it’s a particularly bad assumption if you’re describing your reasoning out loud in public.
1 - No. This was an election for members of the town council, so those two 1-ballot-difference votes decided who got two jobs.
2 - I’m not sure what you mean there. A way of measuring the strength of this effect is to see how voting patterns differ between representatives who win by landslides vs representatives who squeak by. The vulnerable representatives act much more cautiously—and for good reason.
3 - Who voted in each election is public information, so the first answer is YES except for the requirement that there be a special device for it which you tacked on. For identifying your needs, there’s exit polling (there is no way to make sure that you get exit-polled), in which you are often asked what the most important issue is for you. For other polling, I suppose you can lie and say you vote regularly when called, but you might consider that unethical.
The simplest form of lobbying is letters to representatives. Again, I suppose you could lie.
4- Follow it, not you. The population of people who face the same situation with the same logical premises and habits. Copies of computations are the same computation.
Perhaps you would find the fraction of people that would need to be voting so that your voting is no longer ‘worth it’. Then you would vote or not with that probability.
So learning how 900 of the voters (other than you) voted won’t shift your beliefs about how the remaining 100 voters voted in the slightest? No, I don’t think so.
Politicians say they “need your vote” because they’re talking to lots of people. Any one of them doesn’t matter, but in bulk they really do.