Let me elaborate: I broadly agree with the framing here, in that the probability of flipping a vote is going to be related to the margin of the race; in a race decided by a couple hundred votes, a single vote-flip counts for 0.5%; far more than it does in a national election.… if you’re voting in an election where one candidate has a 6% edge, your vote has roughly a 1 in 12 chance of changing the outcome! Thats massive leverage that you can’t hope to replicate in larger elections.
The value (which I believe maps to “goodness”) of that vote flip is going to be related to: - the budget over which the politician has leverage - what fraction of that budget spend affects you - their probability of listening to what you have to say
While the budget is smaller in absolute terms, in terms of how it affects you it basically remains constant with election scale. i.e. the national budget is larger, but spread over 300M people, a local election has a smaller budget spread over a smaller population, but the per-person impact is about the same.
Moreover, precisely because local politicians know that every vote counts, they’re much more responsive to constituents than state or national politicians.
Given that A & B are much larger in local elections, I think there’s a lot of value there. The notable exception is if the policy is made at a higher level of jurisdiction.
if you’re voting in an election where one candidate has a 6% edge, your vote has roughly a 1 in 12 chance of changing the outcome!
This is mostly false! You have to think about σ. If two candidates are tied ex ante, that doesn’t mean your vote is infinitely powerful. The crucial question is probability that your vote will flip the election. And on your particular example, maybe you’d have a ~1/12 chance of flipping the election if your candidate’s vote margin was a random number between −0 and −12, but “your candidate is expected to lose by 12 votes” is lower tractability than that because there’s a 50% chance your candidate will lose by more than 12 votes, and there’s some chance that they’ll win without you, and the crucial −0 scenario is less likely than the −12 scenario.
the per-person impact is about the same.
No, people are affected more by the federal government than their local government. The federal government matters more than all local governments combined. But federal vs local government is not relevant to this post so I don’t want to get into it.
So I did make a math mistake, but I think we’re in broad agreement. Let me be explicit for a race with total expected votes N=400 (e.g. seat on a city council for one district of a small town)
With N=400 sigma = sqrt(400 * 0.5 * 0.5) = 10 a 6-point lead means expected votes would be: A : 212 B : 188 This corresponds to a win probability for A of cdf(12/10) ~88%
Changing one’s vote from A to B changes the expected counts to: A : 211 B : 189 This corresponds to a win probability for A of cdf(11/10) ~86% So yes, it’s only 2% change vs my earlier assertion of 8%, my mistake.
But I think we agree that sigma matters! And my point is that in small local elections, sigma is small, and your vote counts for a lot!
I agree that if you only care about federal policy, this doesn’t apply (I’d missed that in the initial post). But if you care about libraries, or how aggressive the police are, those are local issues where someone can have a strong influence in policy.
Let me elaborate: I broadly agree with the framing here, in that the probability of flipping a vote is going to be related to the margin of the race; in a race decided by a couple hundred votes, a single vote-flip counts for 0.5%; far more than it does in a national election.… if you’re voting in an election where one candidate has a 6% edge, your vote has roughly a 1 in 12 chance of changing the outcome! Thats massive leverage that you can’t hope to replicate in larger elections.
The value (which I believe maps to “goodness”) of that vote flip is going to be related to:
- the budget over which the politician has leverage
- what fraction of that budget spend affects you
- their probability of listening to what you have to say
While the budget is smaller in absolute terms, in terms of how it affects you it basically remains constant with election scale. i.e. the national budget is larger, but spread over 300M people, a local election has a smaller budget spread over a smaller population, but the per-person impact is about the same.
Moreover, precisely because local politicians know that every vote counts, they’re much more responsive to constituents than state or national politicians.
Given that A & B are much larger in local elections, I think there’s a lot of value there. The notable exception is if the policy is made at a higher level of jurisdiction.
This is mostly false! You have to think about σ. If two candidates are tied ex ante, that doesn’t mean your vote is infinitely powerful. The crucial question is probability that your vote will flip the election. And on your particular example, maybe you’d have a ~1/12 chance of flipping the election if your candidate’s vote margin was a random number between −0 and −12, but “your candidate is expected to lose by 12 votes” is lower tractability than that because there’s a 50% chance your candidate will lose by more than 12 votes, and there’s some chance that they’ll win without you, and the crucial −0 scenario is less likely than the −12 scenario.
No, people are affected more by the federal government than their local government. The federal government matters more than all local governments combined. But federal vs local government is not relevant to this post so I don’t want to get into it.
So I did make a math mistake, but I think we’re in broad agreement. Let me be explicit for a race with total expected votes N=400 (e.g. seat on a city council for one district of a small town)
With N=400
sigma = sqrt(400 * 0.5 * 0.5) = 10
a 6-point lead means expected votes would be:
A : 212
B : 188
This corresponds to a win probability for A of cdf(12/10) ~88%
Changing one’s vote from A to B changes the expected counts to:
A : 211
B : 189
This corresponds to a win probability for A of cdf(11/10) ~86%
So yes, it’s only 2% change vs my earlier assertion of 8%, my mistake.
But I think we agree that sigma matters! And my point is that in small local elections, sigma is small, and your vote counts for a lot!
I agree that if you only care about federal policy, this doesn’t apply (I’d missed that in the initial post). But if you care about libraries, or how aggressive the police are, those are local issues where someone can have a strong influence in policy.